Mathematics 105B, Spring 2016

Advanced Mathematics for Science and Engineering, II

Lectures:

Section 1: MWF 10-10:50am, Room 115, Brighton Hall,
and Tuesdays 10:30-11:20am, Room 115, Eureka Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours: MWF 9-9:50am, Tuesdays and Thursdays 4-5pm, and also by appointment. Please come visit!


A description of the course: Math 105B, Spring 2016 (pdf)

Drop Policy


Announcements:

We will be using the following textbook:
Kreyszig, "Advanced Engineering Mathematics," Sac State Custom Edition, Copyright Year 2013.
It can be found in the Sac State Bookstore. It is identical to the 10th Edition of the book, only with some chapters removed and in paperback, to make it slightly cheaper.


Final Exam Schedule. Please take this into account when registering for classes:
Friday, May 20, 8-10am




Homework:


Instructions for Formatting Homework


Homework 1, Due Friday, January 29:
Section 5.1 (2, 4, 6, 8, 10, 12, 15, 16, 18)
In Problem 16, compare your answer with the exact solution.
A solution to Problem 17, using Mathematica.


Homework 2, Due Monday, February 8:
Section 5.2 (2, 4, 6, 12) Note: Problem 6 requires a computer.
Section 5.3 (4, 6, 8, 16). See my handout below for Lecture 5.
Recommended: Section 5.3 (10)


Review for the Exam on Monday, February 15:
Redo old homework and see the Chapter 5 review questions and problems.


Homework 3, Due Friday, February 19:
Section 5.4 (6, 8, 13, 21, 24)
Note: Answers/hints to the odd problems are in the back of the book.


Homework 4, Due Friday, February 26:
Section 11.1 (12, 16, 18)
Section 11.2 (10, 16, 26)


Homework 5, Due Tuesday, March 8:
Section 11.3 (6, 16)
Section 11.4 (2, 3)
Section 11.5 (5, 6, 10)
Section 11.6 (2, 4)
We are then having a review on Tuesday, and Exam 2 on Wednesday.


Homework 6, Due Wednesday, March 30:
Section 11.7 (6, 8, 14abc, 16)
Section 11.8 (12, 14)
Section 11.9 (2, 6, 10)


Homework 7, Due Friday, April 8:
Section 11.9 (16, 18, 20, 24)
Section 12.1 (4, 8, 10, 14ac, 22)


Homework 8, Due Wednesday, April 13:
Click here for the pdf.


Extra problems on the Method of Characteristics.


Homework 9, Due Friday, May 6:
Section 12.6 (12, 14, 16, 18)
Section 12.7 (2, 7, 8, 14)
Section 12.9 (8, 12)


Homework 10, Due Friday, May 13:
Section 12.9 (18)
Section 12.10 (8, 14, 16, 22)
Section 12.11 (2, 8, 10, 14, 18)




Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

I may occasionally type lecture notes.
DateTopicsBookNotesCode
1. M 1/25 Power Series Method for ODE, I. § 5.1
2. T 1/26 Power Series Method for ODE, II. § 5.1
3. W 1/27 Power Series Method for ODE, III. § 5.1
4. F 1/29 Legendre's Equation. § 5.2
5. M 2/1 the Frobenius Method, I. § 5.3 (pdf) (tex)
6. T 2/2 the Frobenius Method, II. § 5.3 (pdf)
7. W 2/3 Bessel Functions, I. § 5.4
8. F 2/5 Bessel Functions, II. § 5.4
9. M 2/8 Bessel Functions, III. § 5.4
10. T 2/9 Bessel Functions, IV. § 5.5
11. W 2/10 Bessel Functions, V. § 5.5
12. F 2/12 Review.
M 2/15 EXAM 1
13. T 2/16 Fourier Series, I. § 11.1
14. W 2/17 Fourier Series, II. § 11.1 (pdf)
15. F 2/19 Fourier Series, III. § 11.1
16. M 2/22 Half-Range Expansions, I. § 11.2 (pdf)
17. T 2/23 Half-Range Expansions, II. § 11.2 (pdf)
18. W 2/24 Forced Oscillations. § 11.3 (pdf)
19. F 2/26 Approximation by Trig Polynomials. § 11.4
20. M 2/29 Sturm-Liouville Problems, I. § 11.5
21. T 3/1 Sturm-Liouville Problems, II. § 11.5
22. W 3/2 Sturm-Liouville Problems, III. § 11.5 (pdf)
23. F 3/4 Orthogonal Series, I. § 11.6
24. M 3/7 Orthogonal Series, II. § 11.6
25. T 3/8 Review.
W 3/9 EXAM 2
26. F 3/11 Fourier Integrals, I. § 11.7
27. M 3/14 Fourier Integrals, II. § 11.7
28. T 3/15 Fourier Cosine and Sine Transforms, I. § 11.8
29. W 3/16 Fourier Cosine and Sine Transforms, II. § 11.8
30. F 3/18 Fourier Transforms, I. § 11.9
M-F 3/21-25 NO CLASS (Spring Break)
31. M 3/28 Fourier Transforms, II. § 11.9
32. T 3/29 Fourier Transforms, III. § 11.9 (gaussian blur png)
33. W 3/30 Fast Fourier Transform. § 12.1
34. F 4/1 Intro to PDE. § 12.1
35. M 4/4 Modeling with PDE, Separation of Variables. § 12.2, 12.3
36. T 4/5 Separation of Variables and Fourier Series, I. § 12.3
37. W 4/6 Separation of Variables and Fourier Series, II. § 12.3
38. F 4/8 d'Alembert's Solution of the Wave Equation, I. § 12.4
39. M 4/11 the Method of Characteristics.
40. T 4/12 the Heat Equation. § 12.5
41. W 4/13 the Heat Equation and Fourier Series, I. § 12.6
42. F 4/15 the Heat Equation and Fourier Series, II. § 12.6
43. M 4/18 Extra Topics.
44. T 4/19 Review.
W 4/20 EXAM 3
45. F 4/22 the Heat Equation and Fourier Integrals, I. § 12.7
46. M 4/25 the Heat Equation and Fourier Integrals, II. § 12.7
47. T 4/26 Modeling a Membrane. § 12.8
48. W 4/27 Rectangular Membrane, I. § 12.9
49. F 4/29 Rectangular Membrane, II. § 12.9
50. M 5/2 Circular Membrane, I. § 12.10
51. T 5/3 Circular Membrane, II. § 12.10
52. W 5/4 Laplace's Equation in Cylindrical Coordinates. § 12.11
53. F 5/6 Laplace's Equation in Spherical Coordinates. § 12.11 (pdf)
54. M 5/9 Extra Topics.
55. T 5/10 Extra Topics.
56. W 5/11 Extra Topics.
57. F 5/13 Review. (pdf)
FINAL EXAM: 5/20, 8-10am