## Ordinary Differential Equations and Applications

**Ordinary Differential Equations and Applications**. Instructors: A. K. Nandakumaran, IISc Bangalore; P. S. Datti, TIFR-CAM, Bangalore; Raju K. George, IIST,Trivandrum.

**Motivation and real life examples**: an introduction about differential equations and examples.

**Preliminaries**: basic concepts from linear algebra and some important preliminaries from analysis like uniform convergence, Arzela-Ascoli theorem, fixed point theorems etc.

**First and second order linear equations**: examples, a systematic procedure to solve first order and development of the concept integrating factor, Second order homogeneous and non-homogeneous equations.

**General existence and uniqueness theory**: Picard's iteration, Peano's existence theory, Existence via Arzela Ascoli theorem, non-uniqueness, continuous dependence.

**Linear systems**: understanding linear system via linear algebra, stability of linear systems, explicit phase portrait in 2D linear with constant coefficients.

**Qualitative analysis**: examples of nonlinear systems, Stability analysis, Lyapunov stability, phase portrait of 2D systems, Poincare-Bendixson theory.

**Introduction to two-point boundary value problems**: linear equations, Green's function, nonlinear equations, existence and uniqueness.
(from **nptel.ac.in**)

Introduction |

References |

Ordinary Differential Equations and ApplicationsInstructors: A. K. Nandakumaran, IISc Bangalore; P. S. Datti, TIFR-CAM, Bangalore; Raju K. George, IIST,Trivandrum. an introduction about differential equations and examples. |