| Linear Algebra |
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| Matrix algebra |
| System of Linear Equations |
| Eigen values and Eigen Vectors |
| Calculus |
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| Functions Of single Variables |
| limits, Continuity and differentiability |
| Indeterminate Forms |
| Mean Value Theoram |
| Evaluation of Definite and Improper Integrals |
| Double and triple Integrals |
| Partial Derivative |
| Total derivative |
| Taylor Seires(in one and two variables) |
| Maxima and Minima |
| Fourier Series |
| Gradient |
| Divergence and Curl |
| vector Identities |
| Directional derivative |
| Line, Surface and Volume Integrals |
| Application of Gauss,Sokes and Greens theoram |
| Differential Equations |
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| First Order Equations (Linear and non-linear) |
| Higher Order linear differntial equations with constant coefficients |
| Euler-Cauchy Eqation |
| Initial and Boundry Value Problems |
| Laplace Transforms |
| Solutions of heat wave and Laplace Equations |
| Complex Variables |
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| Analytic Functions |
| Cauchy- Rieman Equations |
| Cauchy's Integral Theoram and Integral formula |
| Taylor and Laurent Series |
| Probability and statistics |
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| Definations of Probability |
| Sampling Theorams |
| Conditional Probability |
| Mean , Median and Mode and Standard deviation |
| Random variables |
| Binomial,Poison and Normal Distributions |
| Numerical Methods |
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| Numerical solutions of Linear and Non-linear algebraic Equations |
| Integration by trapezoidal and Simpsons rule |
| Single and Multi-steps Method for for differential equations |