B.sc.(Hons.) Syllabus

8/12/2019 B.sc.(Hons.) Syllabus

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UNIVERSITY OF RAJSHAHI

FACULTY OF SCIENCE

DEPARTMENT OF APPLIED MATHEMATICS

B. Sc. (Honours) Syllabus

Session: 2012-2013

Introduction:

The Department of Applied Mathematics started functioning in the year

2002. Originally it was in the Mathematics Department. The Department of

Mathematics was running with two streams from 1972, One is Pure

Mathematics and the other one Applied Mathematics. But in 2002 the stream

of Applied Mathematics Started functioning separately. Now this new

Department of Applied Mathematics has got about 450 students including

M. Phil and Ph. D. research Students.

The research students of this Department are working in different field of

interest, e.g. Fluid dynamics, Meteorology, Magneto-Hydrodynamics,

Quantum mechanics and Relativity.


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UNIVERSITY OF RAJSHAHI

FACULTY OF SCIENCE

DEPARTMENT OF APPLIED MATHEMATICS

B. Sc. (Honours) Part I, Examination, 2013

B. Sc (Honours) Part I Examination will comprise of 950 marks (Theorycourses 700, Practical Math. 100, Tutorial, Terminal and Class Records 100

and Viva-Voce 50) The duration of examination for each 1 unit theory

course is 4 hours and 0.5 unit theory courses 3 hours.

Course No. Title of CoursesFull

Marks

Unit

No.Credit

A.Math.101 Higher Algebra 100 1 4

A.Math.102 Coordinate Geometry 100 1 4

A.Math.103 Calculus -I 100 1 4

A.Math.104 Theory of Matrices 100 1 4

A.Math.111

(Phys.)

Mechanics, Properties of Matter,

Wave and Sound100 1 4

A.Math.-112(Phys.)

Electricity and Magnetism 100 1 4

A.Math.-113(Stat.)

Fundamental of Statistics andProbability

100 1 4

A. Math-114 Functional English** 50 0.5 0

A.Math.120 Practical (Using Mat lab) 100 1 4

A.Math.121Tutorial, Terminal and Class

Records*100 1 4

A.Math.122 Viva-Voce 50 0. 5 2

Total 950 9. 5 38

* The Tutorial, Terminal and Class Records marks shall be awarded for

attendance in the class on the basis of the following table:

Attendance Marks Attendance Marks Attendance Marks

95-100% 20% 90-


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A.Math-101Higher Algebra

1 Unit Full Marks-100 Credit-4[Five questions to be answered out of Eight]

1. Set Theory: Algebra of sets, Cartesian products, De-Morgans Theorem,distributive law, set of numbers, Functions and relations, Injective,

bijective and Subjective functions, Drawing graphs of functions.2. Inequalities: Arithmetic, Geometric and Harmonic means, Weierstrass,

Cauchys and Chebyshevs inequalities.

3. Difference equations, Summation of series.4. Theory of equations: Fundamental theorem of algebra, Relation between

roots and coefficients. Descartes rule of- signs.

5. Solutions of cubic and biquadratic Equations.6.

Complex number. De-Moivres theorem and its applications.7. Functions of complex arguments. Gragorys series.

8. Summation of trigonometric series. Hyperbolic functions. Factorizations.Suggested Books:

1. Bernard and Child : Higher Algebra

2. Barnside and Panton : Theory of equations

3. Hall and Knight : Higher Algebra

4. Das and Mukherjee : Higher Trigonometry

5. S. A. Sattar : Higher Trigonometry6. S. lipschutz : Set Theory

A.Math-102

Coordinate GeometryFull Marks-100

1 Unit Credit-4

[Five questions to be answered out of eight taking at leasttwo from each group]

Section-A1. Transformation of coordinates. Pair of Straight lines.2. Circles and system of circles.3. The general equation of second degree and reduction to standard forms.

Identifications of Comics.

4. The parabola


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5. The ellipse and the hyperbolaSection-B

6. Direction cosines and direction ratios. The plane.7. Straight lines, Shortest distance.8. Sphere, cone and cylinder. The general equation of second degree and

reduction to standard forms. Identification of conchoids

Suggested Books:

1. Askwith H.H. : Analytic Geometry of Conic Sections

2. Smith C : Analytic Geometry of Conic Sections

3. Loney S. L. : Analytic Coordinate Geometry

4. J. M. Kar : Analytic Geometry of Conic Sections5. Bell, J. T : A Treatise on Three dimensional Geometry

6. Smith, C : An Elementary Trealises on Solid Geometry

A.Math-103Calculus-I

Full Marks-1001 Unit Credit-4

[Five questions to be answered out of Eight]

1. Functions: Domain, Range, Polynomials and rational functions,exponential functions, trigonometric functions and their inverse, graphsof functions, hyperbolic functions and their inverses.

2. Limit, continuity and differentiability, indeterminate forms, L, Hospitalsrule, Definitions and basic theorems on limit, continuity and

differentiability, Computations of limits.3. Differentiation: Definition of derivative, Rules of Differentiation,

Successive differentiations, Leibnitz theorem.

4. (a) Expansions of functions: Rolls theorem, Mean value theorem,Taylors and Maclaurins theorem. (b) Maxima and Minima of functionsof one variable: Increasing and decreasing functions, Extreme values of afunction, Minimum values of function, Determination of maxima and

minima, A necessary conditions for maximum and minimum, critical andinflexion points.

5. Partial differentiations: Eulers theorem.


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6. Tangents and normals, Asymptotes.7. Indefinite integrals: Definition and fundamental properties, Method of

substitutions, Integration by parts, Special trigonometric functions andrational fractions.

8. Definite integrals: Definition, Fundamental theorem, General properties,Evaluations of definite integrals, Summation of series by definiteintegral. Reduction formulas and improper integrals.

Suggested Books:

1. Howard Anton : Calculus

2. G. B. Topmas and

R. L. Finny.

: Calculus and analytical Geometry.

3. S.K.Stein and

A.Barcellos

: Calculus and analytical Geometry

4. J. Edwards : Differential Calculus.

5. F. Ayres : Calculus

6. Das and

Mukherjee

: Differential Calculus.

7. Das and

Mukharjee

: Integral Calculus

8. M. R. Spigel : Advanced Calculus

9. Williamson : Integral Calculus

A.Math-104Theory of Matrices



1. Matrices: Different types and kinds of matrices - definition, examples,properties and verification.

2. Adjoint, inverse, block matrix definition and properties.3. The theory and properties of determinants, higher order determinants,

solution of systems of equation by determinant (Crammers rule).4. Elementary transformation, echelon, canonical and normal forms, rank of

a matrix.


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5. System of linear equations, consistency, solution of homogenous andnon-homogenous system by Matrix method and reduction to equivalentsystem.

6. Vector space, subspace, sum and direct sum7. Linear dependence and independence, basis and dimension8. Bilinear and Hermitian forms.9. Quadratic forms, Definite and semi-definite forms of Matrices. Eigen

values and Eigen vectors.

Suggested Books:

1. F. Ayres : Theory of Matrices2. C. C. Mcduffe : Theory of Matrices3. S. Lipschutz : Linear Algebra

4. S. L. Croasman : Elementary Linear Algebra

A.Math-120

Practical (Using MATLAB)Full marks-100

1 unit Credit-4

Section - A: MATLAB 60 marks

1.Testing the continuity and differentiability of a function only by theobservation of the graphs.

2.Solution of Algebraic equation.3.Transformation of coordinates in two dimensions, Graphs of function in

polar coordinates e.g. cardioids, Lemniscates, Equiangular spiral, Rosepetals.

4. Draw three dimensional figures.5.Find maxima and minima, using graph of function.6.Integration.7.Solution of the system of linear equations.8.Find out the determinant, inverse, eigenvalues and eigenvectors etc of a

square matrix.

Section - B: Practical Note Book 30 marksSection - C: Viva - Voce 10 marks


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A.Math-111 (Phys)Mechanic, Properties of Matter, Wave & Sound

Full Marks-100

1 Unit Credit-4[Five questions to be answered out of Eight]

1. Vector Analysis: Vectors and Scalars, Addition and multiplication ofvectors, triple scalar and vector product, derivatives of vectors. Gradient,

divergence, and curl their physical significance.

2. Conservation of Energy and Linear Momentum: Conservative andnon-conservative forces and systems, conservation of energy and

momentum, Center of mass, collision problem.3. Rotational Motions: Rotational variable, rotation with constant angular

acceleration, torque on a particle, angular moment of inertia, combined

translational and rotational motion of rigid body, conservation of angular

momentum.

4. Oscillatory Motions: Hooks law and vibration, simple harmonicmotion, motion combination of harmonic motions, damped harmonic

motion, forced oscillation and resonance.

5. Gravitation: Center of gravity of extended bodies, gravitational fieldand potential their calculations, determination of gravitation constant and

gravity, compound and Katers pendulum, motion of planets and

satellites, escape velocity.

6. Surface Tension: Surface tension as a molecular phenomenon, surfacetension and surface energy, capillary rise or fall of liquids, pressure on a

curved membrane due to surface tension, determination of surface

tension of water, mercury and soap solution, effect of temperature.

7. Elasticity: (a) Moduli of elasticity, Poissons rations, relations betweenelastic constants and their determination, cantilever, flat spiralspring. (b)Fluid Dynamics: Viscosity and coefficient of viscosity poiseales

equation; determination of the coefficient of viscosity of liquid by

Stocks method, Bernoullis theorem and its applications, Torrcellis

theorem, venturimeter.


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8. Wave in Elastic Media: Mechanical waves, types of waves,Superposition principle, wave velocity, power and intensity in wave

motion, interference of waves, complex waves, Standing waves and

resonance. Sound Waves: Audible, Ultrasonic, and infrasonic, waves,

propagation and speed of longitudinal waves, vibrationg systems and

source of sound, beats, Doppler Elects.Suggested Books:

1. Ahmed and Nath : Mechanics properties of Matter

2. Bandopadhya and Ghose : Padartha Bidya (Bengali)3. Emran, et al : General Properties of Matter

4. Halliday and Resnick : Physics (1 and 2)5. Emran : Text Book of Sound6. Saha : Text Book of Sound

A.Math-112 (Phys)Electricity and Magnetism



1. Electrostatistics: Electric dipole, electric field due to a dipole, dipole onexternal electric field, Gausss law and its applications.

2. Capacitor: parallel plate capacitors with dielectrics, dielectric constant;energy stored in an electric field.

3. Electric Current: Electron theory of conductivity: conductor,semiconductors and insulators, superconductors, current and current

density, current and current density, Kirchhoffs Law and its applications.4. Magnetism: Magnetic dipole, mutual potential energy of two small

magnets: magnetic shell, energy in a magnetic field, magnetometers.5. Electromagnetic Induction: Faradays experiment; Faradays law

Amperes law, motional e.m.f. self and mutual inductance;

galvanomenters-moving cell ballistic and deadbeat types.

6. Thermoelectricity: Thermal e.m.f. Seebeck, Peltier and Thomson Effects,laws of thermal e.m.f.s thermoelectric power.7. D. C. and A. C circuits: D.C circuits with LR, RC, LC and LCR in series;

A. C circuits with LR, RC, LC and LCR in series.

Suggested Books:

1. Acharyya : Electricity and Magnetism2. Adans and page : Principles of Electricity


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3. Bandopadhyys : Padarthavidya(Bengali). Constant & Ghose

Theoretical Physics4. Din : Electricity and Magnetism5. Emran, et al : Text Book of Magnetism, ricity and Modern Physics.

6. Halliday and Resnic : Physics (I and II)7. Huz, et al. : Concepts of Electricity and tism.8. Islam, et al. : Tarit Chumbak Tatwa O k Padartha Vidya (Bangali).

9. Kip : Fundamentals of Electricity and Magnetism.

A.Math-113(Stat)

Fundamental of Statistics and ProbabilityFull Marks-100

1 Unit Credit-4


1. Statistics: Meaning & Scope, Variables & Attributes, Collection andPresentation of Statistical Data, Frequency Distribution and GraphicalRepresentation.

2. Univariate Distribution:Central Tendency, Dispersion their Measuresand Prosperities

3. Univatiate Distribution2:Moments, Cumulant Skewness Kurtosis andTheir Measures. Density Function Distribution Function, MomentCumulant Generation Function.

4. Probability: Sample Space, Events, Union Intersection of Events.Additional law of probability. Multiplication law of probability,conditional probability, Bayes Theorem.

5. Mathematical Expectation: Radom Variables and Their Expectations &Variances, Probability Generation Function, Chebysevs Inequality,Conditional Expectation and conditional Variances.

6. Probability Distributions: Binomial, Poison, Normal distribution andBivariate Normal distribution.

7. Bivariate Distribution: Bivariate data, Scatter Diagram, Marginal andconditional Distribution, Correlation, Rank correlation, Partial and

Multiple Correlation, Correlation Ratio.8. Linear Regression: Linear Regression Involving Non-random Variables,

Principle of Lest Squares, Lines of Best fit, Residual Analysis.

Regression Analysis:3-variable regression regression, multiple linearregression model parameters by OLS method. Properties of OLS estimators,Estimation with restriction. Analysis of variance in the General Linear Models.

Polynomial Regression models, Analysis of Residuals.


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Suggested Books:1. Anderson A.J.B. : Interpreting Data, Chapman & Hal London.

2. Cramer, H : The Elements of Probality Theory, Willey,N.Y

3. Hool. P G : Introductory Statistics, Wiley & Sons, NY.

4. Lindley D.V : Introduction to Probability and Statistics, Vol-1, CUP, London.

5. Lipschutz, L : Probability McGraw-Hill, NY.

6. Mosteller, Rourke& Thoms

: Probability, McGraw-Hill, NY.

7. Wolf, FL : Elements of V Probability and StatisticalApplications, 2

ndEd, Addison Wesley.

8. Wonnacot T H &Wonnacot R J

: Introductory Statistics, 3rd

Ed. Wiley and Sons,NY.

9. Yule, G U : An Introduction to the Theory of Statistics.

10. Kendall M. G : Fourteenth Ed, Charles Grriffin, London.

11. Crammer, H : The Elements of Probability Theory, Wiley, NY.

12. Feller, W : Introduction to Probability Theory & its

Applications Vol-1, Third edition, Willey N Y.

13. Gray, J. R : Probability Oliver and Boyd, London.14. Grimmeti, G R &

Strzaker, D R

: Probability and Random Process, Oxford

University Press, London.

A.Math-114Functional English

Full Marks-500.5 Unit Credit-00


1. Parts of Speech, appropriate preposition, tenses, use of passive voice,phrase, conditionals, infinitive, participle, gerunds, correction of

sentence, Framing question.2. Developing vocabulary: suffixes, prefixes, synonyms and antonyms,

conversion of words.

3. Situational writing: posters, notices, slogans memos, advertisements,

press releases, report writing, resume/curriculum vita, paragraph writing.4. Translation from Bengali to English.


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5. Scientific writing for experiments and projects: Distinctive features of

scientific writing: figures, tables, equations, captions numbering, title andsection headings, professional research reporting.

Suggested Books:1. Allen, WS : Living English Structure2. Fitikides, TJ : Common Mistakes in English3. Ahmed, S : Learning English Grammar

4. Thomson, AJ andMartinet, AV

: A Practical English Grammar

5. Swales, J : Writing Scientific English.

6. Wren and Martin : English Grammar and composition7. Vallins, GH : Good English

8. Hornby, As : The Teaching of Structural Words and

Sentence Patterns (stages 1&2), (stages

3&4)9. Sindair, J (Editor-in-

Chief)

: Collins Cobuild English Grammar.


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A.Math-201Calculus-II



1. Functions of several variables: Partial differentiation, total differentiation,differentials, Eulers theorem of homogeneous function, Taylors series forfunctions of several variables, Jacobians.

2. Singular points: Concave and convex curves, Node, cusp, conjugalpoints, The point of inflexion.

3. Maxima and Minima of functions of several variables.4. Curvature of plane curves.5. Curve tracing.

6. Definite integration: Integration under the sign of differentiation and

integration, Improper integrals, Theorem of Frullani, Applications ofdefinite integrals.

7. Gamma and Beta Functions.8. Multiple integrals: Double integration, triple integration, Dirachlet's

Theorem, Change of order of integration, Determinations of arc lengths,areas and volumes.

Suggested Books:1. Edwards J. : Differential Calculus2. Williamson : Integral Calculus

3. M. R. Spiegal : Advanced Calculus

4. Wider : Advanced Calculus.

A.Math-202

Modern AlgebraFull Marks-100

01 Unit Credit-4


1. Groupoid, quasi group, Semigroup, monoid and group. The symmetricand alternation group, Permutation group, Cyclic groups Lagranges

theorem.2. Subrroup, Normal subgraoup cosets, homomorphsim isomorphism and

related theorems.

3. Rings, Subrings, Integral domain, Ideal, quotient ring, field, Theimbedding theorem, The Euclidean rings.


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4. Linear transformations: Range, kernl, nullity, rank, singular and non-

singular transformations, Matrix reorientation of linear transformative.5. Characteristic roots and vectors of linear transformations, Theorems and

problems, Characteristic and minimal polynomials of Square matrices.

6. Linear functionals and dual vector spaces, Annihilators7. Norm and inner products, orthogonal complements, orthonormal sets,

Gram-Schmidt orthogonalization process, Adjoint operators, Hermition,

Unitary, orthogonal and normal perators.

Suggested Books:1. I. N. Herstein : Topics in Algbra

2. M. L. Khanna : Modern Algebra3. Lipschutz : Linear Algebra

A.Math-203

Vector and Tensor AnalysisFull Marks-1001 Unit Credit-4


1. Vectors and scalars: definitions and fundamental laws, Product ofvectors, Reciprocal Vectors, Vector Geometry: Equation of planes, st.

lines and spheres.

2. Vector differentiation: Vector differential operators, gradient, divergenceand curl.3. Vector integration: Greens theorem, Gausss diverges theorem, Stokestheorem and their applications.

4. Curvilinear co-ordinates5. Tensor and Co-ordinate transformations. Covariant and contravariant

vectors, Mixed & invariant tensors, Addition, subtraction and

multiplication of tensors, contraction, symmetric and skew- symmetric

tensors, Quotient Law.

6. Line element and metric tensor. Conjugate and associated tensors.Christoffels symbols and their transformation laws.

7. Geodesics and Parallelism, Covariant derivative of a vector and a tensor,Intrinsic derivative, Tensor form a gradient, divergence and curl.

8. Riemann Christoffel tensor, Curvature tensor, Ricci tensor, Bianchiidentity, Flat space and Einstein space.


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Suggested Books:1. B. Spain : Tensor Calculus2. D. C. Agarwal : Tensor Calculus & Riemannian Geometry3. M. R. Spiegel : Vector and Tensor Analysis4. M.A. Sattar : Vector Analysis5. Synge & Schild : Tensor Calculus

6. M. A. Ansary : Tensor7. C. Weatherburn : An Introduction to Riemannian Geometry and

Tensor Analysis.

A.Math -204Ordinary Differential Equations

Full marks-1001 Unit Credit-4


1. Origin of differential equations, Classification of differential equationsand solution. Initial value problems, Boundary value problems, Linearlydependent and independent set of Functions, Basic existence and unique

ness theorems (statement & applications only) Applications of first

order educations (orthogonal & oblique-trajectories)2. First order educations for which exact solutions are obtainable, Separable

equations and equations reducible to this form, Exact educations and

integrating factors, Linear equations and Bernoulli equation, Special

integrating factors and transformations.3. Construction & differential equations, Mathematical models(Exponential growth and decay, heating and cooling & chemicalreactions) Riccati equation Clairauts equation first order higher degree

equations-solvable for x, y and p.4. Higher order linear homogeneous equation with constant coefficients,

Reduction of order, Basic theorems, Application of Second order linear

differential equations.5. Linear nonhomogeneous equation with constant coefficients, Method of

undetermined coefficients, method of variations of parameters operatormethod.

6. Linear equation with variable coefficients: Cauchy-Euler equation,Legendre equation, Operational factoring, exact equation.

7. Series solutions of linear differential equations, Taylor series method,Frobenius method.


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8. Systems of linear differential equations, Method of elimination, Eulersmethod, Picards iteration method.

Suggested Books:1. S. L. Ross : Differential Equations2. G. F. Simmors : Differential Equations

3. Frank Ayres : Differential Equations4. B. D. Sharma : Differential Equations5. M. A. Ansary : Ordinary Differential Equations.

A.Math.-205FORTRAN Programming



1.

Basic concept/ First Steps in Fortran Programming.2. Essential Data Handling.3. Basic Building Blocks.4. Controlling the flow of a program.5. Repeating parts of a program.6. An introduction to Arrays.7. More control over input and output.8. Functions & Subroutines Basics. Using files to preserve data.Suggested Books:

1. T.M.R. Ellis,Ivor R. Philips,Thomas M.Lahey : Fortran 90 Programming

2. V. Rajaraman : Upgrading to Fortran 903. Cooper Redwine : Computer Programming in

Fortran 90 and 95

A.Math-220Practical (Using FORTRAN)



Section- A: Programming 60 marks1. Solution of quadratic equation using block if statement, case statement

and subroutine.2. Area and perimeter of circle, triangle, quadrangle.3. Sum of some series.


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4. Sum of digits, product of some factors, prime numbers, Fibonaccinumbers and factorial of a number.

5. One dimensional array: Sorting, searching, highest and lowest values,mean, variance, S. D. Curve Fitting.

6. Two dimensional array: Upper & lower triangular, addition, subtraction,multiplication of matrices.

7. Program using function subprograms and subroutine subprogram.Section - B: Practical Note Book 30 Marks

Section - C: Viva - Voce 10 marks

A.Math-211(Phys)Heat and Thermodynamics



1. Thermometry: Gas thermometers and their corrections, measurement oflow and high temperatures, Platinum resistance thermometerthermocouple.

2. Kinetic Theory of gases: Kinetic theory of gas, Deduction of Boyles,Charles and Avogardos Laws, determination of gas constants, meanforce path.

3. Equation of states for gases: Equation of state for a perfect gas itsexperimental study, vander waals equation deduction: physical

significance of a and b defects.4. Liquefaction of gases: Different methods of liquefaction of air nitrogen,

refrigeration

5. Thermal conduction: Thermal conductivity, Fouriers equations of heatflow thermal conductivities of good and bad conductors.

6. Radiation: Radiation pressure, Kirchhoffs law Black body radiation,Stefan Boltzmanns weins law Rayleigh jeans law, Plancks Quantumlaw.

7.

First law of Thermodynamics: Internal energy, work done by expandingfluid, Specific heats of perfect gases, Ratio of Cp to Cv, Isothermal andadiabatic expansions.

8. Second law of Thermodynamics and entropy: Reversible and irreversibleprocesses, carnot cycle, efficiency of heat engines, absolute scale of

temperature Clausius and claperons theorem, Change of entropy inreversible and irreversible processes. Thermodynamics Potentials at


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constant volume and pressure, Maxwells thermodynamics relations,

specific heat equation, joule Thomson effect, production of lowtemperature.

Suggested Books:1. Bhuiyan and Rahman : Text Book of Heat, Thermodynamics and Radiation.

2. Halliday and Resniek : Physics (I and II)3. Saha and Srivastava : A treatise on Heat

4. Leo and Sears : Thermodynamics.

5. Zemansky : Heat and Thermodynamics

6. T. Hossain : Text Book of Heat

7. Haque : Text Book of Heat Thermodynamics and Radiation

A.Math-212 (Phys)Optics and Modern Physics



1. Geometrical Optics: Fermats principle, theory of equivalent lenses;Defect of images, Optical instruments, Dispersion, Rainbow.

2. Nature and propagation light: Properties of light, wave theory andHuygens principles, theories of light.

3. Interference: Youngs experiment, Biprism, Colour of thin film,Newtons ring, Michelson and Fabry-peret interferometers.

4. Atomic Physics: Motion of electronics under electric and magneticfields, Measurement of e/m and e positive sign, thermionic emission,

photoelectric emission, Bohrs atom model, Atomic spectra, X-rays,Matter waves.

5. Nature physics: Basic concept and properties of the nucleus, Nuclearsize, Binding energy, Radioactivity, Elementary knowledge of fission,Fusion and reactors cosmic rays.

6. Electronics: Vacuum diodes and triodes, P-type and n-types,Acmiconductors, P-n junctions, Transistor biasing, Transistor amplifiers,Transmitters and receivers.

Suggested Books:1. Din : Text Book of Optics2. Mathur : Principles of optics

3. Mazumder : Text Book of Light.


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4. Sears : Optics

5. Bandopadhya & Ghose : Padarlhavidya (Bengali).6. Hossain T : Text Book of Heat7. Haque : Text Book of Heat Thermodynamics and

Radiation.8. V. K. Mehta : Principles of Electronics.9. Beiser : Concepts of Modern Physics

10. N. Suabrahmanyam andBrijlal

: Atomic and Nuclear Physics

A.Math-213 (Stat)Statistical Method and Demography


[Five questions to be answered out of Eight]1. Sample Surveys: Basic Concepts of Sample Surveys, Preparation of

questionnaire, Schedules, Instruction ets, Survey enumeration, Pilot

survey, Requirement of a good sample design, Probability and non-probability sampling, Sampling with and without replacement and with

equal and unequal probabilities, Sampling and non sampling errors, Bias,

Accuracy and Precision.2. Simple Random Sampling and Stratified Random Sampling:SRSWR,

SRSWOR, Procedure of selection random sampling Estimation of

population mean and its variance, Principle of Stratification Estimation ofthe population mean and variance in stratified random sampling, Allocationof sample size in different strata.

3. Systematic Random Sampling and Cluster Sampling:Sample selectionprocedure in systematic sampling, Estimation of mean and its sampling

variance, Comparison of systematic with Simple and stratified random

sampling Cluster sampling, Equal and unequal cluster sampling Estimationof mean and variance in cluster sampling.

4. Demography: Basic Concepts of Demography, Birth and death rates,

growth rates, Components of population growth rates, migration,Population projection.

Suggested Books:1. Cochran, W.G. Wiley N.Y. : Experimental Designs Cox, D.R

2. Cochran W. G : Sampling Techniques3. Des Raj : Survey Sampling McGraw Hill.


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B.Sc. (Honours) Part III Examination, 2015

B. Sc. (Honours) Part III Examination will comprise of 1050 marks

(Theory courses 800, Practical Math 100, Tutorial, Terminal and Class

Records 100 and Viva-Voce 50). The duration of examination for each one

unit theory course is 4 hours and 0.5 unit theory course is 3 hours. Acandidate obtaining a GPA of less than 2.50 at the part-I examination shall

not be promoted for next year.

Course No. Title of Courses Full

Marks

Unit No. Credit

A.Math. 301 Real Analysis 100 1 4

A.Math. 302 Complex Analysis 100 1 4

A.Math. 303 Mechanics 100 1 4

A.Math. 304 Methods of Applied Mathematics 100 1 4

A.Math. 305 Partial Differential Equations 100 1 4

A.Math. 306 Discrete Mathematics and

Programming with C

100 1 4

A.Math. 307 Numerical Analysis 100 1 4

A.Math. 308 Integral Equation 50 0.5 2

A.Math. 309 Mathematics for Business 50 0.5 2

A.Math. 320 Practical (Using Program C/C++) 100 1 4

A.Math. 321 Tutorial, Terminal and Class

Record

100 1 4

A.Math. 322 Viva-Voce 50 0.5 2

Total 1050 10.5 42


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A.Math-301Real Analysis



1. Real Number system: Notion & set Rational number, field, ordered set,ordered field, least upper bound and greatest lower-bound, least upper

bound property. The existence theorem and its proof. Dedekind cut and

Dederkind theorem. Dedekind theory equivalence to least upper bound

property and its applications.

2. Basic Topology: Finite and infinite sets, equivalence of sets countablesets, uncountable sets, metric space, open and closed sets, perfect sets.

3. Numerical sequence: Sequence Subsequence, Bounded sequence,convergent sequence, Cauchy sequence, completeness of R.

4. Series: Convergent series, Cauchys criteria for convergent series,comparison test, Cauchy root test Cauchy condensation test, Ration test,

Integral test, Raabes test, Leibnitz test.

5. Continuity: Continuous function continuity and compactness, uniformcontinuity, discontinuities.

6. Differentiation: Derivative of function Rolles theorem, Mean valuetheorem, Generalized-Mean value theorem, Taylors theorem.

7. Function of several variables: Limit and continuity of two variablefunctions, partial differentiations, Schwarzs theorem, Youngs theorem.

8. The Riemann Stieljes integration: Definition and existence of theintegrals, properties of the integrals, Integration and differentiations.

Suggested Books:1. W. Rudin : Principles of Mathematical Analysis.2. M. H. Proter & C. B. Morey : Modern Mathematical Analysis.3. Bortle : Real Analysis4. Royden : Mathematical Analysis.5. Apostal : Mathematical Analysis


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A.Math-302Complex Analysis



1. Complex number system: Complex number, polar form of complexnumber, complex plane, point sets,

2. Complex Function:Single and many valued function Branch points andBranch lines Riemann Surfaces Limits and continuity.

3. Analytic functions: Derivation, Cauchy Riemann equations, Singularpoints, orthogonal families of curves, harmonic function.

4. Complex integration: Cauchys theorem, some consequences ofCauchys theorem, Singularities; Classification of singularities.

5. Complex integration:Cauchys integral formulae, maximum modulustheorem, Fundamental theorem of algebra, Rouches theorem. Theargument principle.

6. Infinite series: Series of function, power series, Taylors theorem,Laurents theorem, analytic continuation.

7. Calculation of Residues: Residues, Residue theorem, Evaluation ofDefinite integrals.

8. Conformal mapping: Some general transformations, lineartransformation, Bilinear Transformations, Application of the conformalmapping.

9.Suggested Books:1. M. R. Spige : Complex Variable.2. M. Z. Khanna : Complex Analysis.3. J. B. Conway : Functions of complex variables.

4. L. V. : Complex Analysis5. D. Sarason : Notes on complex function theory.

A.Math-303Mechanics



1. Static: Equilibrium of coplanar forces, A static equilibrium, Stable andunstable equilibrium, General conditions of equilibrium forces.


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2. Work, Virtual work.3. Equilibrium of a string and chains: The common caterary, General

conditions of equilibrium of string, Catenary of a uniform strength,String under central forces.

4. Centre of gravity: (i) Centre of gravity of an arc (ii) Centre of gravity ofa plane area (iii) Centre of gravity of a solid and surface of revolution(iv) Centre of gravity of any volume.

Dynamics of Particle:5. Motion in a straight line, Simple harmonic motion.6. Motion in a plane referred to a Cartesian and polar co-ordinates, Central

forces, Radial and transverse velocities and accelerations, Apses and

apsidal distances

7. Motion in three dimensions, Accelerations in terms of polar andCartesian co-ordinates.8. Dynamics of a rigid body:(a) Moments and products of inertia: The momental Ellipsoid, Equi-

momental systems, principal axes.(b) `D Alemberts Principle: The general equations of motion,Independence of the motions of translation and rotation, Empulsiveforce.

Suggested Books:

1. S. L. Loney : An Elementary treatise on the dynamic of aparticle and of Rigid Bodies.

2. S. L. Loney : An Elementary treatise on statics3. A. S. Ramsey : Dynamics.

4. P. P. Gupta : Statics5. G. S Malik : Dynamics.

A. Math-304

Methods of Applied Mathematics

01 Unit Full marks - 100 Credit - 4


1. The Laplace Transform:(i) Definition, existence, and basic properties(ii) Differentiation and integration (iii) Inverse Laplace transform, and


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convolution (iv) Solution of linear differential equations with constant

coefficients, and linear systems.2. Bessels Equations:Solution, Generating function, Recurrence relation,

values of Bessel function, Orthogonality, Neuman, and Hankel function,

Modified Bessel function.3. (a) Legendres Equation: Solution, Generating function, Recurrence

relation, Rodrigues formula and Orghogonality of Legendre

polynomials.4. (a) Hermites Equation: Solution, Integral and Recurrence formula,

Orthogonality, Differential formula.

(b) Legueres Equation: Solution, Integral and Recurrence formula,Differential forms, Orthogonality.

5. (a) Hypergeometric Equation: Solution, Hypergeometric function andits properties, Integral formula and liner transformations of

hypergeometric functions.6. Fourier series:Fourier coefficients, sine and cosine series, Dirichletstheorem, Properties and applications.

7. Sturm: Lioville problem, self-adjoint differential equation,Characteristic values and characteristic function, Orthogonality; Greenss

function.8. Fourier transforms: Fourier sine and cosine transforms, Complex

Fourier transform, convolution theorem, Applications to boundary value

problems, Asymptotic expansions.

Suggested Books:1. Jeffreys and Jeffreys : Methods of Mathematical Physics2. Courant and Hilbert : Methods of Mathematical Physics

3. B.S. Rajput : Mathematical Physics4. M R Spiezel : Laplace Transforms5. B. D. Sharma and

R.K. Gupta : Mathematical Method.6. M J Lighthill : Asymptotic Expansion

7. L Apipes : Applied Mathematics for Engg. & Scturts8. M.A. Ansary : Methods of Applied Mathematics


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Math-305

Partial Differential Equations



1. Total Differential Equations: Integrability condition, Solutionmethod for Pdx+Qdy+Rdz=0 and

R

dx

Q

dy

P

dx

2. Formation of PDFs & First order linear PDEs

3. First Order quasilinear and non-linear PDEs.4. Classification of general second order PDEs & canonical forms.5. Second Order homogeneous and nonhomogeneous PDEs.

6. Second Order non-linear PDEs.7. Solutions of Laplaces equations in Cartesian, Cylindrical and

Spherical coordinates.8. Solutions of diffusion (or heat flow) equation.

Solution of wave equation.

Suggested Books:

1. F. Ayres : Differential Equations

2. I.N. Sneddon : Elements of partial Differential Equations

3. R. Dennemeyer : Introduction to partial Differential Equations

4. T Myint U : Partial Differential Equations5. B.D. Sharma : Partial Differential Equations

A.Math-306Discrete Mathematics and Programming with C01 Unit Full marks - 100 Credit - 4


Group-A1. Proposition, Relations and Functions: Propositions, A relational

model for data bank, Properties of binary relations, Equivalence relations& Partitions, Partial ordering relations & lattices, chains & antichairs,

Functions and the Pigeonhole Principle.2. Graphs and planar Graphs: Introduction, Basic terrminology,

Multigraphs and weighted graphs, Paths and circuits, Shortest Paths


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in weighted graphs, rulerian Paths and circuits, Hamiltonian Pathes

and circuits.3. Trees and Cut Sets: Tress, Rooted trees, Path lengths in rooted trees,

Binary search trees spanning trees and custsets, Minimum spanning

trees.4. Latties:Lattices and Algebraic systems, Principle of duality, Baric

Properties of Algebraic system defined by lattices, Distributive and

complemented lattices, Boolean lattices and Boolean algebras,5. Boolean Algebras: Boolean functions and Boolean expressions

Prepositional calculus, Design and implementation of digital

Networks, Switching circuits. Boolean lattices.Group-B

1. Fundamentals of C Programming

2. Operators and expressions of C, input and output.

3. Different Control statements.4. Functions and arrays

Suggested Books:

1. C. L Liu : Elements of Discrete Mathematics

2. Robert J. McElice : Introduction to Discrete Mathematics

3. Alan Doer : Applied diserete structure for computer Science

4. Donald F. Stanat : Discrete Mathematics in computer Science

5. Byron S.Gotteried : Programming with C

6. Stephen G.Kochan : Programming with C

A.Math-307Numerical Analysis


[Five questions to be answered out of Eight]1. Solution of Algebraic and Transcendental Equation: The Bisection

Method, The Iteration Method, Newton-Rapson Method, The Method ofFalse position.

2. Interpolation: Newtons Formula for Interpolation, Gauss's InterpolationFormulae, Lagrange's Interpolation Formula, Hermite InterpolationFormula, Starling Interpolation Formula, Bessel's Interpolation Formula

3. Curve Fitting, Cubic spline and Approximation.


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4. Numerical Solutions of Linear and Non Linear System of Equations:Gaussian Elimination Method Iterative Methods, Matrix Inversion Methodof Factorization.

5. Numerical Differentiation and Integration: The Cubic spline Method,Errors in Numerical Differentiation, Trapezoidal Rule, Simpson's Rule,Trapezoidal Rule.

6. Numerical Solutions of Ordinary Differential Equations: Solution byTaylor's series, Picard's Method of Successive Approximations, EulersMethod, Modified Euler's Method, Runge-Kutta Method.

7. Finite Difference Method8. Numerical Solutions of Partial Differential EquationsSuggested Books:1. S. S. Sastry : Introductory Methods of Numerical Analysis2. P. Henrici : Elements of Numerical Analysis

3. Burden, Faires : Numerical Analysis4. A. R. Bashishtha : Numerical Analysis

A.Math-308Integral Equations

0.5 Unit Full marks - 50 Credit - 2


1. Introduction, Types of IEs, Differentiation under an integral sign,Relation between differential and integral equations.

2. Solution of the VIEs and FIEs of the first and second kinds.3. Fredholms First, Second and Third fundamental theorems.

Fundamental function, IEs with degenerate kernels, Eigenvalues &

eigen functions.

4. Symmetric kernel, Orthogonal & Normalised systems, Schmidtssolution of non-homogeneous IEs, Hilbert Schmidt theorem.

5. Construction of Greens function, Influence function, IE & Greensfunction for BVPs.

6. Singular IEs, Cauchy principal integral, Hilbert kernel & Hilbertformula. Solution of Hilbert type IEs of the first & second kinds.

Suggested Books:

1. Shanti Swarup : Integral Equations


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2. M.D. Raishinghania : Linear Integral Equations

3. R.P. Kanwal : Linear Integral Equations

4. T.G. Tricomi : Integral Equations

5. A.R. Vashishtha : Integral Equations

A.Math-309Mathematics for Business

0.5 Unit Full marks - 50 Credit - 2


1. Set Theory and its applications to business problems, Applications of

Matrices and system of linear equations.

2. Straight lines and its applications to business Break Even interpretations.

3. Mathematics of finance: Simple and compound interest, Present andfuture value, Simple and compound discount, Depreciation, Annuity.

4. Supply and demand function. Application of supply and demand

functions. Elasticity Relation between average and marginal cost

5. Application of differential calculus: Maxima and Minima of a function

and its applications, Marginal Propensity of consume and the multiplier,

Applications of partial derivates.

6. Application of integral calculus; Interpretive application of area

consumers and producers surplus, Applications of differential equation,Dynamic modeling and difference equations.

Suggested Books:1. Mathematics with applications in

Management and Economics: D. Prichet and John. C. Saber.

2. Introductory Mathematics forEconomics and Buseness,

: K. Holden and A.W. Pearson

3. Business Mathematics. : D. C. Sanchetiz. V. K. Kapoor.

4. Business Mathematics : Zambeer uddin, Khanna andhambri.


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A. Math-320

Practical (Using C/C++)

1 Unit Full marks 100 Credit -4

A. Programming 60 Marks1. Solution of Cubic equation using if else statement, switch

statement. Shortest distance between two given lines.

Volume and Surface area of tetrahedron. Sphere cone.2. Cylinder, ellipsoid. Area of great circle.

3. Sun of some series: Sin(x), Cos (x), tan(x) , log(x) and TT ets.4. Prime numbers, factorial of a number and sorting.5. Calculation of interest, income tax, annuity, telephone bill,

electric bill and grading system.

6. Properties of matrices, inverse, eigenvalue, & determinant value.7. Solution of system of linear equations using crammers rule,

gauss elimination method, iteration method.

B Practical Note Book 30 Marks.

C Viva - Voce 10 marks


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B.Sc. (Honours) Part IV Examination, 2016

B. Sc (Honours) Part IV Examination will comprise of 1050 marks (Theorycourses 800, Practical Math 100, Tutorial, Terminal and Class Records 100

and Viva-Voce 50). The duration of examination for each one unit theorycourse is 4 hours and 0.5 unit theory course is 3 hours. A candidate forHonours Part IV of 2016 shall take any eight courses from the following

courses A.Math.-401 - A.Math.-411 with the approval of the department.

Course No. Title of Courses FullMarks

UnitNo.

Credit

A.Math.-401 Hydrodynamics 100 1 4

A.Math.-402 Quantum Mechanics 100 1 4

A.Math.-403 Differential Geometry 100 1 4

A.Math.-404 Classical Mechanics 100 1 4A.Math.-405 Electrodynamics 100 1 4

A.Math.-406 Operations Research 100 1 4

A.Math-407 Astronomy 100 1 4

A.Math.-408 Special Theory of Relativity 100 1 4

A.Math.-409 Thermodynamics and StatisticalMechanics

100 1 4

A.Math-410 Biomathematics 100 1 4

A.Math-411 Honours Project 100 1 4A.Math-420 Practical (C++/FORTRAN) 100 1 4

A.Math-421 Tutorial Terminal and Class Record 100 1 4

A.Math-422 Viva-Voce 50 05 2

Total 1050 10.5 42


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A.Math-401HydrodynamicsFull Marks-100

01 Unit Credit-4


1. Some basic properties of the fluid. Velocity and acceleration of fluidparticles. Lagranges and Eulers method. Martial local and convectivederivatives. Steady and unsteady flows. Uniform and non-uniform flows.

2. Streamline pathlines and Vortex lines, velocity potential, vorticity vector,rotational and irrotational flows, one, two and three dimensional flows,discharge or rate of flow .

3. Significance of the equation of continuity. The equation of continuity.Equation of continuity in curvilinear coordinates. Equation of continuity

in spherical and polar coordinates. Equation of continuity of anincompressible fluid through a channel. Boundary surface.

4. Eulers equation of motion, conservative field of force; Lambshydrodynamical equations of motion; Bernoullis equation; Motionunder conservative body force, Vorticity equations, Helmhomrks

vorticity equation.5. Motion in two-dimension; Stream function Physical meaning of stream

function velocity in polar coordinates. Relation between stream function

and velocity potential.

6. Sources, sinks and doublets, complex potential and complex velocity,stagnation points; complex potential due to a source and a doublet,Uniform stream. Image in two and three dimensions Image of a source anddoublet w. r. to circle. Stokes stream function.

7. Flow and Circulation; Relation between circulation and vorticity.Kelvins circulation theorem, Permanence of irrational motion, Equationof energy; kelvins minimum energy theorem.

Circles theorem, The Theorem of blasius, the force exerted on acircular cylinder by a source, Motion of a circular cylinder, pressure at

points on a circular cylinder, image system for a source outsidecircular cylinder.

8. Vortex motion, vortex tube; strength of a vortex, vortex pair, complex

potential due to vortex motion, vortex rows, Free vortex, Forced vortex,spiral vortex, compound vortex. Image of a vortex filament in a plane,

Image of a vortex outside and inside a circular cylinder


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Suggested Books:1. F. Chorlton : Fluid dynamics Van-Nostrand2. I. M. Milne Thomosn : Theoretical Hydrodynamics3. P.P. Gupta : Hydrodynamics

A.Math-402Quantum Mechanics



1. Basic Concept, Plancks hypothesis, Classical laws, Plancks radiationlaw, Black body radiation, Photo-electric effect, Einsteins Photon

theory, Compton effect.

2.

Wave Particle Dualism for light and matter, De Broglie Model of theAtom, De Broglie wave, phase and group velocities, Wave packets,

Uncertainty principle.3. Thomson Model of the Atom, Rutherford Atom model, Rutherford

scattering of particles, Bohr Model of the Atom, Bohrs theory of the

Hydrogen Spectrum, Spectral Series of Hydrogen Atom, Energy level ofHydrogen Atom, Correspondence principle.

4. Wave Mechanical concepts, Schrodinger wave equation, Interpretationof wave function; Expectation value and Ehrenfests theorem.

5. Energy eigenfunctions, One dimensional square well potential,Interpretative Postulates and energy eigenfunctions.6. Momentum eigenfunctions, Box normalization, Dirac function; Motion

of a free wave packet, Minimum uncertainty product and minimum

packet .7. Linear harmonic oscillator.8. Spherically Symmetric potential in three dimension, Angular momentum

Hydrogen atom. Collision theory: One Dimension square potentialbarrier.

Suggested Books:1. Arther Beiser : Concepts of Modern Physics.2. L. I Schiff : Quantum Mechanics.

3. P. T. Mathews : Introduction of Quantum Mechanics4. Powell and Crassmann : Quantum Mechanics

5. Gupta, Kumar and Sharma : Quantum Mechanics6. Donald Rao : Quantum Mechanics.


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A.Math-403Differential Geometry



1. Curves: Parametric representation, arc length, Tangent, Osculation plane,Normal, Principal normal, Binormal and fundamental planes.

2. Curves: Curvature and torsion, Frenet setet formula, Helices, Osculationcircle osculating sphere, involute and Evolute.

3. Surface: Parametric equations, Parametric curves, Tangent plane, normaland envelope, two and three parameter family of surfaces.

4. First and second fundamental forms, Direction coefficients, orthogonaltrajectories, Double family of curves.

5. Curves on a surface: Normal curvature and sections Meusniers theorem,Principal sections, Curvature and directions, Rodrigues formula, Eulers

theorem, Minimal surface.

6. Developable, Monges Theorem, Conjugate directions, Asymptotic lines,Theorem of Beltrami Enneper.

7. Ruled and skew surfaces parallel surfaces and Bonnets theoremisometric lines.

8. Geodesics: Definitions, Differential equation of geodesics. Canonicalgeodesic equation Geodesic on a surface of revolutions, Clairauts

theorem, Gauss-Bonnet Theorem. Differential Manifolds, connection &

curvature on a Manifold.

Suggested Books:

1. H.Guggen Heimer : Differential Geometry

2. D.J. Struik : Classical Differential Geometry

3. J.N. Sharma and A.R. Basishtha : Differential Geometry

4. M.L. Khanna : Differential Geometry

5. C. Weathcrburn : Differential Geometry of threeDimensions.

6. T.J. Willmore : An Introduction to DifferentialGeometry

7. S. Stamike : Differential Geometry


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A- Math-404

Classical Mechanics



1. Generalized coordinates: Holonomic and non-holonomic systems.Langranges equation for holonomic and non-holonomic dynamicalsystems.

2. Elementary Principles: Mechanics of a particle and system o

particles, constraints, D-Alembertes principle and langrangesequation. Simple applications of Langrange's equation.

3. Introduction to calculus of variation, Eular-Langrange differential

equation, applications.4. Phase space, Hamiltons equations, and Hamiltons principle, principle

of least action, Hamiltons function and Hamilton-Jacoby equation.5. Langrange and Poisson brackets, contact transformation, commentator.6. Motion under a central force; Two body problem, inverse square law,

Centre of mass an laboratory coordinates, Rutherford scattering.7. Motion in rotating frames, motion relative to earth. Foucaults Pendulum.8. Impulsive motion, ignoration of coordinates, small oscillation,

constant of motion.Introduction to the Lagrangian and Hamiltonian formulations forcontinuous systems and fields.

Suggested Books:

1. H. Goldstein : Classical Mechanics2. Rutherford : Classical Mechanics

3. Gupta, Kumar : Classical Mechanics4. B.D. Gupta and S. Saha : Classical Mechanics

A.Math-405

ElectrodynamicsFull Marks-100


1. Electrostatics: The electrostatic field of force. Conductors, condensersand dipole, system of conductors, Electrical images, Electrostatic energy.


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2. Dielectrics: Electro potential & displacement Minimum energy of the field,Uniqueness theorem, Polarization. Green's Reciprocal Theorem.

3. Capacitance and electric energy: Capacitance of a conductors. Capacitorsin series & parallel, Combination of capacitors, Electric energy in term

of Q.V.and C.4. Steady electric current: Electromotance or e, m. f: field aspect, e, m.f:

network aspect. Resistance & conductors, general net work theorem and

Kirchhoffs law.5. Magnetism: Fundamental of magnetostatics, Magnetic field poles and

strength volume vector and vector potential, Mutual and self inductance,

Force on a current, Faradays law.6. Steady current in magnetic material: Equations of Magnetic field and

energy, Magnetic dipole, Electromagnetic induction. Amperes circuital

theorem, Biot Savart law.

7.

Maxwells equations: Derivations, general solutions and deductions, Scalar andvector potentials. Electromagnetic potentials, poynting theorem.

8. Electromagnetic waves: Wave equations for free space conditions, planeelectromagnetic wave in free space. Energy flow due to a planeelectromagnetic wave (pointing vector for free space) plane

electromagnetic waves in isotropic non-conducting media, Planeelectromagnetic wave in conducting media. Interaction ofElectromagnetic waves with matter, Boundary Conditions for the

electromagnetic field vectors (B, E, D, A) at the interface between two

media. Reflection and Refraction at the boundary of two non-conducting.Media, Fresnels equation.

Suggested Books:1. Coulson : Electricity2. V.C.A. Ferraro : Electromagnetic Theory.3. Gupta and Sharma : Mathematical Theory of Electricity

and Magnetism.4. W.J.Duffin : Electricity & Magnetism.

5. S.L.Gupta, V.Kumar : Electrodynamics. And S. P. Singh6. J.D. Jackson : Classical Electrodynamics


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A. Math-406

Operations Research



1. Basic Concepts: Introduction, The nature, Meaning, Scope and role ofoperation Research. Main phases of operation Research. Study, Modelingin operation Research, General methods for solving operation Research

Models. Decision making in operation Research.2. Mathematical Programming: Concept and Basic elements of Linear

Programming (LP) Formulation of Linear Programming Problems.3. Solution of Linear Programming Problems by Graphical Method,

simplex Method, Two phase method, Big-M method.

4. Solution of LPP by Dual simplex method5. Duality in Linear Programming.6. Sensitivity Analysis, Parametric Analysis. Transportation and

Assignment problems.7. Integer Linear programming8. Game Theory: Basic Concept of Game Theory, Two Persons and n-

persons Zero-Sum Game.

Suggested Books:1. Berger J. O : Statistical Decision Theory

2. Charles, A : Decision Making under UncertaintyModels

3. Gass, S. I. : Linear Programming.

4. Hudly, G : Linear Programming.5. Lindly, D. V : Making Decision.

6. Gupta, D.K. and Mohan M. : Linear Programming and Theory of

Games.7. Taha, H.A. : Operation Research: An Introduction.8. Vajda S. : Game Theory.

A. Math-407


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dynamics of a single particle, Equivalence of mass and energy,

Transformation properties of momentum, energy, mass, and force.4.Relativity and Electromagnetism: Interdependence of electric and

magnetic fields, Transformation of Electric & Magnetic fields, Field of a

uniformly moving point charge, Force and Fields near a current-carryingwire, Forces between moving charges,

5.Four-Vector Formalism: Lorentz transformations in 4-vectors, Lorentzand Poincar groups.

6.Spacetime Diagrams: Mikowski space, Simultaneity, Contraction, andDilation, Time order and space separation of events, Proper time,

velocity, acceleration, Twin paradox.7.Principle of Least Action: the Lagrangian, Conservation laws. Maxwells

equations and electromagnetic waves, Maxwells equations in four-vector

formulation.

8.Action integral for the electromagnetic field and the field equations,Noethers theorem, Energy-momentum tensor of the electromagnetic

field.9.Suggested Books:

1. R. Resnick : Introduction to Special Relativity2. A. Qadir : Relativity: An Introduction to the Special Theory

3. U.E. Schrder : Special Relativity4. F.N.H.

Robinson

: An Introduction to Special Relativity and it

applications5. Tolman : Relativity, Thermodynamics and Cosmology6. B. F. Schuttz : Geometrical Methods of Mathematical Physics.

A.Math-409Thermodynamics and Statistical Mechanics



Thermodynamics (group-A)1. Basic concept: Thermodynamic system, State of a system, Thermal

equilibrium and concept of temperature, Scope of thermodynamics, Meaning

of partial derivatives, more relations between partial derivatives.

Equation of state: Intensive and intensive variables, Equation of state,

Equation of state of an ideal gas, other equation of state.


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Boltzman statistics, Statistics of a photon gas, The Fermi Dirac statistics,

Velocity, Speed and energy distribution functions.

Suggested Books:1. F. W. Sears : Thermodynamics and Statistical Mechanics

2. T. Hossain : Heat and Thermodynamics3. Brijlal : Heat and Thermodynamics

A. Math-410

Biomathematics


[Five questions to be answered out of Eight]1. Continuous population models for single species: continuous Growth

Models. Delay Models and its linear Analysis, Periodic solutions,

harvesting a single Natural population.

2. Discrete population Model for a single species: Simple Models, DiscreteLogistic Models Discrete Delay Models, Fishery Management Models.

3. Continuous Models for interacting populations predator prey Models(Lotka-Volterra systems) complexity and stability, Competition Models,Mutualism or symbiosis.

3. Discrete Growth Models for Interaction populations Discrete Growth

Models for Interaction populations, Detailed Analysis of predator PreyModels.

4. Biological waves (Singles Models) Fisher Equation and Propagation

wave solutions, asymptotic solutions and stability of wave not DiffusionReactions Diffusion Models and some Exact Equation.

5. Biological Waves: Multispecies Reaction Diffusion Models.

6. Population Interaction Diffusion Mechanisms Reaction DiffusionMechanisms, Linear stability Analysis and Evolution of spatial pattern.

Dispersion Relation, Turning space, Scale and Geometry Effects in

pattern Formation in Morphogenetic Models. Pattern Generation withsingle spicing Models.

7. Epidemic Models and the dynamics of intentions Diseases.

Suggested Books:

1. J. D. Murry :Mathematical Biology.2. J. N. Kapoor :Mathematical Biology.

A.Math-411


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Honours ProjectFull Marks-100


Honours Project

Each student is required to work on a project and present a project reportfor evaluation. Such projects should be extensions or applications ofmaterials included in different honours courses and may involve field

work and use of technology. There may be group projects or individualprojects.

Implementation and Evaluation of the Project

Implementation:The Academic Committee shall appoint a project Implementation andcoordination Committee (PICC) before the session begins. The PICCshall consist of a project Coordinator (PC) and such other members as

the Academic Committee considers appropriate.The PC shall invite projects from the teachers before the class start. Eachteacher should submit three project proposal should include a shortdescription of the project. Such projects should be extension of

applications of materials included in different honors courses, and mayinvolve field work and use of technology.There may group projects as well as individual projects. For group

projects, students will sign up with the PICC in groups of three. Thesemay not be changed later on without approval of the PICC.The PICC shall assign each group a project. The members of each groupshall work independently on the assigned project under the supervisionof the concerned teacher.The PICC shall monitor with the supervisors the progress of different

projects and arrange weakly discussions on projects and materials.

Completion

The project must be completed the before the termination of the classes.Each student is required to prepare a separate report on the project. Eachreport should be of around 40 pages typed on one side of A4 size white

paper preferable using word processors. Graphs and figures should be


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clearly drawn preferably using computers. Reports of different studentsworking on the same group project should differ in some details andillustrations.The Academic Committee will fix a data for the submission of the

projects to the PICC. Each student must submit three typed copies ofher/his project report to the PICC on or before the date fixed for such

submission.The PICC, on receiving the reports will arrange the presentation of by

individual students before the PICC, This presentation should take palace

soon after the completion of the written examination.Any student who fails to submit the report on the due date or to presentthe thesis on the fixed date will not get any credit for this course.

Evaluation

The distribution of marks for each project shall be as follows:Project Report 60 marks.

Project Presentation 40 marks.

Each project report shall be examined by two examiners, one of whomshall be project supervisor and the other appointed from amongst the

teachers of the department of the recommendation of the PICC. In case

the marks of the two examiners of a project report differ by more than20% a third examiner for that report shall be appointed from amongst the

teachers of the department on the recommendation of the PICC. In suchcases the final marks shall be determined according to the usualprocedure.Each student is required to present her/his work on the project before the

PICC who will evaluate the presentation.The Academic Committee may prepare additional guidelines forevaluation of the projects.

All marks on the projects shall be submitted to the ExaminationCommittee for tabulation with copies to the Controller of Examination.

The project reports shall be returned to the PICC for preservation.


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A. Math-420

Practical (C++/FORTRAN)


Section A: Programming 60 marks

1.

Solution of Polynomial and transcendental equations and system o

Non-linear Equations.

2. Interpolation and Polynomial Approximation.

3. Matrices and solution of systems of linear equations.

4. Numerical Differentiation and Integration.

5. Numerical Solution of ordinary Differential and system of ordinary

differential equations.

6. Numerical solution of partial differential equations and Integralequations.

7. Curve fitting.Section - B: Practical Note Book 30 marks.

Section - C: Viva - Voce 10 marks

Documents

B.sc.(Hons.) Syllabus