In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives. The term ordinary is used in contrast with the term partial differential equation which may be with respect to more than one independent variable.
Ordinary differential equations (ODEs) arise in many contexts of mathematics and science, (social as well as natural). Mathematical descriptions of change use differentials and derivatives. Various differentials, derivatives, and functions become related to each other via equations, and thus a differential equation is a result that describes dynamically changing phenomena, evolution, and variation. Often, quantities are defined as the rate of change of other quantities (for example, derivatives of displacement with respect to time), or gradients of quantities, which is how they enter differential equations.
Specific mathematical fields include geometry and analytical mechanics. Scientific fields include much of physics and astronomy (celestial mechanics), meteorology (weather modelling), chemistry (reaction rates), biology (infectious diseases, genetic variation), ecology and population modelling (population competition), economics (stock trends, interest rates and the market equilibrium price changes).
For more details, see the Wikipedia page and the term on Encyclopedia of Mathematics.
Here is the syllabus of the course Math3405.
MATH2215 Mathematical Analysis or MATH2217 Advanced Calculus II
MATH2207 Linear Algebra
| Ch1: Introduction | Week 1 | ||
| Ch2: First Order Differential Equations | Weeks 2--3 | Problem set | Reference solution |
| Ch3: Linear Systems of Differential Equations | Weeks 4--6 | ||
| Ch4: Linear Differential Equations | Weeks 7--8 | Problem set | Reference solution |
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cancelled | ||
| Ch5: Existence, Uniqueness and Dependence on Parameters | Weeks 9--11 | ||
| Ch6: The Laplace Transform | Week 12 | Problem set | Reference solution |
| Ch7: Nonlinear Autonomous Systems of Differential Equations | Week 13 | Problem set | Reference solution |
Lecture notes in one pdf file. This lecture notes was originally written by Professor Xiaonan Wu and then revised by Yutian Li.
draw the direction field (a.k.a. slope fields)
| Elementary Differential Equations and Boundary Value Problems | William E. Boyce and Richard C. DiPrima | Wiley (10th ed.) | 2012 |
| Thinking about Ordinary Differential Equations | Robert E. O'Malley, Jr | Cambridge University Press | 1997 |
| Ordinary Differential Equations: A Brief Eclectic Tour | David A. Sanchez | Cambridge University Press | 2003 |
| Ordinary Differential Equations | Morris Tenenbaum and Harry Pollard | Dover | 1985 |
| Khan Academy | Differential Equations | Sal Khan | |
| MITOpenCoureseWave | Differential Equations | Haynes Miller and Arthur Mattuck | 2010 |
| WikiBooks | Ordinary Differential Equations | ||
| Free Textbooks | Elementary Differential Equations | William F. Trench | Free textbook by Prof. Trench |
| HKUST Lecture Notes | Introduction to Differential Equations | Jeffrey R. Chansnov | Lecture notes, youtube videos |
| Youtube Videos | Ordinary Differential Equations | commutant | Introduction to ordinary differential equations through examples. |