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Title

Differential Equations: Mathematica Computer Laboratory Projects
Author

John H. Mathews
Organization: California State University Fullerton
Department: Mathematics
URL: http://math.fullerton.edu/mathews/
Education level

College
Materials

Course materials online.
Description

These laboratory projects are suitable for the junior-senior level undergraduate ordinary differential equations course. The labs are written in Mathematica 3, but I plan to upgrade them to Mathematica 4 in the near future.

Topics:
  • First Order Linear Differential Equations
  • Solution of Exact Differential Equations
  • The Logistic Equation
  • The Population Model with Harvesting
  • Projectile Motion and Air Resistance
  • Numerical Approximation Methods for Differential Equations
  • Linear Differential Equations with Constant Coefficients
  • The Method of Undetermined Coefficients
  • The Method of Variation of Parameters
  • Mechanical Vibrations
  • Systems of Differential Equations
  • Spring - Mass Systems
  • The Compartment Model
  • Earthquake Induced Vibrations on Buildings
  • The Eigenvalue Method for Solving Differential Equations
  • The Matrix Exponential Solution of Differential Equations
  • Solution of Differential Equations using Laplace Transforms
  • Laplace Transforms Solution of Differential Equations Involving Square Wave Pulses
  • The Convolution Theorem for Laplace Transforms
  • Power Series Solution of Ordinary Differential Equations
  • Frobenius Series Solution of Ordinary Differential Equations
  • Bessel Functions and A Vibrating Drum
  • Fourier Series Expansions
  • Fourier Series Solution of Differential Equations
Subjects

*Applied Mathematics > Numerical Methods
*Mathematics > Calculus and Analysis > Differential Equations