The syllabus for this course is here.
We will be using Mathematica as the primary computational tool for this course. Mathematica is available only in the Briggs 419 computer lab. The lab will be open during regular building hours and for limited times in the evening and weekends. Check the schedule posted outside Briggs 419 for details.
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 CDF Player from Wolfram Research to read these files instead. You can download the CDF Player from http://www.wolfram.com/cdf-player/.
I showed a brief introduction to Mathematica.
We started in on chapter 2 of the text: here are lecture notes for section 2.2. You should read section 2.2 in the text.
Sections 2.3-2.5: lecture notes. Also, here is a Mathematica notebook illustrating how to implement the chapter 2 algorithms in Mathematica.
Section 2.2: 2, 8, 10. Section 2.3: 6b, 8b, 26. Section 2.4: 8. Section 2.5: 2, 8, 14.
These problems are due on Monday, April 4.
Gauss elimination: here are lecture notes for section 6.1 and section 6.2. You should read those sections in the text.
Section 6.1: 6bd. Section 6.2: 2a, 4a, 6a, 14b. Section 6.3: 6ac, 10.
These problems are due on Friday, April 8.
Two important applications of Gauss elimination - computing the inverse of a matrix and computing a determinant. Here are lecture notes for section 6.3 and section 6.4. You should read those sections in the text.
section 6.5 - the LU decomposition.
section 6.6 - special factorizations.
Also, here is a Mathematica notebook illustrating how to implement the chapter 6 algorithms in Mathematica.
Section 6.4: 8. Section 6.5: 6c, 9c (do these by hand). Section 6.6: 6cd, 12d, 16, 30.
These problems are due on Wednesday, April 13.
Section 7.1 - vector and matrix norms.
Section 7.2 - eigenvalues and eigenvectors.
Section 7.3 - Jacobi and Gauss-Seidel iteration.
Section 7.4 - SOR method.
Here is a Mathematica notebook illustrating how to implement some of the chapter 7 algorithms in Mathematica.
Section 7.1: 2, 12. Section 7.2: 2d, 10d, 14. Section 7.3: 6c, 8c, 18.
These problems are due on Monday, April 18.
Section 7.5 - Condition numbers and iterative refinement.
Section 7.6 - Conjugate gradient method.
Here is a Mathematica notebook that demonstrates the methods discussed in section 7.6.
Section 7.4: 2c, 4c, 10. Section 7.5: 2d, 4d, 6b. Section 7.6: 2, 6d.
These problems are due on Friday, April 22.
Section 3.1 - Lagrange interpolation.
Section 3.2 - Neville's method.
Here is the Mathematica notebook for chapter 3.
Section 3.3 - Newton's divided difference formula.
Section 3.4 - Hermite polynomials.
Section 3.1: 6c, 8c, 18. Section 3.2: 2c. Section 3.3: 4b, 8. Section 3.4: 2d, 4d, 10.
These problems are due on Monday, May 2.
The first midterm exam is coming up on Wednesday, April 27. This exam will cover chapters 2, 6, and 7. Here is a list of topics to review for the exam.
Chapter 4 - Derivative and Integral formulas. Most of the notes and examples for this chapter are in this Mathematica notebook. Here are additional notes for Sections 4.1 and 4.2 and Section 4.7
Section 4.1: 6b, 8b, 10a, 12a. Section 4.2: 8. Section 4.3: 6c, 8c. Section 4.4: 4b, 11b. Section 4.5: 2b, 16. Section 4.7: 2g, 4g.
These problems are due on Monday, May 9.
Sections 5.1 through 5.3 - lecture notes. Mathematica notes for chapter 5 will appear on Friday.
Section 5.4 - deriving Runge-Kutta type methods. The lecture notes for this section are contained in the Mathematica notes for chapter 5.
Section 5.2: 2b, 6c, 8c. Section 5.3: 2b, 6c, 8c. Section 5.4: 4b, 8b, 16b.
These problems are due on Friday, May 13.
Section 5.5 - The Runge-Kutta-Fehlberg method.
Section 5.9 - Systems of first order equations and higher order equations.
Section 5.5: 2b, 2d. Section 5.9: 2b, 2c, 4b, 4c, 8.
These problems are due on Monday, May 16.
Sections 11.1 and 11.2 - The shooting method for boundary value problems.
Section 11.1: 2, 6. Section 11.2: 2, 4b, 4d.
These problems are due on Wednesday, May 18.
Work day - work on homework sets 9 and 10 in class.
The second midterm exam is coming up on Friday, May 20. This exam will cover chapters 3, 4, and 5. Here is a list of topics to review for the exam.
Section 11.3 - The method of finite differences for linear boundary value problems.
Sections 10.1 and 10.2 - Newton's method for nonlinear systems.
Section 11.4 - The method of finite differences for nonlinear boundary value problems.
Section 11.3: 2, 8. Section 10.2: 2ab, 12. Section 11.4: 4ab, 5ab
These problems are due on Wednesday, May 25.
Work day - work on homework set 11 in class.
Section 12.1 - an introduction to the finite difference method for partial differential equations. Here is a set of Mathematica notes for this section that illustrate both basic and more advanced techniques for solving the kinds of problems that show up in section 12.1.
I showed solutions to selected problems from homework set 11. If you would like a copy of these solutions, please email me.
As a follow-up to problem 12 from section 10.2 I showed the method of steepest descent for non-linear systems. Here are some lecture notes outlining the basics of the method and a Mathematica notebook showing how to use a combination of the method of steepest descent and Newton's method to solve problem 12 more effectively.
The final exam will take place at 3 PM on Tuesday, May 31. The exam will be comprehensive and will cover all of the topics previously listed for the two midterms and the new material since the second midterm: solving boundary value problems by the shooting method and the method of finite differences and Newton's method for nonlinear systems of equations.