Series Solutions of Ordinary Differential Equations - Mathematical Methods (Undergraduate Advanced)
Series solutions of ordinary differential equations.
Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
CHE 306: Engineering Analysis IIAdvanced engineering mathematics covering numerical and analytical methods of engineering analysis.
Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
CHE 306: Engineering Analysis II
Advanced engineering mathematics covering numerical and analytical methods of engineering analysis.
Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
Advanced engineering mathematics covering numerical and analytical methods of engineering analysis. Curated for third-year students of engineering at Obafemi Awolowo University, Ile-Ife, Nigeria. Students and professionals with similar learning goal will also find this learning track useful.
See more
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.