Chapter 1 |
Linear Algebra |
Matrix Algebra, Type of matrices, Determinant, Cramer’s rule, Systems of linear equations, Rank of the equation, consistency of the equation, Eigen values and Eigen vectors. |
2 day |
Chapter 2 |
Probability & distribution |
Sampling theorems, Conditional probability, Baye’s theorem, Random variables, Expectation & Variance, Discrete and continuous distributions, uniform, normal, exponential, Poisson, Binomial. Correlation and regression analysis, covariance, correlation coefficient, Mean, median, mode and standard deviation, |
1 day |
Chapter 3 |
Numerical methods |
Solutions of non-linear algebraic equations, Newton Raphson method, Regulafalsi method or (method of false position), secant method, Gauss Elimination Method, Gauss Jordon method, Jacobi iteration method , Gauss Siedel iteration method, Numerical Integration: Trapezoidal rule, Simpson’s 1/3 & 3/8 rule, single and multi-step methods for differential equations, Euler’s method, RungeKutta Method |
1 day |
Chapter 4 |
Calculus |
Limits & continuity, Basic differentiation & integration, Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Vector identities, Directional derivatives, Line, Surface and Volume integrals, Stokes, Gauss and Green’s theorems. |
3 days |
Chapter 5 |
Differential Equations |
First order equation (linear and nonlinear), Higher order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s and Euler’s equations, Initial and boundary value problems, Partial Differential Equations and variable separable method. |
2 days |
Chapter 6 |
Complex Variables |
Analytic functions, Cauchy’s integral theorem and integral formula, Taylor’s and Laurent series, Residue theorem |
1 day |
Chapter 7 |
Laplace Transforms+ Fourier series |
Definition & property of Laplace transform + Fourier Series |
0.5 day |