Mathematics 105B, Spring 2019

Advanced Mathematics for Science and Engineering, II

Lectures:

Section 1 (200 minutes per week): MWF 10-10:50am, Room 127, Library,
and Tuesdays 10:30-11:20am, Room 127, Library

Section 2 (225 minutes per week): MWF 12-1:15pm, Room 261, Amador Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours: Mondays 9-10am, Tuesdays 12-1pm, Wednesdays 11am-noon, and Fridays 9-10am, and also by appointment. Please come visit!


The Official Syllabus:

Math 105B, Spring 2019 (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.


Basic Needs Support If you are experiencing challenges in the area of food and/or stable housing, help is just a click, email or phone call away! Sacramento State offers basic needs support for students who are experiencing challenges in these areas. Please visit our Basic Needs website to learn more about your options and resources available.
Basic Needs Support webpage.



Final Exam Schedule. Please take this into account when registering for classes:
Section 1: Tuesday, May 14, 8-10am

Section 2: Wednesday, May 15, 10:15am-12:15pm




Homework:


Instructions for Formatting Homework


Homework 1, Due Monday, January 28:
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 Wednesday, February 6 (pushed back due to popular demand):
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).
If you want additional practice problems, most books on differential equations have a section on the Frobenius method (often as a lead-up to Bessel's equation).
Some examples:
Zill's "First Course in Differential Equations" (the standard book for Math 45)
Tenenbaum and Pollard's book on differential equations
Schaum's Outline on differential equations


Review for the Exam on Wednesday, February 13:
Redo old homework, work on the practice exam, and see the Chapter 5 review questions and problems.


Homework 3, Due Wednesday, February 20:
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 Monday, February 25:
Section 11.1 (12, 16, 18)
Section 11.2 (10, 16, 26)
Hint: Remember tricks about integrating odd and even functions! It will make some of the integrals easy.


Homework 5, Due Friday, March 8:
Section 11.3 (6, 16) [Note: in Problem 6, you do NOT need to find the Fourier series.]
Section 11.4 (2)
Section 11.5 (6, 10)
Section 11.6 (4)
Remember that Exam 2 is on Friday March 8.


Homework 6, Due Wednesday, March 27:
Section 11.7 (2, 8, 12) [Note: in Problem 2, for the function on the right side, find B(w).]
Section 11.8 (12, 13) [Be sure to follow the helpful instructions.]


Homework 7, Due Monday, April 8
(it was postponed because of your projects in other classes):
Section 11.9 (2, 6, 16, 18, 20, 24)
Section 12.1 (4, 8, 10, 14ac, 22)


Homework 8, Due Wednesday, April 17:
Click here for the pdf.


Homework 9, Due Monday, May 6: (postponed because some of you have exams)
Section 12.6 (12, 14, 16, 18)
Section 12.7 (2, 8)


Homework 10, as review for the final exam:
Section 12.9 (12, 18)
Section 12.10 (14, 19)
Section 12.11 (8, 10, 14, 18)
Also, please work on the review worksheets.


Exams:

Exams and Solutions are posted on Sac CT.




The following lecture schedule is for Section 1 (10am). The noon section covers the same material, but in three (MWF) 75-minute meetings.



Lecture Schedule

I may occasionally type lecture notes.
DateTopicsBookNotesCode
Week 11. T 1/22 Power Series Method for ODE, I. § 5.1
2. W 1/23 Power Series Method for ODE, II. § 5.1
3. F 1/25 Power Series Method for ODE, III. § 5.1
Week 24. M 1/28 Legendre's Equation. § 5.2 (pdf) (tex)
5. T 1/29 the Frobenius Method, I. § 5.3 (pdf) (tex)
6. W 1/30 the Frobenius Method, II. § 5.3 (pdf)
7. F 2/1 Bessel Functions, I. § 5.4
Week 38. M 2/4 Bessel Functions, II. § 5.4
9. T 2/5 Bessel Functions, III. § 5.4
10. W 2/6 Bessel Functions, IV. § 5.5
11. F 2/8 Bessel Functions, V. § 5.5
Week 412. M 2/11 Fourier Series, I. § 11.1
13. T 2/12 Review.
W 2/13 EXAM 1
14. F 2/15 Fourier Series, II. § 11.1 (pdf)
Week 515. M 2/18 Fourier Series, III. § 11.1
16. T 2/19 Half-Range Expansions, I. § 11.2 (pdf)
17. W 2/20 Half-Range Expansions, II. § 11.2 (pdf)
18. F 2/22 Forced Oscillations. § 11.3 (pdf)
Week 619. M 2/25 Approximation by Trig Polynomials. § 11.4
20. T 2/26 Sturm-Liouville Problems, I. § 11.5
21. W 2/27 Sturm-Liouville Problems, II. § 11.5
22. F 3/1 Sturm-Liouville Problems, III. § 11.5 (pdf)
Week 723. M 3/4 Orthogonal Series, I. § 11.6
24. T 3/5 Orthogonal Series, II. § 11.6
25. W 3/6 Fourier Integrals, I. § 11.7
26. F 3/8 Review.
Week 8M 3/11 EXAM 2
27. T 3/12 Fourier Integrals, II. § 11.7
28. W 3/13 Fourier Cosine and Sine Transforms, I. § 11.8
29. F 3/15 Fourier Cosine and Sine Transforms, II. § 11.8
M-F 3/18-22 NO CLASS (Spring Break)
Week 930. M 3/25 Fourier Transforms, I. § 11.9
31. T 3/26 Fourier Transforms, II. § 11.9
32. W 3/27 Fourier Transforms, III. § 11.9 (gaussian blur png)
33. F 3/29 Fast Fourier Transform. § 12.1
M 4/1 NO CLASS (Cesar Chavez Birthday)
Week 1034. T 4/2 Intro to PDE. § 12.1
35. W 4/3 Modeling with PDE, Separation of Variables. § 12.2, 12.3
36. F 4/5 Separation of Variables and Fourier Series, I. § 12.3
Week 1137. M 4/8 Separation of Variables and Fourier Series, II. § 12.3
38. T 4/9 d'Alembert's Solution of the Wave Equation. § 12.4
39. W 4/10 the Method of Characteristics.
40. F 4/12 the Heat Equation. § 12.5
Week 1241. M 4/15 the Heat Equation and Fourier Series, I. § 12.6
42. T 4/16 the Heat Equation and Fourier Series, II. § 12.6
43. W 4/17 Extra Topics.
44. F 4/19 Review.
Week 13M 4/22 EXAM 3
45. T 4/23 the Heat Equation and Fourier Integrals, I. § 12.7
46. W 4/24 the Heat Equation and Fourier Integrals, II. § 12.7
47. F 4/26 Modeling a Membrane. § 12.8
Week 1448. M 4/29 Rectangular Membrane, I. § 12.9
49. T 4/30 Rectangular Membrane, II. § 12.9
50. W 5/1 Circular Membrane, I. § 12.10
51. F 5/3 Circular Membrane, II. § 12.10
Week 1552. M 5/6 Laplace's Equation in Cylindrical Coordinates. § 12.11
53. T 5/7 Laplace's Equation in Spherical Coordinates. § 12.11 (pdf)
54. W 5/8 Extra Topics.
55. F 5/10 Review. (pdf)
FINAL EXAM, Section 1: 5/14, 8-10am
FINAL EXAM, Section 2: 5/15, 10:15am-12:15pm