Bsc Math Syllabus of Physical Sciences

8/8/2019 Bsc Math Syllabus of Physical Sciences

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MATHEMATICS Papers for B.Sc. (Physical Sciences)/

Mathematical Sciences

Preamble . The focus is on introducing

mathematical concepts using examples and problems from various

science domains. Rigorous approaches including proofs and derivations

are exemplified in a few topics. Visual, graphical and application oriented

approaches are introduced, wherever appropriate.

This syllabus should

i) provide a relevant, stimulating and motivating course of advanced study in

mathematics,

including the provision of a suitable foundation for further study in science

ii) develop a variety of skills in modelling, logical reasoning and problem solving;

iii) encourage student interest and satisfaction through the development and use of

mathematics in a variety of applications;

iv) promote an awareness of the relevance of mathematics to other fields of study and

to

other practical applications.


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Paper I Calculus and Matrices

Six Lectures per week (including practicals)

Max. Marks 100 (including internal assessment)

Examination 3 hrs.

Unit I. Matrices (20 L)

R, R2, R3 as vector spaces over R . Standard basis for

each of them. Concept of Linear Independence and examples of different

bases. Subspaces of R2, R3. Translation, Dilation, Rotation, Reflection in

a point, line and plane. Matrix form of basic geometric transformations.

Interpretation of eigenvalues and eigenvectors for such transformations

and eigenspaces as invariant subspaces. Matrices in diagonal form.

Reduction to diagonal form upto matrices of order 3. Computation of matrix

inverses using elementary row operations. Rank of matrix. Solutions of a

system of linear equations using matrices. Illustrative examples of above

concepts from Geometry, Physics, Chemistry, Combinatorics and

Statistics.

Unit II. Calculus (34 L)

Sequences to be introduced through the examples arising in Science

beginning with finite sequences, followed by concepts of recursion and

difference equations. For instance, the sequence arising from Tower of

Hanoi game, the Fibonacci sequence arising from branching habit of trees

and breeding habit of rabbits. Convergence of a sequence and algebra

or convergent sequences. Illustration of proof of convergence of some


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simple sequences such as (1)n/n, I/n2, (1+1/n)n, sin n/n, xn with x < 1.

Graphs of simple concrete functions such as polynomial, trigonometric,

inverse trigonometric, exponential, logarithmic and hyperbolic functions

arising in problems or chemical reaction, simple pendulum,

radioactive decay, temperature cooling/heating problem and biological

rhythms.

Successive differentiation. Leibnitz, theorem. Recursion formulae for

higher derivative.

Functions of two variables. Graphs and Level Curves of functions of two

variables. Partial differentiation upto second order.

Computation of Taylors Maclaurins series of functions such as ex,

log(1 + x), sin (2x), cos x. Their use in polynomial approximation and error

estimation.Formation and solution of Differential equations arising in population

growth, radioactive decay, administration of medicine and cell division.

Unit III. (L14)

Geometrical representation of addition, subtraction, multiplication and

division of complex numbers. Lines half planes, circles, discs in terms of

complex variables. Statement of the Fundamental Theorem of Algerbra

and its consequences, De Moivres theorem for rational

indices and its simple applications.


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Suggested Readings

1. George B. Thomas, Jr., Ross L. Finney : Calculus and Analytic

Geometry, Pearson Education (Singapore); 2001.

2. T.M. Apostal : Calculus, vol. 1, John Wiley and Sons (Asia) : 2002.

3. A.I. Kostrikin: Introduction to Algebra, Springer Verlag, 1984.

Using computer aided software for example, Matlab/ Mathematica/ Maple/ MuPad/

wxMaxima for operations of complex numbers, plotting of complex numbers,

matrices, operations of matrices, determinant, rank, eigenvalue, eigenvector, inverse

of a matrix, solution of system of equations


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Paper II Calculus and Geometry



Examination 3 hrs.

Unit I: Calculus 44

Limit and continuity of a function: ( and sequential approach.

Properties of continuous functions including intermediate value theorem.

Differentiability. Darbouxs theorem, Rolles theorem, Lagranges mean

value theorem, Cauchy mean value theorem with geometrical

interpretations. Uniform continuity.

Definitions and techniques for finding asymptotes singular points,

concavity, convexity, points of inflexion for functions. Tracing of standard

curves.

Integration of irrational functions. Reduction formulae. Rectification.

Quadrature. Volumes.

Unit III: Geometry and Vector Calculus 24

Techniques for sketching parabola, ellipse and hyperbola. Reflection

properties of parabola, ellipse and hyperbola . Classification of quadratic

equations representing lines, parabola, ellipse and hyperbola.

Differentiation of vector valued functions, gradient, divergence, curl and

their geometrical interpretation.


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Spheres, Cylindrical surfaces. Illustrations of graphing standard quadric

surfaces like cone, ellipsoid.

Recommended Books

1. H. Anton, I. Bivens and S. Davis: Calculus, John Wiley and Sons

(Asia) Pte. Ltd. 2002.

2. R.G. Bartle and D.R. Sherbert : Introduction to Real Analysis, John

Wiley and Sons (Asia) Pte, Ltd; 1982

Use of computer aided software for example, Matlab/ Mathematica/ Maple/ MuPad/

wxMaxima in identifying the singular points, points of inflection and tracing of curves.


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Paper III - Algebra



Examination 3 hrs.

Groups: Definition and examples of groups, examples of abelian and nonabelian

groups: the group Zn of integers under addition modulo n and the

group U (n) of units under multiplication modulo n. Cyclic groups from

number systems, complex roots of unity, circle group, the general linear

group GLn (n,R), groups of symmetries of (i) an isosceles triangle, (ii) an

equilateral triangle, (iii) a rectangle, and (iv) a square, the permutation group Sym (n),

Group of quaternions,

Subgroups, cyclic subgroups, the concept of a subgroup generated by a

subset and the commutator subgroup of group, examples of subgroups

including the center of a group. Cosets, Index of subgroup, Lagranges

theorem, order of an element, Normal subgroups: their definition,

examples, and characterizations, Quotient groups.

Rings: Definition an examples of rings, examples of commutative and noncommutative

rings: rings from number systems, Zn the ring of integers

modulo n, ring of real quaternions, rings of matrices, polynomial rings,

and rings of continuous functions. Subrings and ideals, Integral domains

and fields, examples of fields: Zp, Q, R, and C. Field of rational functions.


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Vector spaces: Definition and examples of vector spaces. Subspaces

and its properties Linear independence, basis, invariance of basis size,

dimension of a vector space.

Linear Transformations on real and complex vector spaces: definition,

examples, kernel, range, rank, nullity, isomorphism theorems, invertible

linear transformations (chatacterizations)

Algebra of Linear transformations and matrix of a linear transformation

Linear functional over real & complex vector spaces: definition and

examples.


wxMaxima in Linear Transformations, invertible transformations, group of symmetries,

rectangle, square and permutation groups

Recommended Books

1. Joseph A Gallian: Contemporary Abstract Algebra, fourth edition,

Narosa, 1999.

2. George E Andrews: Number Theory, Hindustan Publishing

Corporation. 1984

3. . C.W. Curtis, Linear Algebra, an introductory approach, Springer-

Verlag, 1991.

4. . David M. Blotin, Linear algebra and Geometry, Cambridge Press,

1979.


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Paper IV Differential Equations



Examination 3 hrs.

Ordinary Differential equations

First order exact differential equations. Integrating factors, rules to find

and integrating factor. First order higher degree equations solvable for

x,y,p=dy/dx. Methods for solving higher-order differential equations.

Basic theory of linear differential equations, Wronskian, and its properties.

Solving an differential equation by reducing its order. Linear homogenous

equations with constant coefficients. Linear non-homogenous equations.

The method of variation of parameters, The Cauchy-Euler equation.

Simultaneous differential equations, total differential equations.

Applications of differential equations: the vibrations of a mass on a spring,

mixture problem, free damped motion, forced motion, resonance

phenomena, electric circuit problem, mechanics of simultaneous

differential equations.

Partial Differential Equations

Order and degree of partial differential equations. Concept of linear and

non-linear partial differential equations. Formation of first order partial


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differential equations. Linear partial differential equation of first order,

Lagranges method, Charpits method. Classification of second order

partial differential equations into elliptic, parabolic and hyperbolic through

illustrations only. Applications to Traffic Flow.

Using Computer aided software for example, Matlab/ Mathematica/ Maple/

MuPadcharacteristics,

vibrating string, vibrating membrane, conduction of heat in solids,

gravitational potential, conservation laws

Recommended Books

1. Shepley L. Ross: Differential equations, Third edition, John Wiley

and Sons, 1984

2. I. Sneddon: Elements of partial differential equations, McGraw-Hill,

International Edition, 1967.


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Paper V Real Analysis



Examination 3 hrs.

Emphasis is on visual ideas of convergence and divergence and series expansions of

elementary fuctions.

Unit I : Real Sequences (30 L)

Finite and infinite sets, examples of countable and uncountable sets. Real

line, bounded sets, suprema and infima, statement of order completeness

property of R, Archimedean property of R, intervals.

Concept of cluster points and statement of Bolzano Weierstrass theorem.

Cauchy convergence criterion for sequences. Cauchys theorem on limits,

order preservation and squeeze theorem, monotone sequences and their

convergence.

Unit II: Infinite Series (38 L)

Infinite series. Cauchy convergence criterion for series, positive term

series, geometric series, comparison test, convergence of p-series, Root

test, Ratio test, alternating series, Leibnitzs test. Definition and examples

of absolute and conditional convergence.

Sequences and series of functions, Pointwise and uniform convergence.


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Mn-test, M-test, change or order of limits.

Power Series: radius of convergence, Cauchy-Hadamard theorem, termby-

term differentiation and integration of power series. Definition in terms

of Power series and their properties of exp (x), sin (x), cos (x).


wxMaxima for Taylor and Maclaurin series of sin x, cos x, log(1+x), ex, (1+x)n,

maxima and minima, inverse of graphs.sequences

References:

Recommended Books

1. T. M. Apostol, Calculus, Voulme-1, John Wiley and Sons(Asia) Pte

Ltd., 2002.

2. R.G. Bartle and D. R Sherbert: Introduction to real analysis, John

Wiley and Sons (Asia) Pte. Ltd., 2000.

3. E. Fischer, Intermediate Real Analysis, Springer Verlag, 1983.

4. K.A. Ross, Elementary Analysis The Theory of Calculus Series

Undergraduate Texts in Mathematics, Springer Verlag, 2003.


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Paper VI Mechanics and Discrete Mathematics



Examination 3 hrs.

The course is an introduction to Mathematics of Discrete Structure. The

advent of modern digital computer has increased the need for

understanding of discrete Mathematics. The tools and techniques in the

system are going to enable students to appreciate the power and beauty

of Mathematics in designing problems-solving strategies in everyday life.

Mechanics (L 30)

Conditions of equilibrium of a particle and of coplanar forces acting on a

rigid Body, Laws of friction, Problems of equilibrium under forces including

friction, Centre of gravity, Work and potential energy.

Velocity and acceleration of a particle along a curve: radial and transverse

components (plane curve ), tangential and normal components (space

curve), Newtons Laws of motion, Simple harmonic motion, Simple

Pendulum, Projectile Motion.

Graph Theory (L 38)

Types of graphs : Simple graph, Directed graph, Multi graph, and


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Pseudo graph. Graph modeling, terminology and basics. Special

Graphs : Complete Graph, Cycles, n-dimensional cubes, Bipartite

Graph, Complete Bipartite Graph.

Subgraph and basic algebraic operations on graphs, connectivity,

path, cycles, tree to be introduced as a connected graph with no

cycles, introduction to shortest path (least number of edges)

problem, solution of shortest path problem for simple graphs using

complete enumeration. Euler and Hamiltonian graphs (for

undirected graphs only) : Koenigsburg Bridge Problem,

statements and interpretations of (i) necessary and sufficient

conditions for Euler cycles and paths (ii) suficient condition for

Hamiltonian cycles, finding Euler cycles and Hamiltonian cycles

in a given graph.

Tree traversal, spanning trees, weighted graphs, minimal

spanning tree using Kruskals algorithm, Prims algorithm,

Huffman codes.


wxMaxima for Projectile motion, Euler and Hamiltonian graphs, Koenigsburg Bridge, ,

Prims algorithm,Huffman codes.

Recommended Books

1. A.S. Ramsay, Statics, CBS Publishers and Distributors(Indian

Reprint), 1998.


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2. A.P. Roberts, Statics and Dynamics with background in

Mathematics, Cambridge University Press, 2003.

3. K.H. Rosen, Discrete mathematis and its applications, McGraw-Hill

International Editions, 1999.

4.. C.F. Gerald and P.O. Wheatley, Applied Numerical Analysis,

Pearson Education Ind. 2004.


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MATHEMATICS and STATISTICS

B.Sc. Life Sciences

4L per week

Unit I (24 L)

Sets. Functions and their graphs : polynomial, sine, cosine, exponential

and logarithmic functions. Motivation and illustration for these functions

through projectile motion, simple pendulum, biological rhythms, cell

division, muscular fibres etc. Simple observations about these functions

like increasing, decreasing and, periodicity. Sequences to be introduced

through the examples arising in Science beginning with finite sequences,

followed by concepts of recursion and difference equations. For instance,

the Fibonacci sequence arising from branching habit of trees and breeding

habit of rabbits. Intuitive idea of algebraic relationships and convergence.

Infinite Geometric Series. Series formulas for ex, log (1+x), sin x, cos x.

Step function. Intuitive idea of discontinuity, continuity and limits.

Differentiation. Conception to be motivated through simple concrete

examples as given above from Biological and Physical Sciences. Use of

methods of differentiation like Chain rule, Product rule and Quotient rule.

Second order derivatives of above functions. Integration as reverse

process of differentiation. Integrals of the functions introduced above.

Unit II (14)

Points in plane and space and coordinate form. Examples of matrices

inducing Dilation, Rotation, Reflection and System of linear equations.

Examples of matrices arising in Physical, Biological Sciences and


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Biological networks. Sum and Produce of matrices upto order 3.

Unit III (20)

Mesures of central tendency. Measures of dispersion; skewness, kurtosis.

Elementary Probability and basic laws. Discrete and Continuous Random

variable, Mathematical Expectation, Mean and Variance of Binomial,

Poisson and Normal distribution. Sample mean and Sampling variance.

Hypothesis testing using standard normal variate. Curve Fitting.

Correlation and Regression. Emphasis on examples from Biological

Sciences.

Suggested Readings

1. H. S. Bear : Understanding Calculus, John Wiley and Sons (Second

Edition); 2003.

2. E. Batschelet : Introduction to Mathematics for Life Scientists,

Springer Verlag, International Student Edition, Narosa Publishing

House, New Delhi (1971, 1975)

3. A. Edmondson and D. Druce : Advanced Biology Statistics, Oxford

University Press; 1996.

4. W. Danial : Biostatistics : A foundation for Analysis in Health

Sciences, John Wiley and Sons Inc; 2004.

Note :It is desirable that softwares should be used for demonstrating

visual, graphical and application oriented approaches.


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Math IB.Sc.( Chemical Sciences)

Calculus

Modeling Rectilinear Motion, Extreme value of a continuous function, The Mean Value Theorem, Using

derivative to sketch the graph of a function, Curve sketching with Asymptotes, LHopital Rule,

Optimization in Physical Sciences, engineering, Business, Economics, and the Life Sciences.

Reductionformulae,derivationsandillustrationsofreductionformulaeofthetypesinnxdx,cosnxdx,tannxdx,secnxdx,(logx)ndx,sinnxcosmxdx,

Volume, Polar forms and Area, Arc length and Surface Area, Physical Applications, Applications to

Business, Economics, and Life Sciences.

Introduction to Vector functions, Differentiation and integration of vector function, Modelling Ballistics and

Planetary motion, Tangential and normal components of Accerlation. gradient, divergence, curl and their

geometrical interpretation.

Functions of several Variables, Limit and Continuity, Partial Derivatives, Tangent planes, Approximation,

and Differentiability, Extrema of functions of two variables, Lagranges Multipliers.

Recommended Books

1. M.J.Strauss, G.L.Bradley, K.J.Smith, Caluculus, Pearson Education, 2007.

2. J.Stewart, Calculus with Early Transcendental functionsCengage Learning, 2008.


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Math II

B.Sc.( Chemical Sciences)

Infinite sequence and series

Sequences, Series, The integral test and estimates of sums, The comparison test,Ratio and Root

test ( Statement and Applications only) Alternating series Power series, Taylor series.

Matrices

Vectors in Rn

, Introduction to Linear Transformations,, Vector spaces, subspaces, Basis and dimension,

Rank of a matrix and Applications, Orthonormal bases in Rn, Eigen values and Eigenvectors,

Diagonalizations.

Recommended Books

1. J.Stewart, Calculus with Early Transcendental functionsCengage Learning, 2008.

2. B.Kolman, D.R.Hill, Introductory Linear Algebra, Pearson 2001


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SEMESTERI:CalculusSECTION I

Limit and.Continuity, Types of discontinuities. Differentiability of functions.

Successive differentiation, Leibnitz.s theorem, Partial differentiation, Euler.s

theorem on homogeneous functions.

SECTION - II

Tangents and normals, Curvature, Asymptotes, Singular points, Tracing of curves.

SECTION III

Rolle.s theorem, Mean Value Theorems, Taylor.s Theorem with Lagrange.s &

Cauchy.s forms of remainder. Taylor.s series, Maclaurin.s series of sin x, cos x,

ex, log(l+x), (l+x)m, Applications of Mean Value theorems to Monotonic functions

and inequalities. Maxima & Minima. Indeterminate forms.

Books Recommended:

1. George B. Thomas, Jr., Ross L. Finney : Calculus and AnalyticGeometry, Pearson Education (Singapore); 2001.

2. H. Anton, I. Bivens and S. Davis : Calculus, John Wiley and Sons(Asia) Pte. Ltd. 2002.

3. R.G. Bartle and D.R. Sherbert : Introduction to Real Analysis, JohnWiley and Sons (Asia) Pte. Ltd. 1982


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SEMESTERIII: IntegrationandDifferentialEquationSECTION I: IntegrationReduction formulae, Integration of irrational and trigonometric functions.

Properties of definite integrals. Quadrature, Rectification of curves, Volumes

and areas of surfaces of revolution.

SECTION-II: Ordinary differential equations

First order exact differential equations including rules for finding

integrating factors, first order higher degree equations solvable for x, y, p, Wronskian

and its properties, Linear homogeneous equations with constant coefficients, Linear

non-homogeneous equations. The method of variation of parameters. Euler.s

equations. Simultaneous differential equations. Total differential equations.

Applications of ordinary differential equations to Mixture Problems, Growth

and Decay, Population Dynamics and Orthogonal trajectories.

SECTION-III: Partial differential equationsOrder and degree of partial differential equations, Concept of linear and

non-linear partial differential equations, formation of first order partial differential

equations. Linear partial differential equations of first order, Lagrange.s method,

Charpit.s method, classification of second order partial differential equations into

elliptic, parabolic and hyperbolic through illustrations only.

Applications to Traffic Flow.

Recommended Books:1. Calculus, H. Anton, 1. Birens and S.Davis, John Wiley and Sons, Inc. 2002.

2. Differential Equations, S.L.Ross, John Wiley and Sons, Third Edition, 1984.

3. Elements of Partial Differential Equations, I.Sneddon, McGraw-Hill

International Editions, 1967.


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SEMESTERIV: AnalyticGeometryandAppliedAlgebraSECTION-I : GeometryTechniques for sketching parabola, ellipse and hyperbola. Reflection

properties of parabola, ellipse and hyperbola and their applications to signals,

classification of quadratic equation representing lines, parabola, ellipse and

hyperbola.

SECTION-II : 3-Dimensional Geometry and Vectors

Rectangular coordinates in 3-space; spheres, cylindrical surfaces cones.

Vectors viewed geometrically, vectors in coordinate system, vectors determine by

length and angle, dot product, cross product and their geometrical properties.

Parametric equations of lines in plane, planes in 3-space.

SECTION - III : Applied AlgebraLatin Squares, Table for a finite group as a Latin Square, Latin squares

as in Design of experiments, Mathematical models for Matching jobs, Spelling

Checker, Network Reliabilit, Street surveillance, Scheduling Meetings, Interval

Graph Modelling and Influencen Model, Picher Pouring Puzzle, Travelling Sales

Person Problem.

Recommended Books:1. Calculus, H. Anton, 1. Birens and S.Davis, John Wiley and Sons, Inc. 2002.

2. Applied Combinatorics, A Tucker, John Waley & Sons, 2003.


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SEMESTERV: AnalysisSECTION-IOrder completeness of Real numbers, open and closed sets, limit point of

sets, Bolzano Weierstrass Theorem, properties of continuous functions,

Uniform continuity.

SECTION-IISequences, convergent and Cauchy sequences, sub-sequences, limit

superior and limit inferior of a sequence, monotonically increasing and

decreasing sequences, infinite series and their convergences, positive term

series, comparison tests, Cauchy.s nth root test, D. Alembert.s ratio test,

Raabe.s test, alternating series, Leibnitz.s test, absolute and conditional

convergence.

SECTION-III

Riemann integral, integrability of continuous and monotonic functions,

improper integrals and their convergences, comparison tests, Beta and

Gama functions and their properties, Pointwise and uniform convergence of

sequences and series of functions, Weierstrass M-test, Uniform convergence

and continuity, Statement of the results about uniform convergence and

integrability or differentiability of functions, Power series and radius of

convergence, Fourier series.

Books Recommended:1. R.G. Bartle and D.R.Sherbert, Introduction to Real Analysis, John Wiley

and Sons (Asia) Pvt. Ltd., 2000.

2. Richard Courant & Fritz John, Introduction to Calculus and Analysis I,

Springer-Verlag, 1999.

3. S. K. Berbarian, Real Analysis, Springer - Verlag, 2000.


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SEMESTERVI: ComputerProgrammingandOptionalSECTION - I Computer ProgrammingProgramming: Preliminaries, constants, variables, type declaration,

expressions, assignment statements, input-output statements, Control

statements, functions, Arrays, simple programs using these concepts.

Control statements, functions, arrays, Format specification.

SECTION-II

Any one of the following :

1. Numerical Analysis

2. Discrete Mathematics

3. Mathematical Statistics

4. Mechanics

5. Theory of Games

1. Numerical Analysis

Solution of linear equations: Gaussian elimination including pivoting

and scaling, Iterative methods: Gauss Jacobi and Gauss Siedel methods,

Convergence of iterative methods, Roots of Non-linear equations, Bisection

method, Newton.s method, rate of convergence.

Interpolation: Lagrangian interpolating polynomials, divided difference,

error analysis, Numerical integration: Newton - cotes integration formula, the

trapezoidal rule, the Simpson.s rule, Gaussian Quadrature.

Books Recommended :1. C.F.Gerald and P.O. Wheatlay, Applied Numerical Analysis, Sixth

edition, Addison -Wesley, New York( 1999).

2. M.K.Jain, S.R.K.lyengar and R.K.Jain, Numerical Methods for Scientific

and Engineering Computation, New Age International Publisher, 4 th Edition,

New Delhi (2003).

2. Discrete Mathematics :

Basics of Graph Theory: Introduction, Paths and cycles, Hamiltonian

cycles and the Travelling Sales person problem, A shortest -Path Algorithm,Representation of Graphs, isomorphism of graphs, Planar graphs.

Boolean Algebras and circuits: Combinatorial circuits, Properties of

combinatorial circuits, Boolean Algebras, Functions and synthesis of circuits.

Books Recommended:1. Richard Johnsonbough, Discrete Mathematics Pearson Eduction Inc.,

2002.

2. C.L.Liu Elements of Discrete Mathematics Mc Graw-Hill Book,1985.

3. Mathematics Statistics :Review Unit : Measures of Central tendency, Measures of dispersion,

classical Definition of Probability.

Measures of skewness and kurtosis Bivariate data, Scatter diagram,principles of least squares and its application in fitting of curves, correlation,

Rank correlation and linear regression.

Axiomatic definition of probability, simple theorems, probability and

conditional probability, events, Bayes theorem with illustrations, Random

variable, concept of mathematical expectations and its simple properties,

moments and moment generating functions.

Discrete and continuous distribuions: Binomial, Poisson, geometric,

uniform and normal distributions and their simple properties, central limit

theorem.


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Books Recommended:1. V.K.Rohtagi, An introduction to Probability Theory and Mathematical

Statistics, John Wiley and Sons, 1976.

2. R.V. Hogg and A.T.Craig, Introduction to Mathematical Statistics - Amerind

Publishers Co. Pvt. Ltd., (1970).

3. A.M.Mood and F.A.Graybil & Boes., Introduction to the Theory of

Statistics, McGraw Hill Book Company, 1963.

4. Mechanics:

Laws of friction, conditions of equilibrium of coplanar forces acting on

a rigid body, centre of gravity, work and potential energy, Principle of virtual

work, General force systems, Total force, Total moment relative to a base point

force, Total moment relative to a base point.

Newton.s Laws of motion, simple Harmonic motion, simple pendulum,

projectiles, constrained motion in a circle, work and energy, orbital motion,

motion of a particle under a central force.

Books Recommended:1. J. L.Synge and B.A.Griffith, Principles of Mechanics, McGraw Hill Int.,

1959.2. A. S. Ramsey Statics, Cambridge University Press, CBS Publication &

Distributors, Delhi 1985.

3. F. Chorlton, A Textbook of Dynamics, CBS Publication & Distributors Delhi,

1985.

5. Theory of Games :Introduction to linear programming, simplex algorithm, Duallty in linear

programming, statement of complementary slackness theorem.

Statement of Fundamental Theorem of rectangular zero-sum games,

properties of optimal strategies, Relation of dominance, Methods of solving

rectangular Zero-sum games, Equivalence of rectangular games and linear

programming.

Books Recommended:1. G.Hadley, Linear Programming, Addison Wesley, 1980

2. S.I.Gass, Linear Programming, 3rd Edition, McGraw Hill, N.Y. 1969.

3. J.C.C.Mckinsey, Introduction to Theory of Games, McGraw Hill Book. Co..

N.Y., 1952.

4. O.R.Meyerson, Game Theory : Analysis of Conflict, Harvard University

Press, Cambridge Mass, 1991.


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Documents

Bsc Math Syllabus of Physical Sciences