CIVIL ENGINEERING CIVIL & STRUCTURAL …...Department of Mathematics With effect from 2018-2019 Batch Page 2 SEMESTER – I Common to Civil & Civil and Structural Engineering (For

Department of Mathematics

With effect from 2018-2019 Batch Page 1

CIVIL ENGINEERING&

CIVIL & STRUCTURAL ENGINEERING

(For students admitted from 2018-19)



SEMESTER – ICommon to Civil & Civil and Structural Engineering


OBJECTIVES:

The objective of this course is to familiarize the prospective engineers withtechniques in calculus, multivariate analysis and linear algebra. It aims to equip thestudents with standard concepts and tools at an intermediate to advanced level thatwill serve them well towards tackling more advanced level of mathematics.

Unit-I Matrix

Symmetric- Skew-symmetric- Orthogonal matrices - Eigen values and Eigenvectors- Cayley-Hamilton Theorem - Diagonalization of Matrices - Orthogonaltransformation and Quadratic to Canonical forms.

Unit-II Sequence & Series

Convergence of sequence and series - tests for convergence - Comparison test -D’Alembert’s ratio test - Raabe’s test - Cauchy’s root test - Fourier series: Halfrange sine and cosine series - Parseval’s theorem.

Unit-III Multivariable Calculus - Differentiation

Evolutes and Involutes - Partial derivatives - Total derivative - Maxima, Minima andSaddle points - Vector differentiation: Directional Derivatives - Tangent Plane andNormal line - Gradient, Divergence and Curl - Solenoidal - Irrotational.

Unit-IV Multiple Integrals

Multiple Integration - Double and Triple integrals (Cartesian and polar) - Change oforder of integration in double integrals - Applications of definite integrals toevaluate surface areas and volumes of revolutions.

Unit –V Vector Integration

Theorems of Green, Gauss and Stokes (without proof) - Beta and Gamma functionsand their properties

Sub.Code : Mathematics - I( Calculus, Multivariable

Calculus & Linear Algebra )

L T P - 3 1 0 Credits :04



Suggested Books

1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2000.2. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition, Pearson,reprint, 2002.

3. Veerarajan T., Engineering Mathematics for first year, Tata McGraw-Hill, New Delhi,2008.

4. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill New Delhi, 11thReprint, 2010.

5. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2010.

6. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 2006.



SEMESTER - IICommon to Civil & Civil and Structural Engineering


OBJECTIVES:

The objective of this course is to familiarize the prospective engineers withtechniques in ordinary differential equations of higher order, Partial differentialequations, Numerical methods and integration. It aims to equip the students withstandard concepts and tools at an intermediate to advanced level that will serve themwell towards tackling more advanced level of mathematics.

Unit- I Ordinary Differential Equations of Higher OrdersOperator D – Rules for finding complementary function – Rules for findingparticular Integral – Working procedure to solve the equation - Method of variationof parameters - Equations reducible to linear equations with constant coefficients:Cauchy's homogeneous linear equation.

Unit- II Partial Differential Equations – First orderFormation of partial differential equations – Solution of a partial differentialequation – Equations solvable by direct integration – Linear equations of first order– Non linear equations of the first order

Unit- III Partial Differential Equations – Higher orderSolution to homogeneous and non-homogeneous linear partial differential equationssecond and higher order by complementary function and particular integral method.Method of separation of variables – Vibration of a stretched string: Wave equation –Solution of Wave equation - D’Alembert’s solution of wave equation – Onedimensional heat flow – Solution of heat equation.

Unit-IV Numerical MethodsSolution of algebraic and transcendental equations - Bisection method – Method offalse position (Regula-Falsi Method) - Newton-Raphson Iterative method-Numericalintegration: Trapezoidal rule - Simpson’s one-third rule - Simpson’s three-eighthrule.

Sub.Code :BSC104

Mathematics - II(Differential equations,

Numerical Methods)

L T P - 3 1 0 Credits:04



Unit- V Numerical Solution of Ordinary Differential Equations

Interpolation with equal intervals – Newton’s forward interpolation formula –Newton’s backward interpolation formula - Interpolation with unequal intervals:Lagrange’s interpolation formula, Newton’s divided difference formula. Picard’smethod – Taylor series method - Modified Euler’s method – Runge’s method –Runge-Kutta method – Predictor-corrector methods: Milne’s method,

Suggested Books

1. Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers,New Delhi, 2011.

2. P. Kandasamy, K. Thilagavathy, K. Gunavathi, Numerical Methods, S. Chand &Company, 2nd Edition, Reprint 2012.

3. Chandrika Prasad, Advanced Engineering Mathematics, Khanna Book PublishingCo. (P) Ltd., Delhi

4. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill5. Sashtry, Advanced Engineering Mathematics (ISBN:9788120336094), PHI



SEMESTER - III

Common to Civil & Civil and Structural Engineering(For students admitted from 2018-19)

Sub.Code :BSC201

Mathematics - III(Transform & Discrete

Mathematics)

L T P - 3 1 0 Credits-04

OBJECTIVES:

The objective of this course is to familiarize the prospective engineers withtechniques in Laplace Transforms, Z – Transform, Relations and Digraphs, OrderRelations and Structures and Trees. It aims to equip the students with standardconcepts and tools at an intermediate to advanced level that will serve them welltowards tackling more advanced level of mathematics.

Unit- I Laplace Transforms

Transforms of elementary functions : 1, tn, eat, sin at, cos at, sinh at, cosh at-Properties of Laplace transforms: Linearity Property, First shifting property, Changeof scale property – Transforms of derivatives - Transforms of integrals -Multiplication by tn - Division by t - Evaluation of integrals by Laplacetransform - Inverse transforms: Method of partial fractions – Other methods offinding inverse - Convolution theorem (Without proof) - Application to differentialequations.

Unit- II Z – Transform

Standard z-transforms of 1, ,n pa n – Linearity property – Damping rule – Shiftingrules – Multiplication by n - Initial and final value theorems (without proof) –inverse z –transforms – Convolution theorem (without proof) – Convergence of z-transforms – Two sided z-transform – Evaluation of inverse z-transforms: Powerseries method, Partial fraction method, inversion integral method – Application todifference equations



Unit- III Relations and Digraphs

Product sets and partitions – Relations and digraphs – Paths in relations and digraphs –Properties of relations – Equivalence relations – Computer representation of relations anddigraphs – Operations on relations – Transitive closure and Warshall’s algorithm.

Unit - IV Order Relations and Structures

Partially ordered sets – Extremal elements of partial ordered sets – Lattices – Finite Booleanalgebras – Functions of Boolean algebras – Circuit designs.

Unit - V Trees

Trees – Labeled trees – Tree searching – Undirected trees – Minimal spanning trees -Graphs – Euler paths and circuits – Hamiltonian paths and circuits – Transport networks –Matching problems – Coloring problems.

Suggested Books

1. Kolman B., Busby R.C. and Ross S., Discrete Mathematical Structures for ComputerScience, Fifth Edition, Prentice Hall of India, New Delhi, 2006.

2. N. Deo, Graph Theory, Prentice Hall of India, 1974.3. Chandrika Prasasd, Advanced Engineering Mathematics, (ISBN: 9789386173522)

Khanna Book Publishing Co. (P) Ltd., Delhi4. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill5. Sashtry,Advanced Engineering Mathematics (ISBN: 9788120336094), PHI6. S. Chakraborty & B.K. Sarkar, Discrete Mathematics and Its Applications, Oxford.



SEMESTER - IV

Common to Civil & Civil and Structural Engineering(For students admitted from 2018-19)

Sub.Code Mathematics – IV(Probability Theory and

Statistics)


Course Outcomes

The objective of this course is to familiarize the students with statisticaltechniques. It aims to equip the students with standard concepts and tools at anintermediate to advanced level that will serve them well towards tackling variousproblems in the discipline.

Unit - I Basic Probability

Probability spaces, conditional probability, Independent random variables, sums ofindependent random variables, Bayes' Theorem, Discrete and Continuous onedimensional random variables - Expectations, Moments, Variance of a sum,Moment generating function, Tchebyshev's Inequality.

Unit- II Probability Distributions

Discrete Distributions – Binomial, Poisson and Negative Binomial distributions,Continuous Distributions - Normal, Exponential and Gamma distributions.

Unit - III Basic Statistics

Measures of Central tendency: Averages, mean, median, mode, Measures ofdispersion – Range, Mean deviation, Quartile deviation and Standard deviation,Moments, skewness and Kurtosis, Correlation and regression – Rank correlation.

Unit - IV Applied Statistics

Curve fitting by the method of least squares- fitting of straight lines, second degreeparabolas and more general curves. Test of significance: Large sample test for singleproportion, difference of proportions, single mean, difference of means, anddifference of standard deviations.



Unit -V Small Samples

Test for single mean, difference of means and correlation coefficients, test for ratioof variances - Chi-square test for goodness of fit and independence of attributes.

Suggested Books

1. T. Veerarajan, Probability, Statistics and Random Processes, Third edition, TataMcGraw- Hill, New Delhi, 2010.2. S.P. Gupta, Statistical Methods, 31st Edition, Sultan Chand and Sons, NewDelhi, 2002.3. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley &Sons,2006.4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition,2000.5. S. Ross, A First Course in Probability, 6th Edition, Pearson Education India,2002.6. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd

Edition,Wiley,1968.7. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2010.



Computer Science Engineering&

Information Technology




Common to Computer Science Engineering & Information Technology(For students admitted from 2018-19)

SEMESTER – I

Sub.Code Mathematics- I(Calculus and Linear

Algebra)


Objectives:

The objective of this course is to familiarize the prospective engineers withtechniques in calculus , Multi-variable calculus and sequence and series. It aims toequip the students with standard concepts and tools at an intermediate to advancedlevel that will serve them well towards tackling more advanced level ofmathematics.

Unit I: Calculus

Evaluation of definite and improper integrals- Beta and Gamma functions and theirproperties - Applications of definite integrals to evaluate surface areas and volumesof revolutions.

Unit II: Numerical Methods

Solution of polynomial and transcendental equations – Bisection method-Newton-Raphson method-Regula-Falsi Method. Interpolation- Newton’s forward andbackward difference formulae- Interpolation with unequal intervals-Newton’sdivided difference and Lagrange’s formulae-Numerical Differentiation.

Unit III: Sequences and Series

Convergence of sequence and series-tests for convergence- Comparison test-D’Almbert’s ratio test- Raabe’s test-Lagrathamic test- Cauchy’s root test- Fourierseries: Half range sine and cosine series-Parseval’s theorem.



Unit IV: Multivariable Calculus (Differentiation)

Limit-Continuity - Partial derivatives, total derivatives- Directional derivatives-Tangent plane and normal line- Maxima, minima and saddle points-Method ofLagrange multipliers-Gradient-Curl -Divergence.

Unit V: Matrices

Matrices: Rank of a matrix-rank-nullity theorem-System of linear equations-Symmetric matrices-Skew symmetric matrices- Orthogonal matrices; Eigen valuesand Eigenvectors- Cayley-Hamilton theorem-Diagonalization of matrices

Suggested Books

1. B.S. Grewal, “Higher Engineering Mathematics”, Khanna Publishers, 2000.2. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, Pearson, 2002.

3. T. Veerarajan, Engineering Mathematics, McGraw-Hill, New Delhi, 2008.

4. B. V. Ramana, Higher Engineering Mathematics, McGraw Hill, New Delhi, 2010.

5. N.P. Bali and M. Goyal, A text book of Engineering Mathematics, LaxmiPublications,2010..





SEMESTER - II

Sub.Code : Mathematics – IIProbability & Statistics

L T P - 3 1 0 Credits:4

Course OutcomesThe objective of this course is to familiarize the students with statistical

techniques. It aims to equip the students with standard concepts and tools at anintermediate to advanced level that will serve them well towards tackling variousproblems in the discipline.

Unit I: Basic Probability:


Unit II: Probability Distributions:


Unit III: Basic Statistics:


Unit IV: Applied Statistics:




Unit V: Small samples:


Suggested Text Books:

1. T. Veerarajan, Probability, Statistics and Random Processes, Third edition, TataMcGraw-Hill, New Delhi, 2010.2. S.P. Gupta, Statistical Methods, 31st edition, Sultan chand and sons, New Delhi,2002.3.Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley &Sons,2006.4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition,2000.5. S. Ross, A First Course in Probability, 6th Ed., Pearson Education India, 2002.6. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rdEd.,Wiley, 1968.7. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2010.




SEMESTER - III

Sub.Code : Mathematics – IIIDifferential Calculus


Course Outcomes

The objective of this course is to familiarize the prospective engineers withtechniques in multivariate integration, ordinary and partial differential equations. Itaims to equip the students to deal with advanced level of mathematics andapplications that would be essential for their disciplines.

Unit 1: Multivariable Calculus (Integration):

Multiple Integration: Double and Triple integrals (Cartesian), Change of order ofintegration in double integrals, Problems on Green, Gauss and Stokes theorems.

Unit II: Ordinary Differential Equations:

Exact, linear and Bernoulli’s equations-Operator D – Rules for findingcomplementary function – Rules for finding particular integral-Second order lineardifferential equations with variable coefficients - Cauchy-Euler equation.

Unit-III: Series Solution and Special Functions:

Validity of series solution - Series solution when x=0 is an ordinary point -Frobenius method (Series solution when x=0 is a regular singularity) - Bessel'sequation - Recurrence formulae for Jn(x) - Generating function for Jn(x) -Equations reducible to Bessel's equation – Orthogonality of Bessel functions -Legendre’s Equation – Rodrigue’s Formula – Legendre Polynomials – GeneratingFunction for Pn(x)- Recurrence formula for Pn(x)-Orthogonality of LegendrePolynomials



Unit IV: Partial Differential Equations:

First order partial differential equations, solutions of first order linear and non-linearPDEs. Solution to homogenous and non-homogenous linear partial differentialequations second and higher order by complimentary function and particular integralmethod.

Unit V: Applications of Partial Differential Equations:

Method of separation of variables – Vibration of a stretched string: Wave equation –Solution of Wave equation - D’Alembert’s solution of wave equation – Onedimensional heat flow – Solution of heat equation.

Suggested Text Books:1. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley &Sons, 2006.2. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition,2000.3. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2010.4. Ramana B.V., Higher Engineering Mathematics, Tata McGraw Hill




Semester- IV

Course code Discrete Mathematics L T P - 3 1 0 Credits -04

Course Outcomes

For a given logic sentence express it in terms of predicates, quantifiers, andlogical connectives. For a given a problem, derive the solution using deductive logicand prove the solution based on logical inference and classify its algebraic structure.Students can evaluate Boolean functions, simplify expressions using the propertiesof Boolean algebra and develop the given problem as graph networks and solve withtechniques of graph theory.

Unit I: Sets, Relation and Function:

Finite and infinite Sets, Countable and uncountable Sets, Size of a Set, Setoperations, Ordered pairs and Cartesian Products, Relations, Types of Relations,Some operations on relations, Properties of relations, Equivalence classes, Partitionof a set, Matrix representation of a relation, Representaion of relations by graphs,Hasse diagrams for Partial Ordering Relation.Principles of Mathematical Induction: The Well-Ordering Principle, Recursivedefinition, The Division algorithm: Prime Numbers, The Greatest Common Divisor:Euclidean Algorithm.

Unit II: Counting Techniques

Basic counting techniques-Inclusion and Exclusion, Pigeon-hole principle,Permutation and Combination.

Unit III: Propositional Logic

Basic Connectives and Truth Tables, Logical Equivalence: The Laws of Logic,Logical Implication, Rules of Inference, The use of Quantifiers.Proof Techniques: Some Terminology, Proof Methods and Strategies, ForwardProof, Proof by Contradiction, Proof by Contraposition.



Unit IV: Algebraic Structures and Morphism

Algebraic Structures with one Binary Operation, Semi Groups, Monoids, Groups,Congruence Relation and Quotient Structures, Permutation Groups, Substructures,Normal Subgroups, Algebraic Structures with two Binary Operation, Rings, IntegralDomain and Fields. Boolean Algebra and Boolean Ring, Identities of BooleanAlgebra, Duality, Representation of Boolean Function, Disjunctive and ConjunctiveNormal Form.

Unit V: Graphs and Trees:

Graphs and their properties, Degree, Connectivity, Path, Cycle, Sub Graph,Isomorphism, Eulerian and Hamiltonian Walks, Graph Coloring, Coloring maps andPlanar Graphs, Coloring Vertices, Coloring Edges, List Coloring, Perfect Graph,definition properties and Example, rooted trees, trees and sorting, weighted trees andprefix codes, Shortest distances by Prim’s and Kruskal’s algorithm..

Suggested Books:1. Kenneth H. Rosen, Discrete Mathematics and its Applications, Tata McGraw –Hill2. Susanna S. Epp, Discrete Mathematics with Applications,4th edition, WadsworthPublishing Co. Inc.3. C L Liu and D P Mohapatra, Elements of Discrete Mathematics A ComputerOrientedApproach, 3rd Edition by, Tata McGraw – Hill.4. J.P. Tremblay and R. Manohar, Discrete Mathematical Structure and It’sApplication toComputer Science”, TMG Edition, TataMcgraw-Hill5. Norman L. Biggs, Discrete Mathematics, 2nd Edition, Oxford University Press.6.Schaum’s Outlines Series, Seymour Lipschutz, Marc Lipson,7. Veerarajan, Discrete Mathematics, Tata McGraw – Hill.



ECE, EEE, EIE, Mechatronics(For students admitted from 2018-19)



Common to ECE, EEE, EIE, Mechatronics(For students admitted from 2018-19)

SEMESTER – I

Objectives:

The objective of this course is to familiarize the prospective engineers withtechniques in calculus, differential equations and sequence and series. It aims toequip the students with standard concepts and tools at an intermediate to advancedlevel that will serve them well towards tackling more advanced level ofmathematics.

Unit-I Sequences and Series

Convergence of sequence and series -Tests for convergence -Comparison,-Ratio-Cauchy’s Root- Raabe’s test-logarithmic test- Fourier series: Half range sine andcosine series- Parseval’s theorem.

Units-II Differential Equations

Second order linear differential equations with constant coefficients – Cauchy_Euler equation, Legendre equation-Method of variation of parameters- First orderpartial differential equations: Formation of PDE - solutions of first order linearPDEs.

Unit-III Calculus

Evaluation of definite integral-Applications of definite integrals - To evaluatesurface areas and volumes of revolutions; Beta and Gamma functions and theirproperties.

Unit-IV Multivariable Calculus

Multiple Integration- double and triple integrals (Cartesian and polar)- change oforder of integration in double integrals- Change of variables (Cartesian to polar),Applications-areas and volumes by double integration- Center of mass and Gravity(constant and variable densities).

Sub.Code : Mathematics - ICalculus & Differential Equations




Unit-V Numerical Methods

Solution of polynomial and transcendental equations – Bisection method-Newton-Raphson method- Regula-Falsi method- Finite differences-Interpolation usingNewton’s forward and backward difference formulae- Central differenceinterpolation- Gauss’s forward and backward formulae

Suggested Books:1. B.S. Grewal, “Higher Engineering Mathematics”, Khanna Publishers, 2000.2. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, Pearson, 2002.








SEMESTER - II

Sub.Code : Mathematics – IILinear Algebra, Transform Calculus

and Numerical Methods


Objectives

This course aims at familiarising the prospective engineers with techniques in LinearAlgebra, Transform Calculus and Numerical Methods. To understand thefundamental concepts in the above said topics. To develop the ability to evaluatethe problems in transform calculus and its application in varies areas.

Unit I : Matrices

Rank of a matrix, System of linear equations; Symmetric, skew-symmetric andorthogonal matrices; Eigenvalues and eigenvectors; Diagonalization of matrices;Cayley-Hamilton theorem, Orthogonal transformation and quadratic to canonicalforms.


Ordinary differential equations: Taylor’s series, Euler and modified Euler’smethods. Runge-Kutta method of fourth order for solving first order equations.Milne’s predicator corrector methods. Partial differential equations: Finite differencesolution two dimensional Laplace equation and Poisson equation, Implicit andexplicit methods for one dimensional heat equation (Bender-Schmidt and Crank-Nicholson methods), Finite difference explicit method for waveequation

Unit III: Transform Calculus- I

Laplace Transforms : Definition, Properties of Laplace transforms: LinearityProperty, First shifting property, Change of scale property – Transforms ofderivatives - Transforms of integrals - Multiplication by tn - Division by t -Evaluation of integrals by Laplace transform - Inverse transforms: Method of partialfractions – Other methods of finding inverse - Convolution theorem (Without proof)Application to differential equations



Unit IV: Transform Calculus- II

Fourier integral theorem (without proof) - Fourier Sine and Cosine integrals –Complex form of Fourier integral - Fourier transform – Fourier sine and Cosinetransforms – Properties of Fourier Transforms: Linear property, Change of scaleproperty, Shifting property -Parseval’s identity for Fourier transforms (withoutproof) – Application of transforms to boundary value problems: Heat conduction,Vibrations of a string, Transmission lines

Unit V: Transform Calculus- III

Standard z-transforms of 1,an , np – Linearity property – Damping rule – Shiftingrules – Multiplication by n - Initial and final value theorems (without proof) –inverse z –transforms – Convolution theorem (without proof) – Convergence of z-transforms – Two sided z- transform – Evaluation of inverse z-transforms: Powerseries method, Partial fraction method, inversion integral method.

Suggested Books:

1. Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers,New Delhi, 2011.2. Alan Jeffrey, Advanced Engineering Mathematics, Academic Press3. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons4. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-WesleyPublishing Company




SEMESTER - III

Sub.Code : Mathematics – IIIProbability and Statistics


Objectives

The objective of this course is to familiarize the students with statistical andprobability techniques. It aims to equip the students with standard concepts and toolsat an intermediate to advanced level that will serve them well towards tacklingvarious problems in the discipline.





Unit III : Basic Statistics:






Unit V: Small samples:


Suggested Books1. T. Veerarajan, Probability, Statistics and Random Processes, Third edition, TataMcGraw-Hill, New Delhi, 2010.2. S.P. Gupta, Statistical Methods, 31st edition, Sultan chand and sons, New Delhi,2002.3. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley &

Sons,2006.4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition,2000.5. S. Ross, A First Course in Probability, 6th Ed., Pearson Education India, 2002.6. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rdEd.,Wiley, 1968.7. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2010.



Electronics and Communication Engineering(For the students admitted from 2018-19)

SEMESTER - IV

Sub.Code : Mathematics – IVCalculus, Special Functions

and Statistics


This course focuses on the topics in Calculus, Ordinary Differential Equations ofhigher order and Designs of Experiment. The fundamentals and the way to solveOrdinary differential equation problems are introduced. Understanding the basicconcepts and their properties are important for the development of the present andfurther courses.

Unit I: Calculus

Homogeneous Functions-Total derivative-Change of variables-Jacobian-Taylor’stheorem for function of two variables-Maxima and Minima of functions of twovariables-Lagranges method of undermined multipliers

Unit II: Multi Variable Calculus

Directional derivatives-Gradient-curl and divergence-Problems on Green-Gauss andStokes theorems- orthogonal curvilinear coordinates-Simple applications involvingcubes, sphere and rectangular parallelepipeds.

Unit III: Special Functions –I

Validity of series solution - Series solution when x=0 is an ordinary point -Frobenius method (Series solution when x=0 is a regular singularity) - Bessel'sequation (Bessel’s functions of the first and second kind) - Recurrence formulae forJn(x) - Expansions for J0 and J1: Value of J1/2 - Generating function for Jn(x) -Equations reducible to Bessel's equation – Orthogonality of Bessel functions

Unit IV: Special Functions-II

Legendre’s Equation – Rodrigue’s Formula – Legendre Polynomials – GeneratingFunction for Pn(x)- Recurrence formula for Pn(x)-Orthogonality of LegendrePolynomials – Hermite Polynomials-Recurrence formulae-Rodrigue’s formula-Orthogonality of Hermite polynomials



Unit V: Design of Experiment

Design of experiments – Completely randomized design: Analysis of variance forone factor of classification – Randomized block design: Analysis of variance for twofactors of classification – Latin square design.

Suggested Books:

1. Grewal B.S, Higher Engineering Mathematics, 41st Edition, Khanna Publishers,New Delhi, 2011.2. Gupta S.P, Statistical Methods, 28th Edition, Sultan Chand and Sons., New Delhi,1997.3. Alan Jeffrey, Advanced Engineering Mathematics, Academic Press4. Erwin Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons5. Gerald C.F and Wheatley P.O, Applied Numerical Analysis, Addison-WesleyPublishing Company



MECHANICAL ENGINEERING




MECHANICAL ENGINEERING(For the students admitted from 2018-19)

SEMESTER – I

Objectives:

The objective of this course is to familiarize the prospective engineers withtechniques in calculus , Multi-variable calculus and sequence and series. It aims toequip the students with standard concepts and tools at an intermediate to advancedlevel that will serve them well towards tackling more advanced level ofmathematics.

Unit I: Calculus

Evaluation of definite and improper integrals- Beta and Gamma functions and theirproperties - Applications of definite integrals to evaluate surface areas and volumesof revolutions.


Solution of polynomial and transcendental equations – Bisection method-Newton-Raphson method-Regula-Falsi Method. Interpolation- Newton’s forward andbackward difference formulae- Interpolation with unequal intervals-Newton’sdivided difference and Lagrange’s formulae-Numerical Differentiation.

Unit III: Sequences and Series

Convergence of sequence and series-tests for convergence- Comparison test-D’Almbert’s ratio test- Raabe’s test-Lagrathamic test- Cauchy’s root test- Fourierseries: Half range sine and cosine series-Parseval’s theorem.

Unit IV: Multivariable Calculus (Differentiation)

Limit-Continuity - Partial derivatives, total derivatives- Directional derivatives-Tangent plane and normal line- Maxima, minima and saddle points-Method ofLagrange multipliers-Gradient-Curl -Divergence.

Sub.Code : Mathematics - ICalculus & Linear Algebra




Unit V: Matrices

Matrices: Rank of a matrix-rank-nullity theorem-System of linear equations-Symmetric matrices-Skew symmetric matrices- Orthogonal matrices; Eigen valuesand Eigenvectors- Cayley-Hamilton theorem-Diagonalization of matrices

Suggested Books1. B.S. Grewal, “Higher Engineering Mathematics”, Khanna Publishers, 2000.2. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, Pearson, 2002.







SEMESTER - II

Mechanical EngineeringFor the students admitted from 2018-19

Sub.Code : Mathematics – IICalculus, Ordinary Differential

Equations, and ComplexVariables


Course OutcomesThe objective of this course is to familiarize the prospective engineers with

techniques in multivariate integration, ordinary and partial differential equations andcomplex variables. It aims to equip the students to deal with advanced level ofmathematics and applications that would be essential for their disciplines.

Unit I: Multivariable Calculus (Integration):

Multiple Integration: Double and Triple integrals (Cartesian) - Change of order ofintegration in double integrals - Problems on Green, Gauss and Stokes theorems.

Unit II: Ordinary Differential Equations of Higher Orders:

Operator D – Rules for finding complementary function – Rules for findingparticular integral - Second order linear differential equations with variablecoefficients: Cauchy-Euler equation - Method of variation of parameters.

Unit III: Partial Differential Equations of Higher Orders:

Definition of Partial Differential Equations- Formation of Partial differentialequations, solutions of a Partial differential equation -Linear equations of the firstorder - Solution to homogenous and non-homogenous linear partial differentialequations of second order by complementary function and particular integralmethod.

Unit IV: Complex Variable – Differentiation:

Differentiation - Cauchy-Riemann equations - Analytic functions - Harmonicfunctions, Finding Harmonic conjugate - Conformal mappings: z+c, 1/z, cz, z2,z+1/z, ez - Mobius transformations and their properties.



Unit V: Complex Variable – Integration:

Contour integrals: Cauchy-Goursat theorem (without proof) - Cauchy Integralformula (without proof) - Taylor’s series - Laurent’s series - Zeros of analyticfunctions –singularities – Residues - Cauchy Residue theorem (without proof) –Simple problems.

Suggested Books1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 36th Edition,20102. Erwin kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley &Sons,2006.3. G.B. Thomas and R.L. Finney, Calculus and Analytic geometry, 9th Edition,Pearson,Reprint, 2002.4. W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and

Boundary Value Problems, 9th Edition, Wiley India, 2009.5. S. L. Ross, Differential Equations, 3rd Ed., Wiley India, 1984.6. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2008.



SEMESTER - IIIMechanical Engineering

For the students admitted from 2018-19

Sub.Code : Mathematics – IIIProbability & Statistics


Course Outcomes

The objective of this course is to familiarize the students with statisticaltechniques. It aims to equip the students with standard concepts and tools at anintermediate to advanced level that will serve them well towards tackling variousproblems in the discipline.





Unit III: Basic Statistics:



Test of significance: Large sample test for single proportion, difference ofproportions, single mean, difference of means, and difference of standarddeviations- Test for single mean, difference of means and correlation coefficients,test for ratio of variances - Chi-square test for goodness of fit and independence ofattributes.



Unit V: Applications Partial Differential Equations

Method of separation of variables – Vibration of a stretched string: Wave equation –Solution of Wave equation - D’Alembert’s solution of wave equation – Onedimensional heat flow – Solution of heat equation.

Suggested Books:1. T. Veerarajan, Probability, Statistics and Random Processes, Third edition, TataMcGraw-Hill, New Delhi, 2010.2. S.P. Gupta, Statistical Methods, 31st edition, Sultan chand and sons, New Delhi,2002.3. Erwin Kreyszig, Advanced Engineering Mathematics, 9th Edition, John Wiley &Sons,2006.4. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition,2000.5. S. Ross, A First Course in Probability, 6th Ed., Pearson Education India, 2002.6. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rdEd.,Wiley, 1968.7. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, LaxmiPublications, Reprint, 2010.

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CIVIL ENGINEERING CIVIL & STRUCTURAL …...Department of Mathematics With effect from 2018-2019 Batch Page 2 SEMESTER – I Common to Civil & Civil and Structural Engineering (For