Vector Calculus | - Stokes theorem, Green and Gauss’s divergence
- Double/triple integrations (their applications)
- Gradient, divergence, curl, and laplacian
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Transforms | - Laplace/inverse transforms
- Fourier integral theorem, fourier transform pair
- Application to solution of linear ordinary differential equations with constant coefficient
- Sine & cosine transforms
- Inverse Z transform
- Solutions of difference equations with Z transform
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Functions of complex variables and complex integration | - Analytic functions
- Conformal mapping
- Bilinear transformation
- Integral theorem & integral formula by Cauchy
- Laurent & Taylor series
- Singularities
- Residues, Residue theorem (its applications)
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Numerical methods | - Interpolation and approximation
- Numerical differentiation & integration
- Solving ordinary differential equations
- Linear system solution with direct and interactive methods
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Applied probability | - Continuous & standard discrete distribution
- Moments, moments generating function & their properties
- Two dimensional random variables
- Covariance
- Regression & correlation
- Probability & random variables
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Calculus and differential equations | - Partial derivatives
- Linear ordinary differential with constant coefficients
- First order linear equations with constant coefficients
- Partial differential equation formation
- Solution of first order PDE/ linear order PDE with constant coefficients
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Matrices & determinants | - Matrix ranks
- Solving system of equations
- Reduction of quadratic to canonical form
- Eigenvectors/ eigenvalues
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