Mathematics 105A, Fall 2015

Advanced Mathematics for Science and Engineering, I

Lectures:

Section 1: MWF 10-10:50am, Room 250, Amador Hall,
and Tuesdays 10:30-11:20am, Room 227, Alpine Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Office Hours: MTWRF 9-9:50am Also by appointment.


A description of the course: Math 105A, Fall 2015 (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, December 18, 8-10am




Homework:



Instructions for Formatting Homework

Homework 1, Due Friday, September 4:
Section 7.1 (6, 8, 14, 18)
Section 7.2 (2, 4, 8, 10, 12, 20, 22, 30abc)
Section 7.3 (4, 8)
Additional Problem: Be creative and think of a "real life" example of a linear system of equations. I want material to use in future classes!

Homework 2, Due Friday, September 11:
Section 7.3 (6, 10, 12, 24)
It would be a good idea to start 7.3(24) over the long weekend--it is a "project"...
Section 7.4 (4, 6, 12, 20, 24, 28, 30, 32, 34)


Homework 3, Due Friday, September 18:
Section 7.7 (4, 10, 12, 14) and REVIEW Sections 7.1-7.5 for the EXAM ON MONDAY
Study the text, and practice doing problems.


Homework 4, Due Friday, October 2:
Section 7.8 (6, 8, 10, 16, 18)
Section 8.1 (4, 12, 16, 24)
Section 8.3 (4, 8, 10)


Homework 5, Due Friday, October 9:
Section 8.4 (2, 4, 10, 14, 16)
Section 4.1 (10, 12)


Exam 2 will have problems similar to those in Section 4.3, but for diagonalizable matrices only, at the level of the lectures.

Homework 6, Due Friday, October 23:
Section 9.2 (16, 22, 26, 28, 36)
Section 9.3 (2, 14, 16, 24, 32)
Please get started over the weekend. Problem 24 in Section 9.3 will take longer than the others.


Homework 7, Due Friday, October 30:
Section 9.4 (10, 18, 20)
Section 9.5 (8, 12, 16, 18, 20, 28, 30, 32)
Section 9.7 (2, 4, 16, 18)
Please get started over the weekend.


Homework 8, Due Friday, November 6:
Section 9.7 (14)
Section 9.8 (6, 8, 9abcd)
Section 9.9 (4, 6, 14bd)
Section 10.1 (2, 4, 6, 10)


Homework 9, Due Friday, November 13:
Section 10.1 (8, 16, 18, 20)
Section 10.2 (4, 6, 8, 11, 14, 16, 18)


Homework 10, Due Wednesday, November 25 (or earlier, or Monday, November 30):
Section 10.3 (3, 4, 12)
Section 10.4 (2, 6, 10, 14, 16)
Section 10.5 (2, 4, 6, 14, 16, 18)
In problems 2-6, do three things: (a) find an expression of the form z=f(x,y) or g(x,y,z)=0, (b) sketch the parameter curves, and (c) calculate and sketch N.
In problems 14-18, find a parametric representation of the given surfaces.


Homework 11, Due Monday, December 7:
Section 10.6 (2, 4, 6, 10)
Section 10.7 (2, 4, 6, 8, 10, 12, 18)


Homework 12, Due Friday, December 11:
Section 10.9 (4, 6, 10, 14, 16, 18)


Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

I will occasionally type lecture notes.
DateTopicsBookNotesCode
1. M 8/31 Introduction, Systems of Linear Equations. § 7.1
2. T 9/1 Matrix Algebra, I. § 7.2-7.3
3. W 9/2 Matrix Algebra, II. § 7.2-7.3
4. F 9/4 e.r.o.s and r.r.e.f.s. § 7.3
M 9/7 NO CLASS (Labor Day)
5. T 9/8 Linear Independence, Rank. § 7.4
6. W 9/9 More on Lin. Independence, Vector Spaces. § 7.4
7. F 9/11 Review and Solutions of Linear Systems. § 7.5
8. M 9/14 Determinants, I. § 7.6-7.7
9. T 9/15 Determinants, II. § 7.7
10. W 9/16 Inverses, I. § 7.8
11. F 9/18 Review.
M 9/21 EXAM 1
12. T 9/22 Inverses, II. § 7.8
13. W 9/23 Eigenvectors and Eigenvalues, I. § 8.1
14. F 9/25 Eigenvectors and Eigenvalues, II. § 8.1
15. M 9/28 Symmetric, Skew-Symmetric, and Orthogonal Matrices, I. § 8.3
16. T 9/29 Symmetric, Skew-Symmetric, and Orthogonal Matrices, II. § 8.3
17. W 9/30 Diagonalization, I. § 8.4
18. F 10/2 Diagonalization, II. § 8.4
19. M 10/5 Systems of ODE, I. § 4.1
20. T 10/6 Systems of ODE, II. § 4.2
21. W 10/7 Constant-Coefficient Systems, I. § 4.3
22. F 10/9 Constant-Coefficient Systems, II. § 4.3
23. M 10/12 Special Topics: the Matrix Exponential and Spirals. § 4.3
24. T 10/13 Review.
W 10/14 EXAM 2
25. F 10/16 Review: Dot Product § 9.2
26. M 10/19 Review: Cross Product § 9.3
27. T 10/20 Review: Vector and Scalar Fields. § 9.4
28. W 10/21 Curves, I. § 9.5
29. F 10/23 Curves, II. § 9.5
30. M 10/26 Gradient and Directional Derivative, I. § 9.7
31. T 10/27 Gradient and Directional Derivative, II. § 9.7
32. W 10/28 Divergence. § 9.8
33. F 10/30 Curl. § 9.9
34. M 11/2 Line Integrals, I. § 10.1
35. T 11/3 Line Integrals, II. § 10.2
36. W 11/4 Line Integrals, III. § 10.2
37. F 11/6 Line Integrals, IV. § 10.2 and extra
38. M 11/9 Double Integrals, I. § 10.3
39. T 11/10 Double Integrals, II. § 10.3
W 11/11 NO CLASS (Veteran's Day)
40. F 11/13 Review
M 11/16 EXAM 3
41. T 11/17 Green's Theorem, I. § 10.4
42. W 11/18 Green's Theorem, II. § 10.4
43. F 11/20 Surfaces, I. § 10.5
44. M 11/23 Surfaces, II. § 10.5
45. T 11/24 Surface Integrals, I. § 10.6
46. W 11/25 Surface Integrals, II. § 10.6
R-F 11/26-27 NO CLASS (Thanksgiving)
47. M 11/30 Divergence Theorem, I. § 10.7
48. T 12/1 Divergence Theorem, II. § 10.8
49. W 12/2 Stokes' Theorem, I. § 10.9
50. F 12/4 Stokes' Theorem, II. § 10.9
51. M 12/7 Extra Topics.
52. T 12/8 Extra Topics.
53. W 12/9 Review.
54. F 12/11 Review.
FINAL EXAM: 12/18, 8-10am