Course Code

BSC_ME401

Category

Basic Science Courses

Course Title

Laplace, Fourier and Z-Transforms

Scheme and Credits

L  

T

P

Credits

Semester - 4 (Four)

2

1

0

3

Pre Requisites 

Limits, Improper integrals, A.P and G.P series.

Objectives: 

To understand various transformation techniques and their use to solve boundary value problems and various linear differential equations

M. No:

Topic

No. of Hrs

Module 1.

Laplace transform: Laplace transform, condition for the existence of Laplace transform, Laplace transform of some elementary functions, differentiation and integration of laplace transform, laplace transform of periodic functions, shifting theorem, Laplace transforms of different functions, Heaviside’s unit function, dirac delta function its Laplace transforms. Heaviside’s expansion theorem .

10

Module 2.

Inverse laplace transforms: initial and final value theorems, convolutions theorem and applications, uses of Laplace transforms in the solutions of linear differential equations.

05

Module 3.

Fourier series: Fourier series, odd and even functions, half range Fourier sine and cosine series.

05

Module 4.

Fourier transform: Finite Fourier transforms, fourier integral formula, properties of fourier transform, Fourier sine and cosine transform, convolution theorem, parseval’s identity for fourier transform Fourier integral formula, applications to solutions of boundary value problems.

10

Module 5.

Z-transform: definition, linearity property, Z-transform of elementary functions, shifting theorems. initial and final value theorem, convolution theorem. 

07

Module 6.

inverse Z-transform: inversion of Z-transforms, use of Z-transforms in solving difference equations .

05

Total number of Hours

42

 Course Outcomes:

At the end of the course, the student will be able to:

  • Evaluate Laplace and Inverse Laplace transforms of various functions and related problems (L5).

  • Evaluate Fourier and Inverse Fourier transforms of various functions and related problems (L5).

  • Apply the methods of laplace and Fourier transforms in solving ODE,and PDE (L3).

S.No:

Text Books 

Author

Publisher

  1. 1

Schaum’s outlines laplace transform

M. R. Spiegel

Tata Mc-Graw Hill

References

  1. 3

Advanced Engg mathematics 

Erwin Kreysing

Wiley Eastern. Pub.

Higher Engg Mathematics 

B.S. Grewal

Khanna publishers

Advanced Engg Mathematics

Michael D Greenberg

PHI,2001