Course Objectives
The main objective of the course is to provide knowledge to the students of probability theory, algebra, solutions of Differential equations, Transform techniques, special functions & their applications in the areas with defence relevance.
Course Outcomes
At the end of the course the student should be able to
- Know the methods for solving differential equations, generating functions.
- Understand basic concepts of Fourier Transform, Laplace Transforms and solve problems with periodic functions, step functions, impulse functions and convolution.
- Demonstrate MATLAB programming for engineering problems.
- Understand the utilization of mathematical methods for solving problems having relevance to defence applications.
Course Content:
|
Unit |
Contents |
Contact Hrs. |
|
1. |
Introduction to Probability and Statistics. Basic Probability theory, statistical distributions, binomial, Poisson, exponential and normal distributions. |
10 |
|
2. |
Introduction to Linear Algebra: Vector space, subspace, row, column and null spaces. Inner product, orthogonality. Gram-Schmidt process and least square approximation. |
10 |
|
3. |
Differential Equations: Ordinary Differential equations (second order), Numerical methods for ODE. PDE, Fourier series, Fourier transform and one-dimensional heat and wave equations. |
10 |
|
4. |
Special functions: Power series method, Frobenious method, Legendre equation, Legendre polynomials, Bessel equation, Bessel functions of first kind, Orthogonal property. |
8 |
|
5. |
Introduction to graph theory: Graphs, degree, types of graphs, and introduction to Ramsey theory. |
7 |
|
6. |
Application areas with defence relevance range from mathematics to computer science. |
5 |
|
Total |
50 |
|