Motivation and real life examples:An introduction about differential equations and why this course – Present various examples like population growth, spring-mass-dashpot system and other nonlinear system. These examples will be recalled as and when necessary – Preliminaries:Basic concepts from linear algebra – Some important preliminaries from analysis like uniform convergence, Arzela-Ascoli theorem, fixed point theorems etc – First and second order linear equations:First order linear differential equations, Exact differential equations and integrating factors – Second order linear differential equations (homogeneous and non-homogeneous. Equation with constant coefficients, analysis of spring-mass-dashpot system.

General Existence and Uniqueness theory:Examples of non-uniqueness, non-existence, importance of existence uniqueness theory, Picard’s iteration, Peano’s existence theory, Existence via Arzela Ascoli theorem, continuous dependence:Methods of solving (series solution) – Linear systems:Understanding linear system via linear algebra, stability of Linear systems, Explicit phase portrait of 2D linear systems with constant coefficients, General case, Non-homogeneous Systems – Qualitative Analysis:Examples of nonlinear systems, Stability analysis, Liapunov stability, phase portrait of 2D systems, Poincare Bendixon theory, Leinard’s theorem – Introduction to two-point Boundary value problems:Linear equations, Green’s function, nonlinear equations, existence and uniqueness:

### Course Curriculum

 General Introduction Details 59:59 Examples Details 58:28 Examples Continued I Details 1:26 Examples Continued II Details 59:41 Linear Algebra Details 52:32 Linear Algebra Continued I Details 57:56 Linear Algebra Continued II Details 1:4:12 Analysis Details 1:2:18 Analysis Continued I Details 55:16 First Order Linear Equations Details 1:31 Exact Equations Details 1:43 Second Order Linear Equations Details 59:37 Second Order Linear Equations Continued I Details 1:25 Second Order Linear Equations Continued II Details 59:31 Well-posedness and Examples of IVP Details 1:1:51 Gronwall’s Lemma Details 59:34 Basic Lemma and Uniqueness Theorem Details 56:55 Picard’s Existence and Uniqueness Theorem Details 58:39 Picard’s Existence and Uniqueness I Details 58:25 Cauchy Peano Existence Theorem Details 59:27 Existence using Fixed Point Theorem Details 59:51 Continuation of Solutions Details 1:17 Series Solution Details 1:13 General System and Diagonalizability Details 58:23 2 by 2 systems and Phase Plane Analysis Details 1:2:2 2 by 2 systems and Phase Plane Analysis Continued I Details 1:7 General Systems Details 1:39 General Systems Continued and Non-homogeneous Systems I Details 1:3:43 Basic Definitions and Examples Details 57:15 Stability Equilibrium Points Details 59:57 Stability Equilibrium Points Continued I Details 54:5 Stability Equilibrium Points Continued II Details 1:16 Second Order Linear Equations Continued III Details 58:43 Lyapunov Function Details 58:39 Lyapunov Function I Details 51:35 Periodic Orbits and Poincare Bendixon Theory Details 1:28 Periodic Orbits and Poincare Bendixon Theory I Details 41:38 Linear Second Order Equations Details 55:2 General Second Order Equations Details 51:2 General Second Order Equations Continued I Details 54:17

## N.A

ratings
• 5 stars0
• 4 stars0
• 3 stars0
• 2 stars0
• 1 stars0

No Reviews found for this course.

6 STUDENTS ENROLLED