SIMIODE Book Maple Resources

Basic ODE Solving

An introduction to solving ODEs symbolically.

Chapter 2 Resources

Direction Fields

Some basic commands for sketching direction fields.

Exercises

Some data and code to aid various exercises.

Projects

The various scripts below do not provide solutions to the projects, just helpful bits of code for easier exploration. Also, the data is already entered.

Chapter 3: Numerical Methods

Basic Numerical ODE Methods

An introduction to solving ODEs numerically in Maple using built-in solvers. Also demos for Euler, improved Euler, and Runge-Kutta fourth order methods. These notebooks and scripts support exercises in Sections 3.1 to 3.3.

Parameter Estimation

This first set of scripts/worksheets show how to fit a function to a sample data set and could form a useful template for Exercises 3.4.1 to 3.4.3, 3.4.8 to 3.4.11, and the projects in Section 3.5. This set of scripts/worksheets shows the computations necessary to fit both k and P in the Hill-Keller model to Usain Bolt's 2008 Olympic data, as was presented in examples in the text.

Exercises

Here are various scripts and worksheets to facilitate the exercises in Section 3.4. The basic worksheet/script above concerning fitting a function to sample data is also helpful.

Projects

Here are various scripts that aid exploration and analysis of the relevant projects.

Chapter 4: Second Order Equations

The computations in Chapter 4 are, for the most part, supported by the above code concerning "Basic ODE Solving".

Projects

Parameter Estimation with Second-Order ODEs: Here are worksheets/scripts to aid with the project in Section 4.6.3.

Chapter 5: The Laplace Transform

Computation of Laplace Transforms and Solving ODEs with the Laplace Transform

These worksheets/scripts provide basic instruction in using Maple to compute Laplace transforms symbolically, and to solve ODEs, including Heaviside and Dirac delta functions.

PID Control Example

Worksheets/scripts to illustrate the incubator PID control method of Section 5.6. In particular, a minor variation of these were used to produce Figure 5.22 in Example 5.44.

Chapter 6: Linear Systems of Differential Equations

Eigenvector and Eigenvalue Analysis

Some worksheets/scripts that show how to solve homogeneous linear systems using eigenvalue/eigenvector techniques, as well as the "dsolve" command.

The Laplace Transform for Systems

Some worksheets/scripts that show how to solve nonhomogeneous linear systems using the Laplace transform, as well as the "dsolve" command.

Project: LSD Metabolism

Some worksheets/scripts that support the LSD pharmacokinetic modeling in Section 6.5.1.

Chapter 7: Nonlinear Systems of Differential Equations

Numerical Solutions and Direction Fields

Some worksheets/scripts that illustrate using software to solve systems of ODEs numerically and draw direction fields.

Implicit or Backward Euler Method

A Maple worksheet to illustrate this method for numerically solving ODEs.

Project: Parameter Estimation for Competing Species

Some worksheets/scripts to aid in the estimation of parameters for the competing yeast species model of Section 7.5.3.

Chapter 8: An Introduction to Partial Differential Equations

Fourier Cosine Series

A Maple worksheeet that illustrates how to compute the terms in a Fourier cosine series.

Discrete Cosine Analysis of Signals

A worksheet that facilitates the project "Frequency Analysis of Signals".