Mathematics 421 – Advanced Calculus for Engineering
(01:640:421) – Spring 2008
Sections 01 and 02 – Professor Bumby

General Information

See the main course page for the background of the course.

See the instructor's home page for contact information and office hours of Prof. Bumby.

Current Semester:

The course will use Sakai for all material during the semester. All enrolled students should have automatic access to the site after logging in to Sakai. Current information about syllabus and homework will be found there. Selected material from the Sakai site will be transferred to this page for archival purposes at the end of the course.

Textbook

Dennis G. Zill and Michael R. Cullen ; Advanced Engineering Mathematics (third edition); Jones and Bartlett, 2006; (ISBN# 0-763-74591-X)

Syllabus

This is a copy of the detailed syllabus that evolved on the Sakai site . Each entry shows the lecture date and sections discussed with a few homework problems. Homework was due two class meetings following the assignment date, allowing for questions about the assignment to be discussed in one class meeting between assignment and collection. Only a few problems were assigned to be handed in, but students were encouraged to do similar exercises for practice (and questions about these practice exercises may be raised in class).

1. Jan. 23
   • 4.1: 12, 26, 38.
   • 4.2: 8, 32.
2. Jan. 28
   • 4.2: 16, 18, 24, 36.
   • 4.3: 2, 6, 18, 24.
3. Jan. 30
   • 4.3: 40,46, 56, 64, 68.
   • 4.4: 50, 52.
4. Feb. 04
   • 4.4: 8, 10, 14, 28, 38, 40.
5. Feb. 06
   • 4.5: 4, 8.
   • 4.6: 2, 8.
6. Feb. 11
   • 4.Review: 10, 16, 20, 34, 36.
7. Feb. 13 (due 2/25)
   • 12.1: 2, 4, 8, 14.
8. Feb. 18 (due 2/27)
   • 12.2: 2, 8, 10, 16.
9. Feb. 20
   • Exam: Chapter 4.
10. Feb. 25
    • 12.3: 14, 22, 26.
    • 12.4: 4, 10.
11. Feb. 27
    • Fourier coefficients Supplement:
    • : : : : : : A, B, C.
12. Mar. 03
    • 12.5: 4, 8, 10.
    • 12.6: 16, 22.
13. Mar. 05
    • 12.Review: 8, 14, 20, 22.
14. Mar. 10 (due Mar. 24)
    • 13.1: 4, 8, 14.
    • 13.2: 2, 8.
15. Mar. 12 (due Mar. 26)
    • 13.3: 2, 4.
    • 13.4: 2, 8.
16. Mar. 24
    • Supplement 4: A, B.
    • 13.4: 14, 16.
17. Mar. 26
    • 13.5: 4, 10, 16.
18. Mar. 31
    • 13.6: 10, 14, 18.
19. Apr. 02 (due Apr. 14)
    • 13.Review: 2, 6, 12.
20. Apr. 07 (due Apr. 16)
    • Review: Redo any three problems that were skipped or got a low grade the first time
21. Apr. 09
    • Exam: Chapter 12 and Sections 13.1-4.
22. Apr. 14
    • 13.7: NONE.
    • 13.8: 2.
23. Apr. 16
    • 8.8: 2, 6, 8, 22.
    • 8.10: 2, 6, 14.
24. Apr. 21
    • 8.15: 2, 4, 8.
    • 9.5: 2, 8.
25. Apr. 23
    • 9.8: 12, 14, 22.
    • 9.12: 2, 4.
26. Apr. 28
    • 14.1: NONE.
    • 14.2: NONE.

Supplements

The following supplements produced during the term have been copied here.

1. Using the Laplace transform. An overview of the properties of Laplace transforms.
2. An operational view of Fourier coefficients. A (not completely successful) attempt to apply the operational method used for working with Laplace transforms to Fourier coefficients. The text insists on explicit evaluation of the integrals for the Fourier coefficients every time they are encountered, instead of remembering previous results and quting them when a similar quantity is to be expanded in a Fourier series. In particular, the use of integration by parts to find the Fourier coefficients a function in terms of the coefficients of its derivative exposes one to errors that are easily avoided.
3. Boundary Value Problems. An expanded treatment of the Sturm-Liouville theory. The treatment in the text was far too brief, so these notes gave more details about the eigenfunction expansions that would be used in the solution of the classical partial differential equations.

Other supplements dealt with solutions of individual homework exercises. They will not be made available outside of the Sakai site.

History

There is a similar version of the course from Spring 2006.

Comments on this page should be sent to: bumby AT math.rutgers.edu

This file was last modified on Tuesday August 01, 2017.