Math 320 Linear Algebra and Differential Equations (Fall 2007)

Lectures
Lectures are by Jeff Viaclovsky on Tuesdays and Thursdays at 1:00-2:15 PM in Ingraham 19. I will have office hours on Tuesdays and Thursdays in Van Vleck 803 from 2:30 - 3:30 PM.
Syllabus
The syllabus can be found here.
Textbook
Differential Equations and Linear Algebra by Edwards and Penney, second edition.

Discussion Sections and TAs

SECTION	LECTURE	TIME	LOCATION	TEACHING ASSISTANT

331	3	M 11:00--11:50	Van Vleck B113	Wang, Bing
332	3	W 11:00--11:50	Van Vleck B113	Wang, Bing
333	3	M 12:05--12:55	Van Vleck B219	Wang, Bing
334	3	W 12:05--12:55	Van Vleck B341	Wang, Bing
335	3	M 14:25--15:15	Van Vleck B219	Ruiz, Melanie
336	3	W 14:25--15:15	Van Vleck B219	Ruiz, Melanie

Bing Wang may be reached at bwang "at" math.wisc.edu. His office hours are MW 1:15-2:30 PM in Van Vleck 522, Phone: 263-7939.

Melanie Ruiz may be reached at ruiz "at" math.wisc.edu. Her office hours are W 1-2 and F 1-3 in Van Vleck 101-1, Phone: 263-9720.

There is also a homework grader, Vidoot Ponnala, who will share grading of the homework with your TA. Email: ponnala "at" wisc.edu.

Examinations, Homework, and Final Grade
There will be weekly homework assignments, 2 in-class exams, and a final exam. The in-class exams are scheduled for October 4 and November 8. The final exam is at 5:05 PM on Monday, December 17. Exams may not be missed or rescheduled, except with a note from the dean. Homework is due on Fridays by 5 PM. It should be given directly to your TA, there will be a box outside of their office. No late homework will be accepted! For the final grade, the two in-class exams will each be worth 20 percent, the final exam 30 percent, and the homework + discussion section is worth 30 percent. See the syllabus for more information on exam policies, grading, etc.
- HW #1: Due Friday, Sep. 14:
  1. Section 1.1: 8, 10, 21, 25.
  2. Section 1.2: 6, 28.
  3. Section 1.3: 22.
  4. Section 1.4: 2, 13, 26, 49.
- HW #2: Due Friday, Sep. 21:
  1. Section 1.5: 6, 13, 16, 31, 32, 36.
  2. Section 1.6: 6, 16, 24, 32, 37.
- HW #3: Due Friday, Sep. 28:
  1. Section 2.1: 6, 10, 12, 21, 29.
  2. Section 2.2: 3, 11, 21, 22, 29.
  3. Section 2.4: 5, 7.
- HW #4: Due Friday, October 12:
  1. Section 3.1: 5, 13, 23.
  2. Section 3.2: 11, 18, 25.
  3. Section 3.3: 9, 10, 32, 35.
  4. Section 3.4: 8, 10, 31, 32.
- HW #5: Due Friday, October 19:
  1. Section 3.5: 2, 6, 11, 30, 36.
  2. Section 3.6: 4, 8, 13, 26, 27, 34, 38, 52.
- HW #6: Due Friday, October 26:
  1. Section 4.1: 11, 16, 20, 22, 28, 32, 35.
  2. Section 4.2: 6, 11, 16, 20, 30.
- HW #7: Due Friday, November 2:
  1. Section 4.3: 13, 15, 19, 21, 22.
  2. Section 4.4: 2, 7, 14, 21, 23, 24.
- HW #8: Due Friday, November 16:
  1. Section 4.5: 2, 8, 13, 15.
  2. Section 4.6: 1, 15, 19, 23.
  3. Section 5.1: 9, 12, 26, 34, 39, 46.
- HW #9: Due Monday, November 26:
  1. Section 5.2: 10, 13, 16, 24.
  2. Section 5.3: 8, 12, 20, 23, 26, 33, 38, 40, 41.
- HW #10: Due Friday, November 30
  1. Section 5.4: 4, 13, 14, 16.
  2. Section 5.5: 4, 10, 17, 32, 33.
  3. Section 5.6: 2, 18.
- HW #11: Due Friday, December 7
  1. Section 6.1: 10, 20, 30.
  2. Section 7.2: 9, 19, 28.
  3. Section 7.3: 2, 9, 12 (graphing not necessary).
- HW #12: Due Thursday, December 13 (bring to class, no late homeworks accepted).
  1. Section 7.3: 2, 9, 12 (plot by hand using method from class, keep a copy of HW 11).
  2. Section 7.3: 15, 16 (with plot).
  3. Section 7.3: 18.
  4. Section 7.5: 2, 5 (with hand plot).
  5. Section 7.5: 7, 16.
- Topics covered
  The plan is to cover material from the following sections of Edwards and Penney:
  
  Chapter 1: Sections 1-6.
  Chapter 2: Sections 1-5.
  Chapter 3: Sections 1-6.
  Chapter 4: Sections 1-4.
  Chapter 5: Sections 1-6.
  Chapter 7: Sections 1-3, 5.
  Chapter 8: Sections 1-2.
  Chapter 9: Sections 1-2.
  
  This plan is approximate, and might change depending on time constraints. The following brief lecture outline will be more accurate, and will be updated very frequently.
- Brief lecture outline
  - Lecture 1: Tuesday, September 4
    1. Syllabus and introduction.
    2. Sections 1.1: Examples of ODEs.
    3. Newton's law of cooling.
    4. Population equation.
    5. Section 1.2: ODE dy/dx = f(x), solved by integration.
    6. Second order ODEs.
  - Lecture 2: Thursday, September 6
    1. Section 1.2: Vertical motion with gravitational acceleration.
    2. Example of boat crossing a river.
    3. Section 1.3: Slope fields and solutions curves.
    4. Isocline = curve of constant slope.
    5. Existence and uniqueness theorem.
    6. Section 1.4: Separable equations.
    7. Derivation of solution of y'' = - y.
    8. Implicit solutions.
  - Lecture 3: Tuesday, September 11
    1. Section 1.4: Cooling and heating.
    2. Section 1.5: Linear first order equations.
    3. Integrating factors.
    4. Mixture problems.
  - Lecture 4: Thursday, September 13
    1. Section 1.6: Substitution methods and exact equations.
    2. Linear substitutions.
    3. Homogeneous equations.
    4. Bernoulli equations.
    5. Exact equations.
  - Lecture 5: Tuesday, September 18
    1. Section 1.6: Exact equations.
    2. Reducible second order equations.
    3. Section 2.1: Population models.
    4. Logistic equation.
  - Lecture 6: Thursday, September 20
    1. Section 2.1: Example of logistic equation.
    2. Section 2.1: Explosion-extinction.
    3. Section 2.2: Equilibrium solutions and stability.
    4. Harvesting and stocking.
  - Lecture 7: Tuesday, September 25
    1. Section 2.2: Bifurcation and dependence on parameters.
    2. Section 2.3: Air resistance.
    3. Section 2.4: Numerical approximation: Euler's method.
  - Lecture 8: Thursday, September 27
    1. Section 3.1: Introduction to linear systems.
  - Lecture 9: Tuesday, October 2
    1. Section 3.2: Matrices and Gaussian elimination.
  - Thursday, October 4
  - Lecture 10: Tuesday, October 9
    1. Exam summary.
    2. Section 3.3: Reduced row-echelon matrices.
    3. Section 3.4: Matrix operations.
  - Lecture 11: Thursday, October 11
    1. Section 3.5: Inverses of Matrices.
  - Lecture 12: Tuesday, October 16
    1. Section 3.6: Determinants.
  - Lecture 13: Thursday, October 18
    1. Section 4.1: The vector space R^3.
  - Lecture 14: Tuesday, October 23
    1. Section 4.2: The vector space R^n and subspaces.
  - Lecture 15: Thursday, October 25
    1. Section 4.3: Linear combinations and independence of vectors.
  - Lecture 16: Tuesday, October 30
    1. Section 4.4: Bases and dimension for vector spaces.
    2. Section 4.5: Row spaces.
  - Lecture 17: Thursday, November 1
    1. Section 4.5: Column spaces.
    2. Section 4.6: Inner products.
    3. Cauchy-Schwarz inequality.
  - Lecture 18: Tuesday, November 6
    1. Section 4.6: Orthogonal vectors in R^n.
    2. Triangle inequality
    3. Orthogonal complements.
    4. Exam review.
  - Thursday, November 8
  - Lecture 19: Tuesday, November 13
    1. Section 5.1: Second order linear equations.
  - Lecture 20: Thursday, November 15
    1. Section 5.2: Higher order linear equations.
    2. Section 5.3: Constant coefficient equations.
    3. Section 5.3: Complex numbers.
  - Lecture 21: Tuesday, November 20
    1. Section 5.3: Repeated imaginary roots.
    2. Section 5.4: Mechanical Vibrations.
  - Thursday, November 22
  - Lecture 22: Tuesday, November 27
    1. Section 5.5: Nonhomogeneous equations and undetermined coefficients.
    2. Section 5.6: Forced oscillations and resonance.
  - Lecture 23: Thursday, November 29
    1. Section 6.1: Introduction to eigenvalues.
  - Lecture 24: Tuesday, December 4
    1. Section 7.1: First order systems and applications.
    2. Section 7.2: Matrices and linear systems.
    3. Section 7.3: The eigenvalue method for linear systems.
  - Lecture 25: Thursday, December 6
    1. Section 7.4: Second order systems and mechanical applications.
    2. Section 7.5: Multiple eigenvalue solutions.
  - Lecture 26: Tuesday, December 11
    1. Chapter 9: Nonlinear problems.
  - Lecture 27: Thursday, December 13
    1. Review for final.
    2. Course evaluations.
  - Monday, December 17
  Contact Information

Math 320 Linear Algebra and Differential Equations (Fall 2007)

Lectures

Syllabus

Textbook

Discussion Sections and TAs

Examinations, Homework, and Final Grade

Topics covered

Brief lecture outline

Contact Information