SIMIODE Book Mathematica 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.
- Exercise 2.2.8
Logistic growth for a yeast population.
- Exercise 2.2.9
The fall of a shuttlecock.
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.
- Money Matters 2: Some simple codes for computing interest for this project.
- Chemical Kinetics: Some codes for examining chemical reaction rates.
Chapter 3: Numerical Methods
Basic Numerical ODE Methods
An introduction to solving ODEs numerically 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/notebooks 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/notebooks 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 notebooks to facilitate the exercises in Section 3.4. The basic notebook/script above concerning fitting a function to
sample data is also helpful.
- Exercise 3.4.1
- Exercise 3.4.2
- Exercise 3.4.3
- Exercise 3.4.8
- Exercise 3.4.9
- Exercise 3.4.10
- Exercise 3.4.11
Projects
Here are various scripts that aid exploration and analysis of the relevant projects.
- Sublimation of CO2: Code that contains the data and a start on analysis.
- Fish Harvesting: Code that contains the data and a start on analysis.
- The Mathematics of Marriage: Code that contains the data and a start on analysis.
- Shuttlecocks and the Akaike Information Criterion: Code that contains the data and a start on analysis.
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 notebooks/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 notebooks/scripts provide basic instruction in using Mathematica 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 notebooks/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 notebooks/scripts that show how to solve nonhomogeneous linear systems using the Laplace transform, as well as the "Dsolve" command.
Project: LSD Metabolism
Some notebooks/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 notebooks/scripts that illustrate using software to solve systems of ODEs numerically and draw direction fields.
Implicit/Backward Euler's Method
A notebook that implements the backward Euler's method.
Project: Parameter Estimation for Competing Species
Some notebooks/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 notebook to illustrate the computation of a Fourier cosine series.
Discrete Cosine Analysis
A notebook that facilitates the project "Frequency Analysis of Signals".