Matrix Algebra: Systems of linear equations, Nullspace, Range, Nullity, Rank, Similarity, Eigenvalues, Eigenvectors, Diagonalization, Jordan Canonical form. Ordinary Differential Equations: Singular points, Series solution Sturm Liouville problem, Linear Systems, Critical points, Fundamental matrix, Classification of critical points, Stability.
Complex Variables: Analytic functions, Cauchy’s integral theorem and integral formula, Taylor and Laurent series, isolated singularities, Residue and Cauchy’s residue theorem chwarz lemma.