Mathematics 105B, Spring 2018

Advanced Mathematics for Science and Engineering, II

Lectures:

Section 1: MWF 10-10:50am, Room 141, Calaveras Hall,
and Tuesdays 10:30-11:20am, Room 1020, Mendocino Hall



Instructor: Michael VanValkenburgh.

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


The Official Syllabus:

Math 105B, Spring 2018 (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 18, 8-10am




Homework:


Instructions for Formatting Homework


Homework 1, Due Friday, January 26:
Section 5.1 (2, 4, 6, 8, 10, 12, 15, 16)
In Problem 16, compare your answer with the exact solution.
A solution to Problem 17, using Mathematica.


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


Review for the Exam on Monday, February 12:
Redo old homework, work on the practice exam, and see the Chapter 5 review questions and problems.


Homework 3, Due Friday, February 16:
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 23:
Section 11.1 (12, 16, 18)
Section 11.2 (10, 16, 26)


Homework 5, Due Tuesday, March 6:
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 28:
Section 11.7 (6, 8, 14abc, 16)
Section 11.8 (12, 14)
Section 11.9 (2, 6, 10)


Homework 7, Due Friday, April 6:
Section 11.9 (16, 18, 20, 24)
Section 12.1 (4, 8, 10, 14ac, 22)


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


Extra problems on the Method of Characteristics.


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


Homework 10, Due Friday, May 11:
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
Week 11. M 1/22 Power Series Method for ODE, I. § 5.1
2. T 1/23 Power Series Method for ODE, II. § 5.1
3. W 1/24 Power Series Method for ODE, III. § 5.1
4. F 1/26 Legendre's Equation. § 5.2 (pdf) (tex)
Week 25. M 1/29 the Frobenius Method, I. § 5.3 (pdf) (tex)
6. T 1/30 the Frobenius Method, II. § 5.3 (pdf)
7. W 1/31 Bessel Functions, I. § 5.4
8. F 2/2 Bessel Functions, II. § 5.4
Week 39. M 2/5 Bessel Functions, III. § 5.4
10. T 2/6 Bessel Functions, IV. § 5.5
11. W 2/7 Bessel Functions, V. § 5.5
12. F 2/9 Review.
Week 4M 2/12 EXAM 1
13. T 2/13 Fourier Series, I. § 11.1
14. W 2/14 Fourier Series, II. § 11.1 (pdf)
15. F 2/16 Fourier Series, III. § 11.1
Week 516. M 2/19 Half-Range Expansions, I. § 11.2 (pdf)
17. T 2/20 Half-Range Expansions, II. § 11.2 (pdf)
18. W 2/21 Forced Oscillations. § 11.3 (pdf)
19. F 2/23 Approximation by Trig Polynomials. § 11.4
Week 620. M 2/26 Sturm-Liouville Problems, I. § 11.5
21. T 2/27 Sturm-Liouville Problems, II. § 11.5
22. W 2/28 Sturm-Liouville Problems, III. § 11.5 (pdf)
23. F 3/2 Orthogonal Series, I. § 11.6
Week 724. M 3/5 Orthogonal Series, II. § 11.6
25. T 3/6 Review.
W 3/7 EXAM 2
26. F 3/9 Fourier Integrals, I. § 11.7
Week 827. M 3/12 Fourier Integrals, II. § 11.7
28. T 3/13 Fourier Cosine and Sine Transforms, I. § 11.8
29. W 3/14 Fourier Cosine and Sine Transforms, II. § 11.8
30. F 3/16 Fourier Transforms, I. § 11.9
M-F 3/19-23 NO CLASS (Spring Break)
Week 931. M 3/26 Fourier Transforms, II. § 11.9
32. T 3/27 Fourier Transforms, III. § 11.9 (gaussian blur png)
33. W 3/28 Fast Fourier Transform. § 12.1
F 3/30 NO CLASS (Cesar Chavez Birthday)
Week 1034. M 4/2 Intro to PDE. § 12.1
35. T 4/3 Modeling with PDE, Separation of Variables. § 12.2, 12.3
36. W 4/4 Separation of Variables and Fourier Series, I. § 12.3
37. F 4/6 Separation of Variables and Fourier Series, II. § 12.3
Week 1138. M 4/9 d'Alembert's Solution of the Wave Equation. § 12.4
39. T 4/10 the Method of Characteristics.
40. W 4/11 the Heat Equation. § 12.5
41. F 4/13 the Heat Equation and Fourier Series, I. § 12.6
Week 1242. M 4/16 the Heat Equation and Fourier Series, II. § 12.6
43. T 4/17 Extra Topics.
44. W 4/18 Review.
F 4/20 EXAM 3
Week 1345. M 4/23 the Heat Equation and Fourier Integrals, I. § 12.7
46. T 4/24 the Heat Equation and Fourier Integrals, II. § 12.7
47. W 4/25 Modeling a Membrane. § 12.8
48. F 4/27 Rectangular Membrane, I. § 12.9
Week 1449. M 4/30 Rectangular Membrane, II. § 12.9
50. T 5/1 Circular Membrane, I. § 12.10
51. W 5/2 Circular Membrane, II. § 12.10
52. F 5/4 Laplace's Equation in Cylindrical Coordinates. § 12.11
Week 1553. M 5/7 Laplace's Equation in Spherical Coordinates. § 12.11 (pdf)
54. T 5/8 Extra Topics.
55. W 5/9 Extra Topics.
56. F 5/11 Review. (pdf)
FINAL EXAM: 5/18, 8-10am