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- Differential Equations (calculus@internet - Mathematica) - Christopher A. Barker
Mathematica Track. 1. Basics (Mathematica Overview; The Environment; Arithmetic; Using Variables; Working with Lists; Vectors & Matrices; Algebraic Operations; Functions; Calculus Operations; Graphics). 2. Differential Equations (Creating Slope Fields; Sketching Graphical Solutions; Using Differential Equation Solvers; Using IVP Solvers; Using Numerical Solvers; Solving Systems with the Computer). 3. Applications of Initial Value Problems (A Suspended Wire; The Simple Pendulum; Population Dynamics; Electric Circuits). 4. Applications of Systems of Differential Equations (Predator-Prey Problems; Epidemiology Problems). 5. Numerical Methods (Euler's Method).
- Ordinary Differential Equations - Dave Rusin; The Mathematical Atlas
A short article designed to provide an introduction to ordinary differential equations, equations to be solved in which the unknown element is a function rather than a number, and in which the known information relates that function to its derivatives. Few such equations admit an explicit answer, but there is a wealth of qualitative information describing the solutions and their dependence on the defining equation. There are many important classes of differential equations for which detailed information is available. Applications to engineering and the sciences abound. Numerical solutions are actively studied. History; applications and related fields and subfields; textbooks, reference works, and tutorials; software and tables; other web sites with this focus.