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Mathematics
Ordinary Differential Equations (Web)
Syllabus
Co-ordinated by :
IIT Kanpur
Available from :
2013-03-22
Lec :
1
Modules / Lectures
Existence and Uniqueness of Solutions
Preliminaries
Picard's Successive Approximations
Picard's Theorem
Continuation and Dependence on Initial conditions
Existence of Solutions in the Large
Existence and Uniqueness of Solutions of Systems
Cauchy-Peano theorem
Linear Differential Equations of Higher Order
Introduction
Linear Dependence and Wronskian
Basic Theory for Linear Equations
Method of Variation of Parameters
Homogeneous Linear Equations with Constant Coefficients
System of Linear Differential equations
Introduction- module 3
Systems of First Order Equations
Fundamental Matrix
Non-homogeneous linear Systems
Linear Systems with Constant Coefficients
Phase Portraits-Introduction
Phase Portraits (continued)
Oscillations and Boundary value Problems
Introduction - module 4
Sturm's Comparison Theorem
Elementary Linear Oscillations
Boundary Value Problems
Sturm-Liouville Problem
Green's Functions
Asymptotic behavior and Stability Theory
Introduction -Module 5
Linear Systems with Constant Coefficient (module5)
Linear Systems with Variable Coefficients
Second Order Linear Differential Equations
Stability of Quasi-linear Systems
Stability of Autonomous Systems
Stability of Non-Autonomous Systems
A Particular Lyapunov Function
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