Course info

Department of Allied Sciences (Mathematics)

Program: - B.tech. (All Branches Except Bio Tech.)

Semester

Two

Course Title

ENGINEERING MATHEMATICS -II

Code

TMA 201

Course Components

Credits

Contact Hours

L

 T

P

Discipline Specific Course (DSC)

03

02

01

00

Examination Duration (Hrs)

Theory

Practical

WEIGHTAGE: EVALUATION

CWA

MSE

ESE

03

00

25

25

50

Pre-requisite

Basic Knowledge of Mathematics

Course Outcomes

CO1

Understand the concept of limit of sequence and convergence of infinite series.

CO2

Apply the methods in solving the ordinary differential equations.

CO3

Implement the series solution for finding the solution of ordinary differential equations.

CO4

Utilize the first order Partial Differential Equation in various Engineering disciplines.

CO5

Illustrate the concept of complex analytic functions and its applications in Engineering fields.

CO6

Solve real integration using the concept of complex integration.

Unit No.

Content

Contact Hours

Unit -1

Sequences and series:

Limits of sequence of numbers, calculation of limits; Infinite series; Tests for convergence; Power series, Taylor and Maclaurin series, convergence of Taylor series, error estimates.

8

Unit -2

Ordinary differential equations:

Ordinary differential equation of first order (Exact, linear and Bernoulli’s equations), Equations of first order but not of first degree: equations solvable for p, equations solvable for y and equations solvable for x. Clairaut’s type. Linear differential equations of nth order with constant coefficients, complementary functions and particular integrals, Cauchy -Euler differential equation, second order linear differential equations with variable coefficients; Method of variation of parameters and applications of ODE.

12

Unit -3

Series solution and special function:

Power series solutions: Legendre’s equations and Legendre polynomials, Frobenius method, Bessel’s equation and Bessel’s functions of the first kind and their properties.

8

Unit -4

Complex variable (Differentiation):

Introduction of complex numbers; Differentiation, Cauchy-Riemann equations, analytic functions, harmonic functions, finding harmonic conjugate; elementary analytic functions (exponential, trigonometric, logarithm) and their properties; Conformal mappings, Mobius transformations and their properties.

8

Unit -5

Complex variable (Integration):

Contour integrals, Cauchy-Goursat theorem (without proof), Cauchy Integral formula (without proof), Liouville’s theorem and Maximum-Modulus theorem (without proof); Taylor’s series, zeros of analytic functions, singularities, Laurent’s series; Residues, Cauchy Residue theorem (without proof), Evaluation of definite integral involving sine and cosine, Evaluation of certain improper integrals using the Bromwich contour.

9

 Total Hours

45