Integrated MSc-PhD Program

SYLLABUS

KSM2C04: Differential Equations

First and second-order equations, general and particular solutions, linear and nonlinear systems, linear independence, solution techniques, Existence and Uniqueness Theorems: Peano’s and Picard’s theorems, Gronwall’s inequality, Dependence on initial conditions and associated flows. Linear system: The fundamental matrix, stability of equilibrium points, Phase-plane analysis, Sturm-Liouville theory, Nonlinear system and their stability: Lyapunov’s method, Frobenius’s theory.

Suggested texts:

1. 1. 1. 1. 1. 1. Philip Hartman, Ordinary differential equations, Classics in Applied Mathematics, vol. 38, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 2002, Corrected reprint of the second (1982) edition [Birkhäuser, Boston, MA; MR0658490 (83e:34002)], With a foreword by Peter Bates.
               2. Lawrence Perko, Differential equations and dynamical systems, third ed., Texts in Applied Mathematics, vol. 7, Springer-Verlag, New York, 2001.
               3. Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, AMS publications.
               4. Ordinary Differential Equations, Nandakumaran, A. K.; Datti, P. S.; George, Raju K.