Differential Equations

Guide Note:Differential Equations are a form of mathematics used for a function that relates the function to its derivatives. They are used in many areas of science and technology.

Fast Facts:

1. One of the earliest and prominent contributors was Sir Isaac Newton
2. Used in applied mathematics, physics, economics and engineering
3. There are 5 different types, both linear and nonlinear
4. Closely related to the theory of difference equations
5. Used as a model in biology
6. Mathematically studied from different perspectives

Edit Guide Note and Fast Facts

The Mahalo Top 7

1. Wikipedia: Differential Equation
2. Wolfram MathWorld: Differential Equation
3. S.O.S Mathematics: Differential Equations 
4. Lamar University: Paul's Online Math Notes: Differential Equations
5. Georgia State University: Differential Equations
6. Ohio State University: An Introduction to Differential Equations
7. Video: Series Solutions of Differential Equations Mini-Lecture (Time: 9:03)

Differential Equations Recent News

• Google News: Differential Equations
• Wolfram Research: Differential Equations, Live and in Color
• Live Science: Inside Movie Animation: Simulating 128 Billion Elements (December 24, 2007) 
• ABC: News in Science - Maths Genius Tames Complex Systems (May 27, 2005)

Differential Equations History

• MFO: The History of Differential Equations, 1670–1950 (517.5 KB) 
• Worcester Polytechnic Institute: History of the Differential from the 17th Century
• Wikipedia: History of Numerical Solution of Differential Equations Using Computers

Notable Figures in Differential Equations

Isaac Newton

• Mahalo's guide to Sir Isaac Newton
• Wikipedia: Isaac Newton | Newton's Law of Motion
• University of St. Andrews: Isaac Newton

Pierre-Simon Laplace

• Wikipedia: Pierre-Simon Laplace | Laplace's Equation
• University of St. Andrews: Pierre-Simon Laplace
• Trinity College Dublin: Pierre-Simon Laplace

Albert Einstein

• Mahalo's guide to Albert Einstein
• Wikipedia: Albert Einstein | Einstein Field Equations
• University of St. Andrews: Albert Einstein

William Rowan Hamilton

• Wikipedia: William Rowan Hamilton | Hamilton's Equations
• University of St. Andrews: William Rowan Hamilton
• Trinity College Dublin: William Rowan Hamilton

Augustin Cauchy

• Wikipedia: Augustin Cauchy | Cauchy-Riemann Equations
• University of St. Andrews: Augustin Cauchy
• Seton Hall University: Augustin Cauchy

Bernhard Riemann

• Wikipedia: Bernhard Riemann | Cauchy-Riemann Equations
• University of St. Andrews: Bernhard Riemann
• United States Naval Academy: Bernhard Riemann

Differential Equations Research

• Rice University: Research Focus : Differential Equations
• University of Cambridge: Applied Partial Differential Equations Research Group
• UCLA: NSF Research Training Group in Applied Differential Equations and Scientific Computing
• Iowa State University: Research on Inverse Problems for Differential Equations
• ERCIM News: Partial Differential Equations in Porous Media Research (July, 1998)

Differential Equations Education Resources

• Pearson Education: Interactive Differential Equations
• EQWorld: Ordinary Differential Equations
• Texas A & M University: Differential Equations Tutorials
• Get HomeWork Help: Differential Equations Homework Help
• Efunda: Ordinary Differential Equations
• University of Massachusetts Dartmouth: Tutorial Solving Differential Equations

Differential Equations Photos and Videos

• Google Image Search: Differential Equations
• Yahoo! Image Search: Differential Equations
• Live Search Images: Differential Equations
• YouTube & Google Video Search: Differential Equations
• YouTube: First Order Differential Equations (Time: 9:03)
• YouTube: OpenLearn: Maths Unit --Differential Equations #3 (Time: 3:55)

Differential Equations Blogs and Forums

• Google Blog Search: Differential Equations
• The Math Forum: Differential Equations
• Physics, Astronomy, Math & Philosophy Forums: Differential Equations
• Physics Forums: Differential Equations
• S.O.S Mathematics: S.O.S Mathematics Cyberboard - Differential Equations
• 5 1/2 Blog: A Moment of Genius: Partial Differential Equations and Flash 8 Filters

Differential Equations Books and Publications

• The Mathematical Association of America: Basic Library List - Differential Equations
• Google Book Search: Differential Equations Books
• Amazon.com: Differential Equations Books
• eBay: Differential Equations Books
• Wolfram World Wide Web Store: Differential Equations Books
• Wikibooks: Differential Equations
• BestBookBuys: Differential Equations Books

Differential Equations Theories

• The Modeling Workshop: Differential Equations - Theory
• University of Oxford: The Theory of Exponential Differential Equations
• Stanford University: Theories Given by Differential e|Equations

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