Series Solutions of Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)
Series solutions of ordinary differential equations.
Enrolment valid for 12 months
Course Chapters
1. Introduction
1. Introduction
Welcome and course outline. Review of ordinary differential equations concepts and definitions.
2. Power Series
2. Power Series
Review of the definition, radius and interval of convergence of power series. Operations of addition, multiplication and division, change of index, and change of variables of power series.
3. Analytic Functions
3. Analytic Functions
Definition of analytic functions. Meaning of ordinary and regular singular points of linear differential equations with variable coefficients.
4. Solutions About an Ordinary Point
4. Solutions About an Ordinary Point
Series solutions of ordinary differential equations about an ordinary point.
5. Solutions About a Regular Singular Point
5. Solutions About a Regular Singular Point
Series solutions of ordinary differential equations about a regular singular point. Frobenius method. Fuchs' theorem.
6. Gamma and Bessel Functions
6. Gamma and Bessel Functions
Definition and use of gamma and bessel functions.
7. Bessel's Equations
7. Bessel's Equations
Definition, solutions and applications of Bessel's equations.
8. Other Classical Equations
8. Other Classical Equations
Definitions, polynomial solutions and applications of some other classical second-order linear ordinary differential equations with variable coefficients - Chebyshev's, Hermite's, Laguerre's, and Legendre's differential equations.