8: Ordinary Differential Equations
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- 8.00: Physical Problems for Ordinary Differential Equations
- Examples of real-world engineering problems whose solutions require use of ordinary differential equations.
- 8.01: Prerequisites to Numerical Methods for Solving Ordinary Differential Equations
- Exploring why some mathematical models require ordinary differential equations. Finding exact solutions to first- and second-order ordinary differential equations, and solving integrals as first-order ordinary differential equations.
- 8.02: Euler’s Method for Solving Ordinary Differential Equations
- Derivation and application of Euler's method for solving ordinary differential equations. Using Euler's method to solve integrals.
- 8.03: Runge-Kutta 2nd-Order Method for Solving Ordinary Differential Equations
- Theory, application, and derivation of the Runge-Kutta second-order method for solving ordinary differential equations
- 8.05: On Solving Higher-Order and Coupled Ordinary Differential Equations
- Expressing higher-order and coupled ordinary differential equations as simultaneous first-order ordinary differential equations and in state-space model form. Numerically solving higher-order and coupled ordinary differential equations.