The syllabus for this course is here.
I will be using Mathematica on occasion in this course, and you are welcome to use it yourself to do your homework. Mathematica is available in the Briggs 419 computer lab. I will not be offering any formal instruction in the use of Mathematica; instead, I will be showing numerous examples in class. If you are interested in reading a Mathematica tutorial, there is a tutorial available in the online help system.
All of the Mathematica files that I am providing below are in the form of Mathematica notebooks. To download these files, right click on the links provided and select the option to download the file to the local disk. You can then open those files in Mathematica. If you are working at a computer that does not have Mathematica installed, you can use the Mathematica Player from Wolfram Research to read these files instead. You can download the Mathematica Player from http://www.wolfram.com/products/player/.
Sections 3.1-3.3.
Section 3.4.
Section 3.5. I also gave a short demonstration of how to use Mathematica to do some simple matrix calculations. The notebook file containing those examples is here.
Section 3.4: 4, 5, 10. Section 3.5: 3, 4, 6. This homework is due on Wednesday, September 23.
Sections 5.1 and 5.2. I also showed how to use Mathematica to do the integrals needed to compute Fourier Sine expansions.
Section 5.1: 2, 5, 7, 8. Section 5.2: 1, 2, 3, 6, 7. Section 5.3: 3bc, 4bc. These problems are due on Monday, Sept. 28.
Sections 5.4 and 5.5
Section 5.6 - using piecewise polynomials with the finite element method. I showed a number of examples in Mathematica. You may also want to look at the the author's Mathematica tutorial, which contains sample calculations for many sections of the text.
Section 5.5: 5, 6. Section 5.6: 3, 4, 5, 6. These problems are due on Friday, Oct. 2.
Section 5.7 - The Green's function method for solving BVPs.
Sections 6.1-6.3 - solving the heat equation in one dimension by the method of Fourier series.
Section 5.7: 7. Section 6.1: 3, 4. Section 6.2: 4. Section 6.3: 3. These problems are due on Monday, Oct. 13
Section 6.4 - solving the heat equation by the finite element method. Here is Mathematica code that implements the necessary computations.
Section 6.5 - finite element method for the heat equation with Neumann boundary conditions. Here is the inevitable Mathematica file to go along with this discussion.
Section 6.6 - The Green's function method for the heat equation and Section 7.1 - D'Alembert's method for the wave equation.
Section 6.4: 5, 6. Section 6.5: 6. Section 6.6: 2. These problems are due on Friday, October 19.
The rest of chapter 7. Here are some examples worked out in Mathematica.
Section 7.1: 1. Section 7.2: 2. Section 7.3: 3. Section 7.4: 4. These problems are due on Friday, Oct. 30.
Section 8.1
Section 8.2
Section 8.3. Here are some examples worked out in Mathematica.
Section 8.4 - finite element method in multiple spatial dimensions. The calculations here require more sophisticated Mathematica techniques, so I have prepared a tutorial to bring you up to speed. Here is the notebook containing the calculations needed to implement the finite element method on a region in the x-y plane.
Section 8.1: 4, 6. Section 8.2: 3, 4, 11. Section 8.3: 2, 3, 8. Section 8.4: 1, 4. These problems are due on Friday, November 6.
Sections 9.1 and 9.2: The discrete Fourier transform and applications.
Section 9.4 - pointwise convergence of Fourier series.
Section 9.1: 2. Section 9.2: 1, 8. These homework problems are due on Monday, November 16.