Matrix Algebra, Systems of linear equations, Eigenvalues, and Eigenvectors
Mean value theorems, Theorems of integral calculus, Evaluation of definite and improper integrals, Partial Derivatives, Maxima and minima, Multiple integrals, Fourier series, Vector identities, Directional derivatives, Line integral, Surface integral, Volume integral, Stokes’s theorem, Gauss’s theorem, and Green’s theorem.
First-order equations (linear and nonlinear), Higher-order linear differential equations with constant coefficients, Method of variation of parameters, Cauchy’s equation, Euler’s equation, Initial, and boundary value problems, Partial Differential Equations, and Method of separation of variables.
Analytic functions, Cauchy’s integral theorem, Cauchy’s integral formula, Taylor series, Laurent series, Residue theorem, and Solution integrals
Probability and Statistics
Sampling theorems, Conditional probability, Mean, Median, Mode, Standard Deviation, Random variables, Discrete and Continuous Distributions, Poisson distribution, Normal distribution, Binomial distribution, Correlation analysis, and Regression analysis.
Solutions to non-linear algebraic equations, and Single and Multi‐step methods for differential equations.
Fourier Transform, Laplace Transform, and z‐Transform.