CURRICULUM & DETAILED SYLLABI of MATHEMATICS · 2021. 3. 30. · 5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005. QUESTION PAPER PATTERN: The Semester

1

Dr. AMBEDKAR INSTITUTE OF TECHNOLOGY

(An Autonomous Institution, Aided by Govt. of Karnataka and

Affiliated to Visvesvaraya Technological University, Belgaum) Mallathalli, Outer Ring Road, Bengaluru–560 056

CURRICULUM & DETAILED SYLLABI

of MATHEMATICS

for

I TO IV Semesters, Bridge course for III & IV Semesters (Lateral Entry) &

Open Electives

(FOR THE STUDENTS ADMITTED DURING THE ACADEMIC YEAR 2020-2021)

2

For FIRST Semester B E (Common to all branches)

SUBJECT TITLE: CALCULUS & LINEAR ALGEBRA Subject Code

: 18MA11

Number of Credits: 4 = 3 : 1 : 0

(L–T– P)

No of lecture hours per

week: 05 (L=3+T=2)

Exam Duration

: 3 Hrs

Exam Marks: CIE + Assignment +

SEE = 40 + 10 + 50 = 100

Total No. of lecture hours:

65 (L=41+T=24)

Course objective: This course is intended to impart to the students the skills of employing the basic

tools of differential, integral and vector calculus and linear algebra for solving basic and difficult

engineering problems. Unit

No.

Syllabus content No. of hours

Theory Tutorial

1 Differential Calculus: Radius of curvature–in Cartesian, parametric and

polar forms (without proof). Taylor’s and Maclaurin’s series expansions

(without proof) for functions of single variable. Partial Differentiation:

Definition. Total derivatives, differentiation of composite functions.

Jacobian-problems. Applications-Maxima and minima of functions of two

variables, Lagrange’s method of undetermined multipliers with one

subsidiary condition.

10 06

2 Integral Calculus: Multiple Integrals: Double integrals, evaluation by

change of order of integration and by changing to polar co-ordinates.

Applications to find area and volume. Triple integrals-simple applications

involving cubes, sphere and rectangular parallelopiped. Beta and Gamma

functions: Definition, relation between them –simple problems.

10 06

3 Vector Calculus: Scalar and vector point functions, Gradient of a scalar

field, directional derivative, divergence and curl of a vector field. Vector

identities (without proof). Vector integration-Green’s theorem in the

plane, Stoke’s and Gauss Divergence theorem (without proof).

Applications: work done by force and flux.

11 06

4 Linear Algebra: Rank of a matrix, determination of rank by elementary

transformation (Echelon and normal forms). Consistency of a system of

linear homogeneous and non-homogeneous equations. Gauss elimination

and Gauss–Jordan methods. Eigenvalues and eigenvectors, properties (no

proof), Diagonalization of matrices – of order two.

10 06

Course Outcomes: After the successful completion of the course, the students are expected to:

CO1: apply the basic concepts of calculus like differentiation and integration for problem solving.

CO2: use the idea of gradient, divergence and curl involved in vector fields to analyze and solve problems

arising in engineering fields.

CO3: identify the practical importance of Maxima and minima of functions of two variables.

CO4: apply the concepts in problem solving and relate the solutions to practical situations in various

engineering streams.

CO5: assess the concepts of linear algebra and their applications in various fields of engineering.

3

Course Outcomes (CO) Mapping with Programme Outcomes (PO)

CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:

1. B.S. Grewal, Higher Engineering Mathematics (44th Edition), Khanna Publishers, New Delhi.

2. B.V. Ramana, Higher Engineering Mathematics, Tata McGraw Hill publications, New Delhi, 11th

Reprint, 2010

REFERENCE BOOKS.

1. Erwin Kreyszig, Advanced Engineering Mathematics (Latest Edition), Wiley Publishers, New Delhi.

2. H. C. Taneja, Advanced Engineering Mathematics, Volume I & II, I.K. International Publishing

House Pvt. Ltd., New Delhi.

3. N.P. Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications, Reprint,

2010.

4. V. Krishnamurthy, V.P. Mainra and J.L. Arora, An introduction to Linear Algebra, Affiliated East–

West press, Reprint 2005.

5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.

QUESTION PAPER PATTERN:

The Semester End Examination (SEE) is for 100 marks.

1. There shall be five full questions carrying 20 marks each and all are compulsory

2. Question No.1 shall consist of 20 MCQ carrying 1 mark each. These 20 questions shall be set from

the entire syllabus with 5 questions from each unit.

3. The remaining FOUR Questions shall be descriptive in nature and there shall be two questions from

each unit.

4. There shall be internal choice in Unit 1-4.

4

For Second Semester BE (Common to all branches)

Course Outcomes: After the successful completion of the course, the students are expected to:

CO1: analyze the basic concepts of differential equations and solve through standard methods.

CO2: use the concepts of partial differential equations to solve practical problems arising in a variety of


CO3: identify the practical importance of solutions of Fourier series and their utility.

CO4: apply logical thinking to problem-solving and identify an appropriate mathematical tool for solving

various engineering problems.

CO5: utilize the knowledge of complex variables for constructing physical models connected to diverse

engineering Phenomena.

SUBJECT TITLE: DIFFERENTIAL EQUATIONS & COMPLEX VARIABLES

Subject Code:

18MA21

Number of Credits: 4 = 3 : 1 : 0

(L–T– P)


week: 05 (L=3+T=2)

Exam

Duration:3 Hrs

Exam Marks: CIE + Assignment +

SEE = 40 + 10 + 50 = 100

Total No. of lecture hours:

65 (L=41+T=24)

Course objective: The purpose of the course is to help the students to understand and apply the

concepts of ODE’S, PDE’s, infinite series and complex variables to solve tough engineering problems.

Unit

No.


Theory Tutorial

1 Differential Equations: Exact and reducible to exact differential equations.

Nonlinear differential equations- Clairaut’s equations and Bernouli’s

equations. Applications-orthogonal trajectories.

Linear differential equations of higher order with constant coefficients-

inverse differential operator, Cauchy’s and Legendre’s DE’s.

10 06

2 Partial Differential Equations: Formation of Partial differential equations

(PDE) by eliminating arbitrary constants and arbitrary functions. Solution

of PDE by direct integration. Lagrange’s PDE. Solution of first and second

order PDE by the method of separation of variables (two variables).

Applications: solutions of one-dimensional heat and wave equations by the

method of separation of variables.

10 06

3

Fourier Series: Introduction. Dirichlet’s conditions. Fourier series of

periodic function with period 2 and arbitrary period. Half range Fourier

series. Applications to practical harmonic analysis.

10 06

4 Complex Variables: Analytic Function-Definition. Cauchy Riemann

equations in Cartesian and polar coordinates (no proof). Construction of

analytic functions, Harmonic conjugate. Cauchy’s theorem and Cauchy’s

integral formula-problems. Discussion of transformations- 2w z , zw e

and 1/w z z ( 0.z )

11 06

5


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:



Reprint, 2010

REFERENCE BOOKS.





2010.

4. G.F. Simmons and S.G. Krantz, Differential Equations, Tata McGraw Hill, 2007.

5. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th Ed., Tata McGraw Hill

publications, New Delhi, 2004.



1. There shall be five full questions carrying 20 marks each and all are compulsory

2. Question No.1 shall consist of 20 MCQ carrying 1 mark each. These 20 questions shall be set from

the entire syllabus with 5 questions from each unit.

3. The remaining FOUR Questions shall be descriptive in nature and there shall be two questions from

each unit.

4. There shall be internal choice in Unit 1-4.

6

For THIRD Semester B E (CV ONLY) SUBJECT TITLE: TRANSFORM CALCULUS & SPECIAL FUNCTIONS

Subject Code

:18MA31CV

Number of Credits: 3

= 2 : 1 : 0 (L–T– P)

No of lecture hours per week: 04

(L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100

Total No. of Lecture hours: 52

Course objective: This course is proposed to impart to the students the skills to identify and

solve the problems in their field of study involving the application of transform calculus and

special functions.

Unit

No.


Theory Tutorial

1 Laplace Transforms: Definition. Transforms of some standard

functions. Basic properties, transform of derivatives and integrals

(no proofs). Periodic function and unit impulse functions-problems.

Inverse Laplace Transforms-Properties (no proofs). Inverse

transforms by using partial fractions and convolution theorem.

Unit step functions-problems.

06 05

2 Fourier Transforms: Infinite Fourier transforms. Fourier sine and

cosine transforms. Inverse Fourier transforms (no properties)-

simple functions.

Initial & Boundary Value Problems: Solving ODEs by using

Laplace transforms. Fourier transform of derivatives (no proof).

Application of Fourier transforms to boundary value problems.

06 05

3 Statistical techniques: Curve fitting by method of least squares:

y=ax+b, y=ax2+bx+c and y=abx. Correlation–Karl Pearson’s

coefficient of correlation, Regression analysis –lines of regression

(without proof)- problems.

05 05

4 Chebyshev Polynomials- Definition. Derivation of Chebyshev

polynomials Tn(x). Orthogonality property. Some theorems on

Chebyshev polynomials. Recurrence relations. Generating

functions-problems.

05 05

5 Legendre’s Polynomials: Series solution of Legendre’s

differential equation of first kind. Derivation of Legendre

polynomials Pn(x), Generating functions. Orthogonality property.

Recurrence relations. Rodrigue’s formula (without proof) -

problems.

05 05

7

Course Outcomes:

After the successful completion of the course, the students are expected to:

CO1: apply the concepts of integral transforms, polynomials and curve fitting for problem solving.

CO2: use the Laplace transforms and Fourier transforms tools for solving problems involving mass and

convective heat transfer.

CO3: express an engineering problem in terms of Legendre’s and Chebyshev polynomials.

CO4: describe the applications of polynomials for solving certain specific fundamental problems of civil

engineering.

CO5: apply a variety of statistical techniques to solve problems of engineering in fields like, industry

standard statistical software & air and ground water pollution.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:

1. B.S. Grewal, Higher Engineering Mathematics (43rd Edition, 2015), Khanna Publishers, New Delhi.

2. Erwin Kreyszig, Advanced Engineering Mathematics (10th Edition, 2016), Wiley Publishers, New Delhi.

REFERENCE BOOKS/Web sources:

1. B.V. Ramana, Higher Engineering Mathematics, Tata McGraw Hill publications, New Delhi.

2. H. C. Taneja, Advanced Engineering Mathematics, Volume I & II, I.K. International Publishing House

Pvt. Ltd., New Delhi.

3. Dennis G, Zill Michael R, Gullen, Advanced Engineering Mathematics (2nEdition), CBS Publishers &

Distributors, New Delhi-110 002 (India)

4. Andrei D. Polyanin and Alexender V. Manzhirov, Chapman & Hall/CRC, Taylor & Francis Group, New

York.



1. There shall be five full questions (one question for each unit) carrying 20 marks each and all are

Compulsory.

2. There shall be internal choice in all the Units.

8

For FOURTH Semester B E (CV ONLY) SUBJECT TITLE: NUMERICAL METHODS & PROBABILITY

DISTRIBUTIONS

Subject Code

:18MA41CV


= 2 : 1 : 0 (L–T– P)


(L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100



solve problems in their field of study involving the application of numerical and probability

distribution techniques.

Unit

No.


Theory Tutorial

1 Solution of linear equations & eigenvalue problems: Solution of

linear system of equations- iterative methods of Gauss Jacobi,

Gauss Seidel and relaxation methods. Eigen values of a matrix by

power method and inverse power method. Ill-conditioned linear

systems.

06 05

2 Solutions of non-linear equations: Regula-Falsi method and

Newton-Raphson method. Interpolation using Newton’s forward

and backward difference formulae. Interpolation with unequal

intervals- Newton’s divided difference and Lagrange’s formulae.

05 05

3 Numerical differentiation, integration and solutions of ODE’S:

Numerical differentiation using Newton’s forward and backward

difference formulae. Numerical Integration-Simpson’s 1/3rd, 3/8th

rules and Weddle’s rule. Solutions of first order ODE’s-Euler’s

modified method, Runge-Kutta fourth order method.

06 05

4 Calculus of variations: Variation of a function and a functional,

Euler’s equation-standard variational problems and the

Brachistochrone problem. Isoperimetric problems. Rayleigh Ritz

method -problems.

05 05

5 Probability distributions: Recap of Random Variables. Discrete

probability distributions- Binomial, Poisson and Geometric

distributions; Continuous probability distributions-Exponential and

Normal distributions.

05 05

9

Course Outcomes:


CO1: analyze the basic concepts of numerical methods, calculus of variations and probability distributions.

CO2: apply appropriate numerical technique to solve civil engineering problems.

CO3: apply the concepts of calculus of variations to understand and solve problems relating to materials

science and structural engineering.

CO4: apply the least squares method of curve fitting to a set of experimental data points connected to civil

engineering problems.

CO5: comprehend the utility of the variety of probability distribution functions in diverse areas of civil

engineering fields like structural, construction planning, air and ground water pollution.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:

1. B.S. Grewal, Higher Engineering Mathematics (43rd Edition, 2015), Khanna Publishers, New Delhi.








4. Andrei D. Polyanin and Alexender V. Manzhirov, Chapman & Hall/CRC, Taylor & Francis Group, New

York.




Compulsory.


10

For THIRD Semester B E (ME/IM ONLY) SUBJECT TITLE: TRANSFORMS & BOUNDARY VALUE PROBLEMS

Subject Code

:18MA31ME/IM


= 2 : 1 : 0 (L–T– P)


(L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100



solve problems in their field of study involving the application of transforms and boundary value

conditions.

Unit

No.


Theory Tutorial

1 Laplace Transforms : Definition. Transforms of some standard

functions. Basic properties, transforms of derivatives and integrals

(no proofs). Periodic function and unit impulse functions-problems.

Inverse Laplace Transforms-Properties (no proofs). Inverse

transforms by using partial fractions and convolution theorem. Unit

step functions-problems.

06 05

2

Fourier Transforms: Infinite Fourier transforms. Fourier sine and

cosine transforms. Inverse Fourier transforms (no properties)-

simple functions.

Initial & Boundary Value Problems: Solving ODEs by using


Application of Fourier transforms to boundary value problems.

06 05

3 Statistical Techniques: Curve fitting by method of least squares:

y=ax+b, y=ax2+bx+c and y=abx. Correlation–Karl Pearson’s

coefficient of correlation, Regression analysis –lines of regression

(without proof)- problems.

05 05

4 Fourier Series Solution: Classification of second order PDE’s-

problems. One dimensional heat equation-ends of the bar are kept

at zero temperature and insulated. Insulated at one end-problems.

Special functions: Series solution of Bessel’s and Legendre’s

differential equation of first kind.

05 05

5 Bessel’s and Legendre’s Solution: Solution of two dimensional

Laplace equation. The Laplacian in plane polar, cylindrical and

spherical coordinates, solutions with Bessel functions and Legendre

functions. D'Alembert's solution of the wave equation.

05 05

11

Course Outcomes:


CO1 analyze the basic concepts of integral transforms, statistical techniques and boundary value problems.

CO2: apply appropriate statistical technique to solve problems connected to mechanical and industrial

engineering.

CO3: apply the least squares method of curve fitting to a set of experimental data points connected to solid

and fluid mechanical problems.

CO4: use Bessel’s and Legendre’s functions in partial differential equations and obtain series solution of

ordinary differential equations.

CO5: solve boundary value problems involving heat conduction and diffusion using Laplace equations.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:



Reprint, 2010.



REFERENCE BOOKS:




3. R. Haberman, Elementary Applied Partial Differential equations with Fourier Series and Boundary Value

Problem, 4th Ed., Prentice Hall, 1998.

4. Manish Goyal and N.P. Bali, Transforms and Partial Differential Equations, University Science Press,

Second Edition, 2010.




Compulsory.


12

For FOURTH Semester B E (ME/IM ONLY) SUBJECT TITLE: NUMERICAL METHODS & APPLIED STATISTICS

Subject Code

:18MA41ME/IM


= 2 : 1 : 0 (L–T– P)


(L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100



solve problems in their field of study involving the application of numerical methods and

principles of variational calculus.

Unit

No.


Theory Tutorial





05 05

2 Numerical Differentiation, Integration and Solutions of ODE’S:





06 05

3 Numerical Solutions of Partial Differential Equations: Solutions

of Laplace and Poisson equations-Jacobi’s method, Gauss-Seidel

method and Relaxation method. One dimensional heat equation-

Bender-Schmitt method and Crank-Nicholson method. Wave

equation-Finite difference method.

06 05

4 Tests of Hypothesis: Review of random variables. Normal

distributions. Introduction to sampling distributions, standard error,

Type-I and Type-II errors. Large sample test based on normal

distribution for single mean and difference of means. Small

samples tests based on t, F and 2 - distributions.

05 05

5 Calculus of Variations: Variation of a function and a functional,

Euler’s equation-standard variational problems and the

Brachistochrone problem. Isoperimetric problems. Rayleigh Ritz

method -problems.

05 05

13

Course Outcomes:


CO1: analyze the basic concepts of calculus of variations, numerical and statistical methods.

CO2: construct finite element models using calculus of variations for problems connected to

solid and fluid mechanics.

CO3: apply numerical methods to identify and solve problems related to fluid mechanics, gas

dynamics, heat and mass transfer, thermodynamics, vibrations, automatic control systems,

kinematics, design etc.

CO4: understand the basics of hypothesis testing.

CO5: implement a variety of statistical techniques to solve problems of engineering connected to

industrial production, quality management and design of experiment.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:



REFERENCE BOOKS:

1. S.S. Sastry, Introductory methods of numerical analysis, PHI, 4th Edition, 2005.


2010.


4. M. K. Venkataraman, Higher Engineering Mathematics for Engineering & Science, -National publishing

co., Chennai. .

5. Veerarajan T., Engineering Mathematics (for semester III), Tata McGraw-Hill, New Delhi, 2010.

QUESTION PAPER PATTERN: The Semester End Examination (SEE) is for 100 marks.

1. There shall be five full questions (one question for each unit) carrying 20 marks each and all

are Compulsory.


14

For THIRD Semester B E (EC/EE/EI/TE/ML ONLY) SUBJECT TITLE : TRANSFORMS & APPLICATIONS

Subject Code :

18MA31EC/EE/EI/

TE/ML

Number of Credits:

3 = 2 : 1 : 0 (L–T– P)


(L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100


Course objective: This course is proposed to impart analytical skill in solving mathematical

problems as applied to the respective branches of Engineering.

Unit

No.


Theory Tutorial

1 Laplace Transforms: Definition. Transforms of some standard

functions. Basic properties, transforms of derivatives and integrals

(no proofs). Periodic function. Transforms of unit step and impulse

functions-problems. Inverse Laplace Transforms-Properties (no

proofs). Inverse transforms by using partial fractions and

convolution theorem. Unit step function-problems.

06 05

2

Fourier Transforms: Infinite Fourier transforms. Properties-

linearity, scaling, shifting and modulation (no proof). Convolution

theorem and Parseval’s identity (no proof)-problems. Relation

between Fourier and Laplace transform. Fourier sine and cosine

transforms-Transforms of simple functions.

06 05

3 Initial & Boundary Value problems. Solutions of ODEs using


Application of Fourier transforms to boundary value problems-one

dimensional heat conduction and wave equations.

05 05

4 Z-Transforms: Definition. Z-transforms of basic sequences and

standard discrete functions. Properties-linearity, scaling, first and

second shifting, multiplication by n, initial and final value theorem

-problems. Inverse Z-transforms by partial fractions method-

problems.

05 05

5 Difference Equations: Definition. Formation of Difference

equations. Linear & simultaneous linear difference equations with

constant coefficients-problems. Solutions of difference equations

using Z-transforms.

05 05

15

Course Outcomes:


CO1: understand and analyze the basic concepts of integral transforms, Z-transforms and difference

equations.

CO2: apply integral transforms, Z-transforms and difference equations for solving problems connected to

continuous and discrete-time signal processing.

CO3: analyze electrical circuits and stability of communication systems.

CO4: apply difference equations to solve problems of stability of dynamical electrical systems.

CO5: analyze heat dissipation issues of electrical circuits using boundary value conditions.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:



Reprint, 2010.



REFERENCE BOOKS:




3. R. Haberman, Elementary Applied Partial Differential equations with Fourier Series and Boundary Value

Problem, 4th Ed., Prentice Hall, 1998.

4. Manish Goyal and N.P. Bali, Transforms and Partial Differential Equations, University Science Press,

Second Edition, 2010.



Compulsory.


16

For FOURTH Semester B E (EC/EE/EI/TE/ML ONLY) SUBJECT TITLE: PROBABILITY, NUMERICAL & OPTIMIZATION

TECHNIQUES

Subject Code :

18MA41EC/EE/EI/

TE/ML


= 2 : 1 : 0 (L–T– P)


(L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100




Unit

No.


Theory Tutorial





06 05

2 Numerical Differentiation, Integration and Solutions of ODE’S:





06 05

3 Probability Distributions: Review of random variables. Discrete

and continuous random variables-problems. Binomial, Poisson,

Geometric, Exponential, Normal and Gamma Distributions.

05 05

4 Joint Probability Distributions and Markov Chains:

Introduction, Joint probability and Joint distribution of discrete

random variables, Markov chains, Classification of Stochastic

processes, Probability vector, Stochastic matrix, Regular stochastic

matrix, Transition probabilities and Transition probability matrix.

05 05

5 Optimization: Linear programming, Mathematical formulation of

linear programming problem (LPP), Types of solutions, Graphical

method, basic feasible solution, canonical and standard forms and

simplex method.

05 05

17

Course Outcomes:


CO1: understand and analyze the basic concepts of numerical methods, probability distribution

functions and optimization techniques.

CO2: apply the various types of numerical techniques and solve the engineering problems.

CO3: apply the various optimization techniques to solve problems of engineering and

technology.

CO4: identify and solve problems involving random variables, probability distributions and

Markov chains connected to digital signal processing, information code theory and structural

engineering.

CO5: acquire the ability to translate the discrete time Markov chain in terms of a transition

matrix and a transition probability to other.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:



Reprint, 2010.


1. Kreyszig, Advanced Engineering Mathematics (10th Edition, 2016), Wiley Publishers, New Delhi.

2. S.S. Sastry, Introductory methods of numerical analysis, PHI, 4th Edition, 2005.


2010

4. Rao S.S., “Optimization Theory and Applications”, Wiley Eastern Limited, New Delhi, 1984H. C.

5. T. Veerarajan, Probability, Statistics and Random Processes, McGraw Hill Education Private Limited,

2008.


1. There shall be five full questions (one question for each unit) carrying 20 marks each and all

are Compulsory.


https://www.goodreads.com/author/show/4076303.T_Veerarajan

18

For THIRD Semester B E (For CS/IS branch only)

SUBJECT TITLE: DISCRETE MATHEMATAL STRUCTURES

Subject Code:

18MA31CS/IS Number of Credits: 3 = 2 : 1 : 0 (L : T : P)


week: 04 (L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE + Assignment +Group

Activity+ SEE = 40+ 05+05 + 50 = 100

Total No. of lecture

hours: 52

Course objectives: This course is proposed to enhance the student’s ability to think logically,

mathematically and algorithmically and use the concepts of discrete mathematical structures to

solve problems connected to computer and information science & engineering.

Unit No. Syllabus Content No. of hours

Theory Tutorial

1 Fundamentals of Logic: Propositions-Logical Connectives, Tautologies,

Contradictions. Logic Equivalence–Laws of Logic, Duality, Inverse,

Converse and Contrapositive, Application to Switching Networks. Logical

Implication – Rules of Inference. Quantifiers-Types, Use of Quantifiers.

05 05

2 Set Theory: Sets and Subsets, Set Operation, Laws of Set Theory, Addition

Principle, A First Word of Probability.

Principle of Counting: Sum Rule, Product rule, Permutation, Combination,

Combination with Repetition.

05 05

3 Properties of Integers: Mathematical Induction-The Well Ordering

Principle, Induction Principle, Method of Mathematical Induction,

Recursive Function.

Principle of Inclusion & Exclusion: Concepts, Generalization,

Derangement-Nothing in its Right Place, Rock Polynomial-N*N Board,

Expansion Rule and Product Rule.

06 05

4 Graphs and Planar Graphs: Basic Technologies, Theorems, Isomorphism,

Planar Graph, Euler’s Formula, Elementary Reduction, Graph Coloring,

Chromatic Polynomial and Hamilton Decomposition Theorem. 05 05

5 Trees and Cut-sets: Trees, Properties, Rooted Tree, Optimal Tree, Prefix

Code, Huffman’s Procedure, Spanning Tree, Minimal Spanning Tree,

Prim’s Algorithm and Kruskal’s Algorithm, DijKstra’s Algorithm, Cut Set,

Network Flow-Max Flow-Min Cut Theorem.

06 05

CO1: Demonstrate the knowledge of fundamental concepts in discrete mathematics and graph theory.

CO2: Apply the concepts of logics, mathematical induction and set theory to solve the problems in

computer science domain.

CO3: Analyze given problem and find solution by applying appropriate counting technologies and inclusion

– exclusion principle.

CO4: Analyze given problem and solve by applying different graph algorithms and concepts of trees, cut

set.

CO5: Develop a variety of algorithms using appropriate technology/programming languages.

19


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO2

CO5: PO1, PO2,PO4

Text Books :

1. Ralph P. Grimaldi: Discrete and Combinatorial Mathematics, 5th Edition, Pearson Education, 2004.

2. J. P. Tremblay and R. Manohar, Discrete Mathematical Structures with Applications to Computer

Science”,Tata McGraw-Hill.

Reference Books:

1. C L Lium& D P Mohapatra, Elements of Discrete Mathematics, A Computer Oriented Approach, The

McGraw-Hill Companies.

2. Kenneth H. Rosen: Discrete Mathematics and its Applications, 6th Edition, McGraw Hill, 2007.

3. D S Chandrasekharaiah, Discrete Mathematics Structures, Prism book PVT LTD.




Compulsory.


20

For FOURTH Semester B E (For CS/IS branch only)

SUBJECT TITLE: PROBABILITY, STATISTICS & QUEUEING THEORY

Subject Code:

18MA41CS/IS Number of Credits: 3 = 2 : 1 : 0 (L : T : P)


week: 04 (L=2+T=2)

Exam Duration:

3 Hrs

Exam Marks: CIE + Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100

Total No. of lecture

hours: 52

Course objectives: This course is proposed to impart to the students the skills to identify and solve real life

problems in their field of study involving the application of the concepts of statistical methods & queuing

theory.

Unit No. Syllabus Content No. of hours

Theory Tutorial

1 Probability Distributions: Recap of Random Variables. Moments

moment generating function, expectations. Discrete probability

distributions-Binomial, Poisson and Geometric distributions; Continuous

probability distributions-Exponential, Normal, Gamma and Weibull

distributions.

05 05

2 Two dimensional Random variables: Joint probability mass function,

Marginal probability function, conditional probability function, Joint

density function, marginal density function, conditional probability

density function, covariance, correlation coefficient.

05 05

3 Statistical Techniques: Curve fitting by method of least squares: y =

ax+b, y = ax2+bx+c and y= abx, Correlation–Karl Pearson’s coefficient of

correlation, Regression analysis –lines of regression (without proof)-

problems.

05 05

4 Random Process: Classification of random process, description of

random process, stationary random process – first order, second order and

Strict-sense stationary processes, Autocorrelation and Cross-correlation

functions, Ergodic process.

06 05

5 Queuing Theory: Basic characteristics of Queuing models- Transient and

steady states, Kendall’s notation of a Queuing system, Steady state

probabilities for Poisson Queue systems, Markov process, Poisson

process, birth and death process, Queuing models: Model I-

M/M/1:( /FIFO) and Model II- M/M/1:(N/FIFO).

06 05

21

Course Outcomes: After the successful completion of the course the students are expected to:

CO1: Understand of basic rules of random variables and moments of random variables.

CO2: Create probability functions of transformation of random variables and use these techniques to

generate data from various distributions.

CO3: Develop probabilities in joint probability distributions and derive the marginal and conditional

distributions of bivariate random variables.

CO4: Apply the concepts of probability theory to discrete time Markov chain and establish the Markovian

queuing models.

CO5: apply a variety of statistical techniques to solve problems of industry standard statistical software.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:

1. S. Kishore, S. Trivedi, Probabilty and Statistics with Reliability, Queuing and Computer Science.

2. S D Sharma, Operation research, McGraw Hill Education Private Limited.

3. Sundaran Pillai, Probabililty, Statistics and Queuing theory PHI.


1. S.C.Gupta and B.K.Kapur, Fundamentals of Mathematical Statistics.

2. Ivo Adan and Jacques Resing, Queueing Systems, Lecture notes, Netherlands (2015).

3. Arnold O. Allen, Probability, Statistics and Queing theory with computer Science Applications,

Academic Press, INC. New York.

4. T. Veerarajan, Probability, Statistics and Random Processes, McGraw Hill Education Private Limited,

2008.




Compulsory.

2. There shall be internal choice in all the Units

https://www.goodreads.com/author/show/4076303.T_Veerarajan

22

For THIRD Semester B.E. (Lateral Entry : Common to all branches)

Subject Title: BASIC ENGINEERING MATHEMATICS-I

Subject Code:

MADIP31

Exam Marks: CIE

+ Assignment

+Group Activity

40+ 05+05 = 50


Total No. of lecture hours: 50

No. of Credits: 00

Course objective: To develop a basic Mathematical knowledge required for higher semesters with

few examples of its engineering applications.

Unit

No.

Syllabus content No. of

hours

1 Differential Calculus: Polar curves, angle between polar curves and condition

for orthogonality. Pedal equation for polar curves, Radius of curvature–in

Cartesian, parametric, polar and pedal forms (with proof)-problems. Taylor’s

and Maclaurin’s expansions.

10

2 Partial Differentiation: Partial derivatives, Homogeneous functions, Euler’s

theorem (with proof and no extended theorem). Total differential and

differentiability, Derivatives of composite and implicit functions, change of

variables.

10

3 Integral Calculus: Reduction formulae for sin ,n xdx cos ,n xdx

dxxx nm cossin . Evaluation of the integrals using reduction formula with

standard limits-Problems. Tracing of curves in Cartesian and Polar forms

(Cissoid, Astroid, Cardioid and Lemniscate).

10

4 Multiple Integrals: Double integrals in Cartesian and polar coordinates,

change of order of integration, Area enclosed by plane curves, Change of

variables in double integrals, Area of a curved surface. Triple integrals-

Volume of solids.

10

5 Differential Equations: Solution of homogeneous, Linear and Exact

differential equations and its reductions. Solutions of Linear differential

equations of higher order with constant coefficients-inverse differential

operator.

10

Course Outcomes:

After the successful completion of the course, the students are able to

CO1: analyze the basic concepts of calculus like differentiation and integration

CO2: apply the concepts of partial differentiation and differential equations arising in a variety of

engineering applications

CO3: assess the practical importance of polar curves, Jacobians and radius of curvature

CO4: apply the concepts in problem solving and relate the solutions to the various engineering streams

CO5: use the skills in understanding Mathematical knowledge


CO1: PO1, PO2

CO2: PO1, PO2

23

CO3: PO1, PO2

CO4: PO1

CO5: PO1

TEXTBOOKS:



Reprint, 2010.

REFERENCE BOOKS.





2010.

4. V. Krishnamurthy, V.P. Mainra and J.L. Arora, An introduction to Linear Algebra, Affiliated East–

West press, Reprint 2005.

5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005.

24

For FOURTH Semester B.E. (Lateral Entry: Common to all branches))

Subject Title: BASIC ENGINEERING MATHEMATICS-II

Subject Code:

MADIP41

Exam Marks: CIE

+ Assignment

+Group Activity

40+ 05+05 = 50


Total No. of lecture hours: 50

No. of Credits: 00

Course objective: To develop a basic Mathematical knowledge required for higher semesters with

few examples of its engineering applications.

Unit

No.

Syllabus content No. of

hours

1 Partial Differential Equations: Formation of Partial differential equations

(PDE) by elimination of arbitrary constants/functions. Solution of non-

homogeneous PDE by direct integration. Solution of homogeneous PDE

involving derivative with respect to one independent variable only. Solution

of PDE by the Method of separation of variables (first and second order

equations).

10

2 Vector Calculus I:

Vector Differentiation: Scalar and vector point functions – Gradient,

Directional derivative, Divergence, Curl, Solenoidal and Irrotational vector

fields. Vector identities involving Gradient, Divergence and Curl.

Applications-Velocity, acceleration, conservative, Solenoidal, irrotational

and angular momentum fields.

10

3 Vector Calculus II:

Vector Integration: Line, surface and volume integrals-simple problems,

Green’s theorem in a plane, Stoke’s and Gauss divergence theorem (without

proofs). Applications-involving simple problems of triangles, cubes,

rectangular parallelopiped and solid figures.

10

4 Functions of a Complex Variable: Review of continuity, differentiability.

Definition-analytic function, Cauchy-Riemann equations in Cartesian and

polar forms. Harmonic and orthogonal properties of analytic function.

Construction of analytic functions.

10

5 Complex Integration: Complex line integrals, Cauchy’s theorem and

Cauchy’s integral formula. Singularities, poles and residues and Residue

theorem (without proof). Discussion of transformations- 2w z , zw e and

1/w z z ( 0.z )

10

25

Course Outcomes: After the successful completion of the course, the students are able to

CO1: analyze the basic concepts of partial differential equations and their solutions through standard

methods.

CO2: use the idea of gradient, divergence, curl involved in vector fields arising in fields and wave

transmission theory.

CO3: assess the practical importance of Laplace and inverse Laplace transforms and their utility in network

analysis, circuit theory and convection problems.

CO4: apply logical thinking to problem-solving in context and identify an appropriate solution for various


CO5: use the skills in understanding Mathematical knowledge.


CO1: PO1, PO2

CO2: PO1, PO2

CO3: PO1, PO2

CO4: PO1, PO4

CO5: PO1, PO2

TEXTBOOKS:



Reprint, 2010.

REFERENCE BOOKS.





2010.

4. G.F. Simmons and S.G. Krantz, Differential Equations, Tata McGraw Hill, 2007.

5. J. W. Brown and R. V. Churchill, Complex Variables and Applications, 7th Ed., Mc-

Graw Hill, 2004.

26

For Elective- I

SUBJECT TITLE: ADVANCED NUMERICAL METHODS

Subject Code:

MAE01

Number of Credits: 3 =

3: 0 : 0 (L–T– P)


(L=3)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100


Category: Inter-

disciplinary

Teaching Department:

Mathematics

Prerequisite: Nil



Unit

No.


Theory

1 Errors and Approximations: Errors in arithmetic operations, Error in

a function, Approximation by Taylor’s series

Algebraic and Transcendental Equations: solution by Muller and

Chebyshev methods.

07

2 Iterative Methods: Aitken’s 2 -method, Newton-Raphson method,

Generalized Newton-Raphson method, General iteration method.

Methods for complex roots.

Polynomial equations: Birge-Vieta Method and Bairstow method.

08

3 System of Linear Equations: Triangularization method, Cholesky

method and partition method.

Eigenvalues and Eigenvectors: Bounds on Eigenvalues, Jacobi and

Givens methods for symmetric matrices.

08

4 Interpolation, Numerical differentiation and Numerical

Integration: Review of forward and backward differences, Central

differences: Gauss forward and backward difference formulae,

Stirling’s, Bessel’s, Laplace-Everett’s formula. Review of numerical

integration, Boole’s rule and Euler-Maclaurin’s formula.

08

5 Partial Differential Equations: Review of Numerical methods to solve

partial differential equations, Point Jacobi’s method, Gauss-Seidel

method, solution of elliptic equations by Relaxation method.

08

27

Course outcomes:


CO1: analyze the concepts of errors, approximations and algebraic/transcendental equations

CO2: apply the iteration methods which are very helpful in a variety of engineering problems

CO3: assess the importance of interpolation, numerical differentiation and integration and apply in

problems

CO4: make use of partial differential equations in variety of engineering problems

CO5: identify the skills in understanding Mathematical knowledge.

Course outcomes (CO) mapping with Programme outcomes (PO)

CO1: PO1 and PO2

CO2: PO1 and PO2

CO3: PO1 and PO2

CO4: PO1 and PO2

CO5: PO1 and PO2

Text Books:

1. M.K.Jain, S.R.K. Iyengar and R.K.Jain, Numerical Methods for Scientific and Engineering

Computations, New age international (Latest Edition)

2. Babu Ram, Numerical Methods, Pearson Publishing (Latest Edition)

3. A.K. Jaiswal and Anju Khandelwal, A textbook of Computer based Numerical and Statistical

Techniques, New Age International Publishers (Latest Edition)

Reference Books/ Web Sources:

1. B.S. Grewal, Numerical Methods in Engineering and Science, Khanna Publishers, New Delhi

(Latest Edition)

2. N.P.Bali and Manish Goyal, A text book of Engineering Mathematics, Laxmi Publications

(Latest Edition)

3. M.K.Jain and M.M. Chawla, Numerical Analysis for Scientists and Engineers, S.B.W.

Publishers, India (latest Edition)




compulsory


28

For Elective- II

SUBJECT TITLE: APPLIED LINEAR ALGEBRA

Subject Code:

MAE02


3 : 0 : 0 (L–T– P)


Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment + Group

Activity + SEE =

40+05 + 05 + 50 = 100


Category: Inter-

disciplinary


Mathematics

Prerequisite: Nil



Unit

No.


Theory

1 Linear Equations: System of linear equations and its solution sets,

elementary row operations and echelon forms, consistency, uniqueness,

solution of homogeneous and non-homogeneous equations, matrix

operations, elementary matrices, Invertible matrices.

08

2 Vector Spaces: Vector spaces, subspaces, null space, column space and

row space. Linear independence, bases and dimension, computation

concerning subspaces, Rank of a matrix and Rank-nullity theorem.

08

3 Linear Transformation: Definition and types of linear transformation

(Shear, reflection, rotation), Kernel and range of linear transformation,

Isomorphism. Matrix of linear transformation and algebra of linear

transformation.

07

4 Diagonalization: Characteristic equation, Eigenvalue and Eigenvector,

properties of eigenvalues (no proof), Power method, Cayley-Hamilton

theorem (no proof), power of matrix by Cayley-Hamilton theorem,

reduction to diagonal form.

08

5 Inner Product Spaces: Inner product and Inner product spaces,

orthogonal and orthonormal sets, orthogonal projection, Gram-Schmidt

process (no proof) and least square problems.

08

29

Course Outcomes: After the successful completion of the course, the students are able to

CO 1: : apply the concept of row operations to solve the system of linear equations.

CO 2: Illustrate about various types of vector spaces, to find the minimum spanning set for the vector

spaces.

CO 3: Demonstrate about various types of applicable transformation and the role of matrix associated with

any linear transformation.

CO 4: Use various methods to obtain the Eigen values and power of a matrix.

CO 5: assess the concepts of linear algebra for the orthogonalization of the vectors.


CO1: PO1 and PO2

CO2: PO1 and PO2

CO3: PO1 and PO2

CO4: PO1 and PO2

CO5: PO1 and PO2

TEXT BOOKS:

1. David C. Lay : Linear Algebra and its Applications -3rd Edition, Pearson Educaton(Asia) Pvt. Ltd, 2005.

2. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, New Delhi, 40th Edition.

REFERENCE BOOKS/WEB SOURCES:

1. Gilbert Strang: Linear Algebra and its Applications-4th edition Cengage Learning 2005.




compulsory


30

For Elective- III

SUBJECT TITLE: MATHEMATICAL TRANSFORMS & TENSOR

ANALYSIS

Subject Code:

MAE03


3: 0 : 0 (L–T– P)


(L=3)

Exam Duration:

3 Hrs

Exam Marks: CIE +

Assignment +Group

Activity+ SEE =

40+ 05+05 + 50 = 100


Category: Inter-

disciplinary


Mathematics

Prerequisite: Nil



Unit

No.


1 Complex Inversion Integral for Laplace Transforms- Introduction,

use of residue theorem in obtaining inverse Laplace transforms,

inverse Laplace transforms of functions with branch points, inverse

Laplace transforms with infinitely many singularities.

08

2 Hankel Transforms-Introduction, definition, some elementary

theorems. Hankel inversion theorem, Mac-Roberts proof of Hankel

inversion theorem, Parseval’s theorem. Applications of Hankel

transform to boundary value problems.

08

3 Mellin Transforms - Introduction, definition, properties, Mellin

transform of derivative and integrals, Faltung theorem, direct and

inverse transforms. Applications of Mellin transforms.

08

4 Integral Equations: Definition. Abel’s integral equation. Integro-

differential equation. Applications of Laplace transform in solving

Voltea integral equation type-problems.

07

5 Tensor Analysis: Introduction. Kronecker deltas and its properties.

Higher order tensors-Quotient law- Riemannian space-Length of a

vector-angle between two vectors. Christoffel symbols. Covariant

differentiation of fundamental tensor. Covariant derivative of a

covariant vector. Gradient, Divergence and Curl.

08

31

Course outcomes:


CO1: apply the concepts of IBVP of transforms and residual methods.

CO2: adopt the tool of complex inverse Laplace transform which is very helpful in variety of problems like

control theory, electrical circuits and time-varying wave forms

CO3: utilize integral transforms, mathematical techniques and its applications.

CO4: apply different forms of tensor analysis in variety of engineering problems like structural mechanics,

stability communications and networks.

CO5: demonstrate skills in understanding mathematical knowledge

TEXTBOOKS:

1. B.S. Grewal, Numerical Methods in Engineering and Science, Khanna Publishers, New Delhi

(Latest Edition)

2. P.P.Gupta, Integral Transforms (Latest Edition), Kedar Nath Ram Nath publishers.

REFERENCE BOOKS:

1. Lokenath Debnath and Dambaru Bhatta, Integral Transforms and Their Applications, 2nd Edition,

Chapman & Hall, Taylors and Francis Group, London.

2. Hutton, D., Fundamentals of Finite Element Analysis, 2nd Edition, McGraw-Hill, New Delhi.




CO1: PO1 and PO2

CO2: PO1 and PO2

CO3: PO1 and PO2

CO4: PO1 and PO2

CO5: PO1 and PO2



i) There shall be five full questions (one question for each unit) carrying 20 marks each and all are

compulsory

ii) There shall be internal choice in all the Units.

Documents

CURRICULUM & DETAILED SYLLABI of MATHEMATICS · 2021. 3. 30. · 5. D. Poole, Linear Algebra: A Modern Introduction, 2nd Edition, Brooks/Cole, 2005. QUESTION PAPER PATTERN: The Semester