## 1. Linear Algebra

- Matrix Algebra (Multiplication, Rank, and Inverse)
- Solution of the system of Linear Equations
- Eigen Values and Eigen Vectors (Plus Cayley Hamilton Theorem & Inverse)

## 2. Calculus

- Taylor and Maclaurin Series
- Rolle’s, Mean Value, and Cauchy’s Mean Value Theorems
- Partial Derivatives (Multivariable Function)
- Maxima, Minima and Saddle Point ( Function in two variables)
- Gradient of Function
- Directional Derivative of the Function
- Divergence of the Vector Field
Curl of the Vector Field

## 3. Differential Equations

- First order equations (Leibnitz’s and Bernoulli’s Linear Equations)
- Higher order linear differential equations with constant coefficients
- Cauchy’s homogenous equation
- Laplace Transforms

## 4. Complex Variables

- Complex Number Basics
- Representation on Complex Plane or Argand’s Plane
- Polar and Euler form of the complex number
- Triangle Inequality.

## 5. Probability and Statistics

- Conditional Probability (Baye’s Theorem)
- Binomial Distribution (Repeated Trials / Bernoulli’s Trials)
- Poisson Distribution
- Normal Distribution
- Mean, Median, and Mode
- Standard Deviation & Variance

## 6. Numerical Mehods

- Numerical solutions of linear algebraic equations:
- Numerical solutions of non-linear algebraic equations:
- Integration by trapezoidal rule
- Integration by Simpson’s rule:
- Single and multi-step methods for the numerical solution of differential equations: