Math 105A, Spring 2020

Mathematics 105A, Spring 2020

Advanced Mathematics for Science and Engineering, I

Lectures:

Section 1: MWF 10-10:50am, Room 104, Brighton Hall,
and Tuesdays 10:30-11:20am, Room 105, Eureka Hall

Instructor: Michael VanValkenburgh.

Office: Room 140, Brighton Hall
Tentative Office Hours:
Tuesdays 1-2pm and Thursdays 11am-12:50pm, and by appointment

A description of the course: Math 105A, Spring 2020 (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: Tuesday, May 12, 8-10am

Homework:

(If you want an early start, see the webpage from Fall 2018---it will probably be similar.)

Instructions for Formatting Homework

Homework 1, Due Monday, January 27:
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 Tuesday, February 4:
Section 7.3 (6, 10, 12, 24)
Section 7.4 (4, 6, 12, 20, 24, 30)

Homework 3, Due Monday, February 10 (the day of the first exam!!):
Section 7.4 (28, 32, 34)
Section 7.7 (4, 10, 12, 14) and review Sections 7.1-7.5
Also, study the book, and work on as many other problems as you can.

Homework 4, Due Monday, February 24:
Section 7.8 (6, 8, 10, 16, 18)
Section 8.1 (4, 12, 24)
Section 8.3 (8, 10)

Homework 5, Due Monday, March 2:
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, March 4 (Coming up fast!).

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

Exams:

Exams and Solutions are posted on Canvas.

Lecture Schedule

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


		FINAL EXAM: Section 1: Tuesday, May 12, 8-10am