Index of Demonstration Files

Depending on your web browser, you may have to right-click on the links to Excel^® worksheets and/or Maple^® worksheets, save them somewhere on your computer or external drive and open them from the saved location.

Set of standard graphs of some polynomial, exponential and trigonometric functions + conic sections

Illustration of conic sections

1.   First Order ODEs

Tutorial on partial fractions (questions; solutions)
Commands (HTML) for a Maple worksheet for several examples from the lecture notes.
Example 1.5.1   Euler Method   Excel spreadsheet,   Maple worksheet
Example 1.5.2   RK4 Method   Excel spreadsheet

2.   Second Order Linear ODEs

Commands (HTML) for a Maple worksheet for several examples from the lecture notes.
Mass-spring system:   response to a varying amount of damping (PDF)
Example 2.5.1   Modified RK4 Method   Excel spreadsheet,   Maple worksheet
Example 2.5.2   Cauchy-Euler ODE   Maple worksheet

3.   Laplace Transforms

Tutorial examples for complex numbers (PDF) (and solutions)
Commands (HTML) for a Maple worksheet for several examples from the lecture notes.

4.   Partial Differentiation

Example 4.1.1   3D Plot of   Maple worksheet
Commands (HTML) for a Maple worksheet for two examples from Section 4.2 (higher partial derivatives)
Example 4.6.1   3D Plot of surface   Maple worksheet
Example 4.6.2   3D Plot of surface   Maple worksheet
Example 4.6.3   3D Plot of surface   Maple worksheet
Example 4.7.2   3D Plot of intersection of two surfaces   Maple worksheet
Example 4.8.3   Max/min problem with finite boundary (HTML)   +   Maple worksheet

5.   Series

Excel spreadsheets displaying the first six Taylor polynomials and the remainder terms for f (x) = sin x
Section 5.09   Coefficients of a binomial expansion   (1 + x)ⁿ   Excel spreadsheet
Example 5.09.1   Numerical evaluation of the terms and partial sums of a binomial expansion   sqrt(1 + 2x)   Excel spreadsheet
Example 5.10.1   Graphs of some partial sums of a Fourier series   Maple worksheet
Example 5.10.2   Graphs of some partial sums of the Fourier series of the square wave   Maple worksheet
Example 5.10.3   Graphs of some partial sums of the Fourier series of   f (x) = x
                            Maple worksheets for sine series and cosine series
Tutorial example for power series convergence:   Question   Solution
Example 5.11.1   Series solution of an ODE   Maple worksheet
Example 5.11.2   Series solution of an ODE   Maple worksheet
Example 5.11.3   Series solution of an ODE   Maple worksheet + Commands (HTML)