Mathematics 105A, Fall 2018

Advanced Mathematics for Science and Engineering, I

Lectures:

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

Section 2: MWF 1-1:50pm, Room 105, Brighton Hall,
and Tuesdays 1:30-2:20pm, Room 105, Brighton Hall



Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Tentative Office Hours:
Mondays 11-12, Tuesdays 12-1, Wednesdays 2-3, and Thursdays 2-3

A description of the course: Math 105A, Fall 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:
Section 1: Friday, December 14, 8-10am

Section 2: Monday, December 10, 12:45-2:45pm




Homework:

(If you want an early start, see the webpage from Fall 2017---it will probably be similar.)

Instructions for Formatting Homework

Homework 1, Due Friday, August 31:
Section 7.1 (6, 8, 14, 18)
Section 7.2 (2, 8, 10, 12, 20, 22, 30abc)
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!
Hints: In Section 7.2 (2), give a brief explanation of your answer. In Section 7.2 (10b), you need to prove it for a general mxn matrix A and a general nxp matrix B.


Homework 2, Due Friday, September 7:
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, 30)


Homework 3, Due Friday, September 14:
Section 7.4 (28, 32, 34)
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 28:
Section 7.8 (6, 8, 10, 16, 18)
Section 8.1 (4, 12, 24)
Section 8.3 (8, 10)


Homework 5, Due Friday, October 5:
Section 8.3 (16, 20)
Section 8.4 (4, 10, 14) SEE COMMENTS BELOW
Section 4.1 (10, 12)
Note: the homework in Section 8.4 has some typos. The instructions are:
Verify that A and B=P^(-1)AP have equal eigenvalues. If y is an eigenvector of B, show that x=Py is an eigenvector of A. Show the details of your work.
Also, Exam 2 is on Wednesday, October 10.


Homework 6, Due Friday, October 19:
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 29:
Section 9.4 (10, 18, 20)
Section 9.5 (12, 16, 18, 20, 28, 30, 32)
Section 9.7 (2, 4, 18)


Homework 8, Due Monday, November 5:
Section 9.7 (14)
Section 9.8 (6, 8, 9abcd)
Section 9.9 (4, 6, 14bd)
Section 10.1 (2, 4, 6, 10)
And study for the exam on Friday, November 9.


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. (Do not turn in---mostly review of Calc. 3):
Section 10.3 (3, 4, 12)
Section 10.4 (2, 6, 10)---moved to HW 11
Section 10.5 (2, 4, 6) For these problems, 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.


Homework 11, Due Tuesday, December 4:
Section 10.4 (2, 6, 10)
Section 10.6 (2, 4, 10)
Section 10.7 (2, 6, 10, 12)


Homework 12, for review. (Do not turn in.):
Section 10.9 (4, 6, 10, 16)
It would be good review to try other problems from that section, too (odd answers are in the back).





Exams:

Exams and Solutions are posted on Sac CT.




Lecture Schedule

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