| Course Content |
Time Allocated |
| L |
T |
P |
A |
| |
DIFFERENTIAL EQUATIONS
|
Introduction
- Different types of DEs and solutions
|
1
|
|
|
|
Modelling with Differential Equations
- Applications in geometry and physical systems
|
2
|
1 |
|
|
First Order Differential Equations
Solutions methods
- Variable separable
- Exact equations
- Linear differential equations
- Reducible forms
|
3 |
2
|
|
|
Constant Coefficient Linear Differential Equations
Homogeneous Equations; Complementary Solutions
- First order, second order and higher order equations
Inhomogeneous Equations; Particular Integral
- Trial solutions (undermined coefficients)
- Variation of parameters
- D-operators
|
4 |
3 |
|
|
Solutions in Series – Introduction
|
2 |
1 |
|
|
Laplace Transformation
- Definitions and standard theorems
- Inverse Transformation
- Using in solving ODEs
- Converting PDEs to ODEs
|
4 |
2 |
|
|
System of Ordinary Differential Equations
- State space representation
- Eigenvalue methods
|
2
|
1
|
|
|
Numerical Solutions to ODE
- Eular methods
- Runge Kutta methods
- Variable (Adaptive) step size algorithms
|
2 |
1 |
|
|
| |
| PROBABILITY |
| Introduction
|
1 |
|
|
|
Concept of Probability
- Conditional probability and independence, Random variables,Probability functions, Mathematical expectation, Moment generating functions, Joint, Marginal and Conditional distributions
|
7 |
2 |
|
|
Discrete probability distributions
- Bernoulli (Point binomial) distribution. Binomial distribution, Poisson Distribution, Geometric distribution, Hyper geometric distribution, Multinomial distribution
|
2 |
2 |
|
|
| Total = 30 + 15 = 45 |
30 |
15
|
|
|