Applied Engineering Mathematics : 2HS306

Learning Outcomes: 
• Understand all basic fundamentals of numeric methods transforms.
• Prepare him/herself for solving the problem by applying differential equations and transforms.
• Apply knowledge of transforms and numerical methods in various application of his/her branch.
Syllabus: 
Unit NoTopics
1

Theory of complex Variable:

Analytic functions, Cauchy-Riemann equation, Line integral, Cauchy’s theorem and Cauchy’s integral. Simple form of conformal transformation with application of the solution of two-dimensional problems.

2

Finite Differences And Difference Equations:

Finite differences interpolation. Newton’s and LaGrange’s formula. Difference equation with constants co-efficient. Solution of ordinary and partial differential equations with boundary conditions by finite difference method.

3

Numerical Methods:

Roots of algebraic equations. Solution of linear simultaneous equations. Solution of linear simultaneous equations. Numerical differentiation and integration. Numerical methods to solve first order, first degree ordinary differential equations.

4

Laplace Transforms:

Definition, Laplace transform of elementary functions. Properties of Laplace transform, Inverse Laplace transforms. Transform derivatives, Transform of integration. Multiplication by tn, Division by t, Convolution theorem. Unit step and Heaviside’s unit function, Dirac-delta function. Periodic functions Solution of ordinary linear differential equations Simultaneous equations with constant coefficient applied to electrical circuits.

5

Fourier Series:

Definition of periodic function. Euler’s formula. Functions having points of discontinuity. Change of intervals. Odd and even functions. Expansion of odd or even periodic functions. Half range cosine and sine series. Elements of harmonic analysis.

6

Difference equations:

first order, second order and nth order, with integer argument and their solutions; First order, second order, nth order, with continuous variables and their solutions; The state space form &Kalman-Bucy filter, Riccati Matrices (Equations) and applications

Text Books: 
Name : 
Higher engineering mathematics
Author: 
by B. S. Grewal
Name : 
A textbook for Higher Engineering Mathematics
Author: 
by N.P. Bali
Usha Paul
Reference Books: 
Name: 
Text book of engineering mathematics
Author: 
A. B. Mathur
V. P. Jaggi
Name: 
Higher Engineering Mathematics vol -3
Author: 
Dr. K.R. Kachot
Name: 
Engineering mathematics
Author: 
by Srivastava
Name: 
Applied Mathematics vol.-I and II
Author: 
P.N.Wartikar
J. N. Wartikar
Name: 
Applied Numerical Analysis
Author: 
C.F. Gerald
P.O. Wheatley
Publication: 
Pearson
Syllabus PDF: 
AttachmentSize
PDF icon AEM.pdf165.16 KB
branch: 
CBA
BDA
MA
Cyber Security
Course: 
2018
Stream: 
B.Tech