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Calculus Derivative Help

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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineering, physics, economics, and other disciplines.

Differential equations arise in many areas of science and technology, specifically whenever a deterministic relation involving some continuously varying quantities (modeled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time value varies. Newton's laws allow one (given the position, velocity, acceleration and various forces acting on the body) to express these variables dynamically as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly.

Differential Equation Types:

  1. Linear differential equations.

  2. First-Order Differential Equations

  3. Modeling via Differential Equations

  4. Analytic Technique: Separation of Variables

  5. First-Order Systems

  6. Modeling via Systems

  7. The Geometry of Systems

  8. Euler’s Method for Systems

  9. Linear Systems

  10. Straight Line Solutions

  11. Complex Eigenvalues

  12. Second Order Linear Equations

  13. Forcing and Resonance

  14. Non Linear Systems

  15. Equilibrium Analysis

  16. Halmiltonian Analysis

  17. Laplace Transformations

  18. Numerical Methods

  19. Numerical Error in Euler’s Method

  20. Improving Euler’s Method

  21. The Runge-Kutta Method

  22. Discrete Dynamical Systems

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