Applied Engineering Mathematics

GANPAT UNIVERSITY

FACULTY OF ENGINEERING & TECHNOLOGY

Programme

Bachelor of Technology

Branch/Spec.

Computer Science & Engineering (CBA/CS/BDA)

Semester

III

Version

1.0.0.1

Effective from Academic Year

2022-23

Effective for the batch Admitted in

June 2021

Subject  code

2HS306

Subject Name

APPLIED ENGINEERING MATHEMATICS

Teaching scheme

Examination scheme (Marks)

(Per week)

Lecture (DT)

Practical(Lab.)

Total

CE

SEE

Total

L

TU

P

TW

Credit

3

1

0

0

4

Theory

40

60

100

Hours

3

1

0

0

4

Practical

0

0

0

Pre-requisites:

Trigonometry, Continuity, Integration, Differentiation

Learning Outcome:

After successful completion of this course, students will be able to:

• Understand all basic fundamentals of numerical methods and transforms.
• Apply differential equations and transforms for various examples.
• Apply knowledge of transforms and numerical methods in various applications of Computer Science.
• Understand basics of Machine Learning.

Theory syllabus

Unit

Content

Hrs

1

Finite Differences And Difference Equations :

Finite differences interpolation - Newton’s Forward, Newton’s Backward, Newton’s Divided Difference and Lagrange’s Interpolation. Difference equation with constants coefficient. Solution of ordinary and partial differential equations with boundary conditions by finite difference method.

8

2

Numerical Methods:

Roots of algebraic equations - Bisection, Regula Falsi, Secant and Newton Raphson method, Solution of linear simultaneous equations - Jacobi and Gauss Seidel method, Numerical differentiation - Picard’s, Taylor’s, Euler’s, Modified Euler’s and RK method,  Numerical Integration - Trapezoidal, Simpson’s ⅓ and Simpson’s ⅜ method.

12

3

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.

10

4

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..

10

5

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 and Kalman-Bucy filter, Riccati Matrices (Equations) and applications

5

Mooc Course

Course Name: Numerical Methods

Link: https://onlinecourses.nptel.ac.in/noc22_ma21/preview

Course Name : Engineering Mathematics II

Link : https://onlinecourses.nptel.ac.in/noc22_ma08/preview

Practical content

  Not Applicable

Text Books

1

Higher Engineering Mathematics by Dr. B. S. Grewal

2

A textbook for Higher Engineering Mathematics by N.P. Bali and Usha Paul

Reference Books

1

Text book of engineering mathematics by A. B. Mathur and V. P. Jaggi

2

Higher Engineering Mathematics vol -3 by Dr. K.R. Kachot

3

Engineering mathematics by Srivastava

4

Applied Mathematics vol.-I and II by P.N.Wartikar and J. N. Wartikar

5

Applied Numerical Analysis by C.F. Gerald and P.O. Wheatley, Pearson Publication

Course Outcomes:

COs

Description

CO1

Understand all basic fundamentals of numerical methods and transforms.

CO2

Apply differential equations and transforms for various examples

CO3

Apply knowledge of transforms and numerical methods in various applications of Computer Science.

CO4

Understand basics of Machine Learning..

Mapping of CO and PO