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
Suggested books and references:
Hoffman, K. and Kunze, R., Linear Algebra (2nd Ed.)
Herstein, I. N. and Winter, D. J., Matrix Theory and Linear Algebra, Macmillan, 1989.
Simmons G. F., Differential Equations, Tata McGraw-Hill, 1985.
Churchill, R. V., Complex Variables and Applications, McGraw-Hill, 1960.