The syllabus for this course is here.
I will be using Mathematica extensively 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/.
I showed an introductory example in Mathematica designed to introduce a number of the major issues we will deal with in this course.
I covered section 2.2.
Mathematica notes containing examples of all of the major methods from chapter 2 are available here.
Section 2.3
Sections 2.4 and 2.5
Section 2.2: 8. Section 2.3: 4, 6c, 8c, 10c. Section 2.4: 2ac. Section 2.5: 8 This homework is due on Monday, October 6.
I started in on chapter 6, covering section 6.1. For those of you who have taken Math 210, much of this will be review. If you have not taken Math 210, you will need to read section 6.1 carefully to learn those aspects of linear algebra we will be using in this course. Here are some supplementary lecture notes, and a Mathematica notebook to demonstrate how to do Gauss elimination steps with Mathematica.
Section 6.2
Sections 6.3 and 6.5
Sections 6.4 and 6.6. Here are some Mathematica notes to go along with this material.
Section 6.1: 6d. Section 6.2: 6d. Section 6.3: 2c. Section 6.5: 4c, 6c, 10. Section 6.6: 6c, 10c, 12c, 16. This homework is due on Friday, Oct. 17.
Sections 7.1 and 7.2
Section 7.3. Here are some lecture notes to explain why the Jacobi algorithm works. I also talked about ways in which the basic algorithm can be made faster. One method is to use a special algorithm for multiplying matrices by vectors. These notes explain how to implement that strategy in a C++ program. Here is a Mathematica notebook that demonstrates the Jacobi, Gauss-Seidel, and SOR algorithms.
Section 7.2: 2df, 4df, 9. Section 7.3: 6c, 8c, 14d, 28. This homework is due on Friday, October 24.
Chapter Three: Mathematica notes are available here.
Section 3.1: 6c, 8c. Section 3.2: 7a. Section 3.3: 2c, 10. This homework is due on Friday, Oct. 31.
The first midterm exam is coming up on Wednesday, October 29. Here are a list of topics for the exam and some sample questions.
Sections 4.1 and 42.
Section 4.3 - here are some Mathematica notes.
Sections 4.4 (Composite Integration) and 4.7 (Gaussian Quadrature). Notes on composite integration appear at the end of these Mathematica notes, while notes on Gaussian Quadrature are here.
Section 4.1: 6b, 8b, 10a, 12a. Section 4.2: 8. Section 4.3: 6c, 8c. Section 4.4: 4b, 11b. Section 4.7: 2g, 4g. These problems are due on Wednesday, November 12.
The Euler method and variations, sections 5.2, 5.3, 5.4. Mathematica lecture notes for this material are here. Here are some additional lecture notes on the midpoint and Runge-Kutta methods.
Section 5.2: 1c, 3c, 6b, 8b. 5.3: 6b, 8b. 5.4: 11a, 15a. These problems are due on Wednesday, November 19.
Section 5.9, systems and higher order equations. Mathematica notes.
Section 5.5, Error estimates and the Runge-Kutta-Fehlberg method. Lecture notes are available here, and Mathematica notes are here.
The second midterm is coming up on Wednesday, November 19. This exam will cover chapters 3 and 4. Here is a list of topics and some sample questions.
Sections 11.1 and 11.2, the shooting method. Here are Mathematica notes.
Sections 11.3 and 11.4, the finite difference method and section 10.2, Newton's Method in several variables. Here are Mathematica notes for section 11.3 and for section 10.2.
Section 5.5: 3c, 3d. Section 5.9: 2c, 4d. Section 11.1: 4bd. Section 11.2: 4ac, 5ac. These problems are due on Wednesday, December 3rd.
Section 11.3: 4bd. Section 11.4: 4ac. Unlike earlier sections, I will not provide Mathematica code to solve the problems from 11.4. Your assignment is to develop the necessary Mathematica code to solve these problems and then solve them. This homework is due on the last day of classes.
Section 12.1, using the method of finite differences to solve elliptic PDEs. Here are Mathematica lecture notes.
The final exam will be on Thursday, December 11 at 1:30 PM. Here is a list of topics to review for the final. We will be using Mathematica for the final, so here is a notebook with useful bits of code that I will allow you to use on the final.