Algebra of Matrices 
Matrix Inverse
System of linear equations
Determinant of a Matrix
Eigenvalues and Eigenvectors
Matrix Diagonalization
Cayley-Hamilton Theorem
Taylor’s theorem
Gradient of Vector Calculus
Line and surface integrals
Green’s theorem
Stokes theorem and Gauss divergence theorem (without proofs)
Analytic Functions 
Cauchy- Riemann equations
Line Integral
power series solutions
Taylor’s series
Fourier series
Half Range Fourier Series
Axioms of probability
Conditional Probability
Bayes’ Theorem
Discrete and Continuous Random Variables
Correlation and regression
Numerical Methods: The Trapezium Rule and Simpson's Rule
Legendre polynomials
Euler-Cauchy Equations
Laplace equation
Separation of variables method
Sequence and series