Mathematics 105A, Fall 2017

Advanced Mathematics for Science and Engineering, I

Lectures:

Section 1: MWF 10-10:50am, Room 127, Library,
and Tuesdays 10:30-11:20am, Room 3004, ARC



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Tentative Office Hours:
M 9-9:50am, T 9-10:15, and WF 11-11:50am. Also by appointment.


A description of the course: Math 105A, Fall 2017 (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:
Friday, December 15, 8-10am




Homework:

(If you want an early start, see the webpage from Fall 2015---it will probably be similar.)

Instructions for Formatting Homework

Homework 1, Due Friday, September 1:
Section 7.1 (6, 8, 14, 18)
Section 7.2 (2, 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 8:
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 15:
Section 7.7 (4, 10, 12, 14) and REVIEW Sections 7.1-7.5 for the EXAM ON MONDAY
Also, study the text, and work on as many other problems as you can.
I will give you a practice exam next week that we will work on together.

Homework 4, Due Friday, September 29:
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 6:
Section 8.3 (16, 20)
Section 8.4 (2, 4, 10, 14, 16)
Section 4.1 (10, 12)
Also, Exam 2 is on Wednesday, October 11.


Homework 6, Due Friday, October 20:
Section 9.2 (16, 22, 26, 28, 36)
Section 9.3 (2, 14, 16, 32)
Recommended, but not required: Section 9.3 (24).

Homework 7, Due Monday, 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)


Homework 8, Due Monday, 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: Additional problems to study for the exam. (Do not turn in.)
Section 10.1 (8, 16, 18, 20)
Section 10.2 (4, 6, 8, 11, 14, 16, 18)
Also, I gave out a practice Exam 3.


Homework 10, Due Wednesday, November 22 (or earlier):
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 Tuesday, December 5 (or earlier):
Section 10.6 (2, 4, 6, 10)
Section 10.7 (2, 4, 6, 8, 10, 12, 18)


Homework 12, Due Friday, December 8:
Section 10.9 (4, 6, 10, 14, 16, 18)


Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

DateTopicsBook
Week 11. M 8/28 Introduction, Systems of Linear Equations. § 7.1
2. T 8/29 Matrix Algebra, I. § 7.2-7.3
3. W 8/30 Matrix Algebra, II. § 7.2-7.3
4. F 9/1 e.r.o.s and r.r.e.f.s. § 7.3
Week 2M 9/4 NO CLASS (Labor Day)
5. T 9/5 Linear Independence, Rank. § 7.4
6. W 9/6 More on Lin. Independence, Vector Spaces. § 7.4
7. F 9/8 Review and Solutions of Linear Systems. § 7.5
Week 38. M 9/11 Determinants, I. § 7.6-7.7
9. T 9/12 Determinants, II. § 7.7
10. W 9/13 Inverses, I. § 7.8
11. F 9/15 Review.
Week 4M 9/18 EXAM 1
12. T 9/19 Inverses, II. § 7.8
13. W 9/20 Eigenvectors and Eigenvalues, I. § 8.1
14. F 9/22 Eigenvectors and Eigenvalues, II. § 8.1
Week 515. M 9/25 Symmetric, Skew-Symmetric, and Orthogonal Matrices, I. § 8.3
16. T 9/26 Symmetric, Skew-Symmetric, and Orthogonal Matrices, II. § 8.3
17. W 9/27 Diagonalization, I. § 8.4
18. F 9/29 Diagonalization, II. § 8.4
Week 619. M 10/2 Systems of ODE, I. § 4.1
20. T 10/3 Systems of ODE, II. § 4.2
21. W 10/4 Constant-Coefficient Systems, I. § 4.3
22. F 10/6 Constant-Coefficient Systems, II. § 4.3
Week 723. M 10/9 Special Topics: the Matrix Exponential and Spirals. § 4.3
24. T 10/10 Review.
W 10/11 EXAM 2
25. F 10/13 Review: Dot Product § 9.2
Week 826. M 10/16 Review: Cross Product § 9.3
27. T 10/17 Review: Vector and Scalar Fields. § 9.4
28. W 10/18 Curves, I. § 9.5
29. F 10/20 Curves, II. § 9.5
Week 930. M 10/23 Gradient and Directional Derivative, I. § 9.7
31. T 10/24 Gradient and Directional Derivative, II. § 9.7
32. W 10/25 Divergence. § 9.8
33. F 10/27 Curl. § 9.9
Week 1034. M 10/30 Line Integrals, I. § 10.1
35. T 10/31 Line Integrals, II. § 10.2
36. W 11/1 Line Integrals, III. § 10.2
37. F 11/3 Line Integrals, IV. § 10.2 and extra
Week 1138. M 11/6 Double Integrals, I. § 10.3
39. T 11/7 Double Integrals, II. § 10.3
40. W 11/8 Review
F 11/10 NO CLASS (Veteran's Day)
Week 12M 11/13 EXAM 3
41. T 11/14 Green's Theorem, I. § 10.4
42. W 11/15 Green's Theorem, II. § 10.4
43. F 11/17 Surfaces, I. § 10.5
Week 1344. M 11/20 Surfaces, II. § 10.5
45. T 11/21 Surface Integrals, I. § 10.6
46. W 11/22 Surface Integrals, II. § 10.6
R-F 11/23-24 NO CLASS (Thanksgiving)
Week 1447. M 11/27 Divergence Theorem, I. § 10.7
48. T 11/28 Divergence Theorem, II. § 10.8
49. W 11/29 Stokes' Theorem, I. § 10.9
50. F 12/1 Stokes' Theorem, II. § 10.9
Week 1551. M 12/4 Extra Topics.
52. T 12/5 Extra Topics.
53. W 12/6 Review.
54. F 12/8 Review.
FINAL EXAM: Friday, 12/15, 8-10am