Series Solutions of Ordinary Differential Equations
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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.
Course Chapters
1Introduction
Welcome and course outline. Review of ordinary differential equations concepts and definitions.
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2Power 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.
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3Analytic Functions
Definition of analytic functions. Meaning of ordinary and regular singular points of linear differential equations with variable coefficients.
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4Solutions about an Ordinary Point
Series solutions of ordinary differential equations about an ordinary point.
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5Solutions about a Regular Singular Point
Series solutions of ordinary differential equations about a regular singular point. Frobenius method. Fuchs' theorem.
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6Gamma and Bessel Functions
Definition and use of gamma and bessel functions.
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7Bessel's Equations
Definition, solutions and applications of Bessel's equations.
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8Other 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.
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