Mathematics 309, Sec. 501, Fall 2020

Linear Algebra for Differential Equations

Last updated Thu 10 Dec 2020

SKIP PAST THE ANNOUNCEMENTS if you so desire ._. (or to near the bottom)

ANNOUNCEMENTS

• 6 Nov:Solutions for the second test are posted at the bottom of the page.
• 21 Oct:Homework deadlines extended: Homework 9 to Monday, Oct.26; Homework 10 to Monday, Nov. 2.
• 16 Oct:Homework assignment 9 has been modified (by removing two problems from the long list for Sec. 5.4).
• 28 Aug: Effective Sept. 4, the Friday office hour will start at 10:30.

COURSE PROCEDURES AND RESOURCES

• ZOOM class meetings: 936 4829 7557 ._. MWF 4:15-5:05
  Students will receive passcodes for classes and office hours through another channel.
• Course handout (syllabus) in DOC equivalent ._. in PDF (Please read.)
• Instructor: S. A. Fulling
  Office: Blocker 620H (but I'm not there during the pandemic)
  ZOOM office hours: 957 9632 7828 ._. T 2-3, R 3-4, F 10:30-11:30
  To preserve the privacy of other students you may be briefly kept in a Zoom waiting room or sent to a breakout room.
  Email: fulling@math.tamu.edu
  
• eCampus (Submit homework; submit group work and read that of others; take tests; check your grades.)
• Instructions for taking a test in eCampus during remote learning
• Groups
• Lecture notes:
  1. My old Math. 311 notes, published as a textbook (Linearity)
  2. Professor Vogel's notes on Fourier series and Bessel functions
  I will frequently, but not always, follow these in class. (This page of lecture notes contains material copyrighted by third parties, so you need to log in using your TAMU NetID username and password. If you have a problem, probably I mistyped your username in the password file; e-mail me.)
• Old (Fall 2018) class home page

WEEKLY SCHEDULE AND ASSIGNMENTS

1. Aug 18-24: (1) The vector concept (2) Systems of linear equations

   Readings

   • Linearity Secs. 1.1 and 1.3. (There is nothing in Leon that precisely corresponds to these.)
   • Leon Sec. 1.1, and start on Sec. 1.2.

   Homework 1 (due Friday, Aug. 28)

   1. From Leon Sec. 1.1 (p. 10): 1(b), 4(b), 5(b).
   2. From Leon Sec. 1.1 (p. 10): 6(a,f,h). (Use row reduction of augmented matrices, of course.)
   3. Essay question: A paleontologist said in a lecture, "In 10,000 BCE, at Lake Baikal the temperature rose 5 degrees Centigrade within 100 years." To make this more meaningful to the general public, a newspaper reporter translated it as, "Twelve thousand years ago, at Lake Baikal the temperature rose 41 degrees Fahrenheit within 100 years." What mistake did the reporter make, and what is the correct number?

2. Aug 25-31: Matrices

   Readings: Leon Secs. 1.2, 1.3, 1.4, and pages 64-66 in Sec. 1.5

   Homework 2 (due Friday, Sept. 4)

   1. Leon Sec. 1.2 (pp. 23-26): 5(c,d,i,k), 10, 21
   2. Leon Sec. 1.3 (pp. 45-46): 1, 9(a,b)
   3. Leon Sec. 1.4 (pp. 58-60): 1, 7, 30
   4. Leon Sec. 1.5 (p. 69): 10(a,b,d,e,f) (You don't need to learn "elementary matrices" from Sec. 1.5 to do these. Use the row-reduction method taught in class.)

3. Sep 1-7: (1) Determinants (2) Definition of a vector space

   Readings

   • Leon Chap. 2. (Linearity Sec. 2.5 will tell you less about determinants than Leon; Secs. 7.1 and 7.2 will tell you more.)
   • Leon Sec. 3.1.

   Homework 3 (due Friday, Sept. 11)

   1. Leon Sec. 2.1 (p. 94): 4(a,b,c)
   2. Leon Sec. 2.2 (p. 100): 2(a), 12
   3. Leon Sec. 2.3 (p. 109): 15(d), 16(a)
   4. Leon Sec. 3.1 (p. 118): 5, 6, 11

4. Sep 8-14: Spanning and linear independence

   Readings: Leon Secs. 3.2 (emphasis on spanning) and 3.3

   Homework 4 (due Friday, Sept. 18)

   1. Leon Sec. 3.2 (p. 129): 11(a,b,d), 12(a,b,e), 14, 15
   2. Leon Sec. 3.3 (pp. 140-141): 1(a,b,d), 2(a.b.e), 4, 5, 8(a,c), 11

5. Sep 15-21: Bases

   Readings: Leon Secs. 3.4 and 3.5

   Homework 5 (due Friday, Sept. 25)

   1. Leon Sec. 3.4 (p. 146): 3, 5(a,b,c), 8, 10
   2. Leon Sec. 3.5 (pp. 156-157): 1(a,c), 2(b,c), 3(a), 5(a,b(i)), 10

6. Sep 22-28: (1) Linear transformations (2) TEST (not including Secs. 3.5, 3.6, and 4.1)

   Readings: Leon Sec. 4.1

   Homework 6 (due Friday, Oct. 2)

   1. Leon Sec. 4.1 (p. 177): 1(a,d,e), 3, 9(a,b), 10

7. Sep 29 - Oct 5: Matrices of linear transformations and changes of basis

   Readings: Leon Secs. 4.2 and 4.3

   Homework 7 (due Friday, Oct. 9)

   1. Leon Sec. 4.2 (pp. 190-192): 2(a), 3, 5(a,b), 6, 13, 14(a), 15, 18(c)
   2. Leon Sec. 4.3 (pp. 197-198): 1(a,d), 2, 6, 15

8. Oct 6-12: Subspaces

   Readings:

   • Leon Secs. 3.2 (review), 3.6
   • Linearity Sec. 5.3

   Homework 8 (due Friday, Oct. 16)

   1. Leon Sec. 3.2 (pp. 128-129): 1. 3(a,d,e,f,g), 6(a,e), 8, 22
   2. Leon Sec. 3.6 (pp. 162-164): 1(a,b), 2, 4(a,b,d,e)), 16, 21, 25
   3. Leon Sec. 4.1 (p. 178): 17, 19, 23, 25

9. Oct 13-19: Inner products and orthogonality

   Readings: Leon Chapter 5. (Omit the 3 applications on pp. 209-215, and Sec. 5.3, and pp. 252-263 except for the 5 properties at top of p. 252. We will come back to pp. 258-263 later.) Leon tells us more about inner products than we have time to absorb in this course; use Linearity Secs. 6.1-6.2 and the lectures based on them as a guide to what I consider most important.

   Homework 9 (due Friday, Oct. 23)

   1. Leon Sec. 5.1 (p. 216): 13
   2. Leon Sec. 5.2 (p. 224): 2
   3. Leon Sec. 5.4 (pp. 246-247): 3, 6, 9, 12, 13, 28 (REVISED 10/16)
   4. Leon Sec. 5.5 (pp. 263-264): 4, 8
   5. Leon Sec. 5.6 (p. 274): 3, 4
   6. Leon Sec. 5.7: 2 (use Gram-Schmidt, not Thm. 7.2)

10. Oct 20-26: Eigenvectors and diagonalization

    Readings: Leon Chapter 6, except Secs. 6.5, 6.7, 6.8

    Homework 10 (due Friday, Oct. 30)

    1. Leon Sec. 6.1 (p. 299): 1(a,c,d,g,h,j), 7, 8
    2. Leon Sec. 6.2 (p. 310): 2(a) (Use the matrix method, of course.)
    3. Leon Sec. 6.3 (p. 327): 1(a,d), 2(a,d), 3(a,c,d)
    4. Leon Sec. 6.4 (p. 340): 5(a,f)
    5. Leon Sec. 6.6 (p. 369): 3(a,c,d), 7(a,b,e)

11. Oct 27 - Nov 2: (1) Introduction to PDEs (2) TEST (through Chapter 6)

    Readings: Vogel Chapters 1 and 2

    Homework 11 (due Friday, Nov. 6)

    1. Vogel Ch. 1 (p. 6): 1, 2
    2. Vogel Ch. 2 (p. 9): 1(c,d), 2, 3

12. Nov 3-9: Fourier series basics

    Readings:

    • Vogel Chapter 3
    • Leon pp. 258-263

    Homework 12 (due Friday, Nov. 13): Vogel Ch. 3 (p. 15), all

13. Nov 10-16: Fourier series solutions

    Readings: Vogel Chapter 4

    Homework 13 (due Friday, Nov. 20): Vogel Ch. 4 (p. 19), all

14. Nov 17-23: Bessel functions

    Readings: Vogel Chapter 5

    Homework: You're welcome to try pp. 25-26, but nobody will grade it.

TEST SOLUTIONS

• Test A
• Test B
• Final Exam

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e-mail: fulling@math.tamu.edu