MATHEMATICAL METHODS
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.
Books
- Hoffman, J. and Kunze, R., Linear Algebra, Prentice-Hall, 1970.
- 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.