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 Wolframe CDF Player from http://www.wolfram.com/cdf-player/.
Sections 3.1-3.3. Lecture Notes
Section 3.4. Lecture Notes
Section 3.5. Lecture Notes
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 21.
Sections 5.1 to 5.3. Lecture Notes
Here is a Mathematica notebook that shows how to use Mathematica to do the integrals necessary to compute Fourier Sine expansions.
Sections 2.2 and 5.4. Lecture Notes
Section 5.1: 2, 5, 7, 8. Section 5.2: 1, 2, 3, 6, 7. Section 5.3: 3bc, 4bc. Section 5.4: 1, 2, 7. These problems are due on Wednesday, Sept. 28.
Sections 5.5 and 5.6. Lecture Notes
Here is a Mathematica notebook that shows how to use Mathematica to do the integrals necessary to implement the Finite Element form of the Galerkin method.
Sections 6.1 and 6.2. Lecture Notes
Here is a Mathematica notebook that shows how to use Mathematica to solve the heat equation by the method of Fourier series.
Section 5.5: 7, 8. Section 5.6: 5, 6, 7, 9. Section 6.1: 3, 4. Section 6.2: 4. Section 6.4: 5, 6. These problems are due on Wednesday, Oct. 5.
Section 6.4: solving the heat equation by the finite element method. The finite element method will require us to solve or approximate the solution to some systems of first order ODEs. To do this most efficiently, you need to understand some simple methods for solving ODEs numerically. Here is a Mathematica notebook that illustrates some of these techniques. Once you have reviewed the numerical solution techniques, you can go on to work with the notebook that shows how to use these techniques with the finite element method.
Section 6.5: solving the heat equation with Neumann boundary conditions by the finite element method. Here is the Mathematica notebook that shows how to implement these methods.
Sections 7.1 and 7.2. Lecture Notes
Here is a Mathematica notebook that shows how to use Mathematica to solve the wave equation by the method of Fourier series.
Section 7.3, finite element method for the wave equation. Here are lecture notes and a Mathematica notebook
Section 7.5, finite difference method for the wave equation. Here are lecture notes and a Mathematica notebook
Section 6.5: 6. Section 7.1: 1. Section 7.2: 2. Section 7.3: 3. Section 7.5: 4,5. These problems are due on Wednesday, Oct. 12.
Sections 9.1 and 9.2. Here are lecture notes.
Section 9.5, Green's function for the heat equation. Lecture Notes
Section 9.1: 2, 5, 8. Section 9.2: 2. Section 9.5: 4. These problems are due on Wednesday, Oct. 19.
The first midterm exam is coming up on Friday, October 14. The exam will cover chapters 3, 5, and 6. Here is a a list of topics to review and some sample exam questions
Section 9.6, Green's function for the wave equation. Lecture Notes
Section 11.1: Lecture Notes
Section 9.6: 7 Section 11.1: 5, 9, 10 These problems are due on Wednesday, Oct. 26.
Section 11.2: Lecture Notes
Section 11.3: Lecture Notes
Here is a Mathematica notebook to accompany this material.
Section 11.4: The finite element method in multiple spatial dimensions. Here are some lecture notes that explain the basics of the method, and a Mathematica notebook that works out all the gory details. Some of the code in that notebook is fairly advanced. You will need to work through this tutorial workbook before you attempt to understand what is going on in the main notebook.
Section 11.2: 2, 4, 5, 11. Section 11.3: 7. Section 11.4: 1, 6. These problems are due on Friday, Nov. 4.
The second midterm exam is coming up on Wednesday, Nov. 2. The exam will cover chapters 7 and 9. Here is a a list of topics to review and some sample exam questions.
Green's functions for the Laplace operator. Here are lecture notes for section 11.5 and section 11.6.
Sections 12.1 and 12.2, Complex Fourier series and the Fast Fourier Transform. Here are lecture notes and a Mathematica notebook that demonstrates how to use the FFT to compute complex Fourier coefficients.
Convergence theorems for Fourier series. Here are lecture notes for section 12.4 and section 12.5 and a Mathematica notebook to accompany section 12.5.
Section 11.5: 6. Section 11.6: 6. Section 12.1: 1. Section 12.2: 2, 5.
These problems are due on Wednesday, November 16.
Sections 10.1 through 10.3, Sturm-Liouville boundary value problems. Here are lecture notes for sections 10.1 and 10.2, lecture notes for section 10.3 and a pair of Mathematica notebooks with examples.
Sections 8.1 and 8.2, the method of characteristics. Here are lecture notes and a Mathematica notebook that shows some examples of sets of characteristic curves.
The final exam will be on Sunday, November 20 from 3:00-5:30. Here is a review sheet to help you prepare.