Korea Advanced Institute of Science and Technology(KAIST) (via Coursera)
This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications.
The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramer’s Rule for solving linear systems of equations, eigenvalues and eigenvectors.
Table of Contents
Differential Equations Part I Basic Theory
Chapter 1 Introduction
Chapter 2 First Order Differential Equations
Chapter 3 Mathematical Modelling and Applications
Chapter 4 Linear Second Order Equations
Chapter 5 Applications of Second Order Equations
Differential Equations Part II Series Solutions
Chapter 1 Euler Equations
Chapter 2 Series Solutions of Linear Equations
Chapter 3 Special Functions: Bessel Functions and Legendre Polynomials
Differential Equations Part III Systems of Differential Equations
Chapter 1 Systems of Linear Equations
Chapter 2 Stability of Autonomous Systems
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