Math 320 Linear Algebra and Differential Equations (Fall 2009 Lec 002)

Lectures
Lectures are by Jeff Viaclovsky on Tuesdays and Thursdays at 11:00AM-12:15 PM in Van Vleck B239. I will have office hours on Tuesdays and Thursdays in Van Vleck 803 from 4:30 - 5:30 PM.
Syllabus
The syllabus can be found here.
Textbook
Differential Equations and Linear Algebra by Edwards and Penney, third edition.

Discussion Sections and TAs

SECTION	LECTURE	TIME	LOCATION	TEACHING ASSISTANT

321	2	M 09:55--10:45	Van Vleck B123	Akichika Ozeki
322	2	W 09:55--10:45	Van Vleck B123	Akichika Ozeki
323	2	M 12:05--12:55	Van Vleck B119	Diane Holcomb
324	2	W 12:05--12:55	Van Vleck B119	Diane Holcomb
325	2	M 13:20--14:10	Van Vleck B215	Diane Holcomb
326	2	W 13:20--14:10	Van Vleck B215	Diane Holcomb

Akichika Ozeki may be reached at ozeki "at" wisc.edu. His office hours are Mon 11:00AM-12:00PM, Wed 11:00AM-12:00PM in 516 Van Vleck, Phone: 263-2433.
Akichika Ozeki's homepage for 320.

Diane Holcomb may be reached at holcomb "at" math.wisc.edu. Her office hours are Mon 2:30PM-3:30PM, Wed 2:30PM-3:30PM, in 101-23 Van Vleck, Phone: 263-1350.
Diane Holcomb's homepage for 320.

There is also a homework grader, Derek Thompson, who will share grading of the homework with your TA. Email: dsthompson2 "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 8 and November 12. The final exam is at 07:45AM-09:45PM on Sunday, December 20 in Location TBA. 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. 11:
  1. Section 1.1: 7, 10, 21, 25.
  2. Section 1.2: 6, 28.
- HW #2: Due Friday, Sep. 18:
  1. Section 1.3: 22.
  2. Section 1.4: 4, 13, 26, 49.
  3. Section 1.5: 6, 13, 16, 31, 32, 36.
- HW #3: Due Friday, Sep. 25:
  1. Section 1.6: 6, 8, 16, 18, 20, 34, 37.
  2. Section 2.1: 5, 6, 21, 28. NOTE: On problems 5 and 6, use the isocline method from class to draw the slope field, and then use the slope field to sketch solution curves (you don't need to use a computer).
- HW #4: Due Friday, Oct. 2:
  1. Section 2.2: 4, 9, 14, 21, 29. NOTE: On problems 4, 9, and 14, use the isocline method from class to draw the slope field, and then use the slope field to sketch solution curves (you don't need to use a computer).
  2. Section 2.3: 2, 3, 24.
  3. Section 2.4: 4, 7.
- HW #5: Due Friday, October 16:
  1. Section 3.1: 4, 14, 23.
  2. Section 3.2: 11, 18, 24.
  3. Section 3.3: 7, 13, 32, 35.
  4. Section 3.4: 4, 8, 10, 31, 32.
- HW #6: Due Friday, October 23:
  1. Section 3.5: 4, 8, 12, 18, 30, 36.
  2. Section 3.6: 3, 10, 14, 25, 28, 36, 38, 52.
- HW #7: Due Friday, October 30:
  1. Section 4.1: 11, 16, 20, 22, 28, 32, 35.
  2. Section 4.2: 6, 11, 16, 20, 30.
- HW #8: Due Friday, November 6:
  1. Section 4.3: 13, 15, 19, 21.
  2. Section 4.4: 2, 7, 14, 21, 24.
  3. Section 4.5: 2, 8, 13, 15.
- HW #9: Due Friday, November 20:
  1. Section 4.6: 1, 15, 19, 23.
  2. Section 5.1: 9, 12, 26, 34, 39, 46.
- HW #10: Due Monday, November 30:
  1. Section 5.2: 8, 14, 24.
  2. Section 5.3: 6, 9, 12, 16, 23, 26, 33, 40, 41.
- HW #11: Due Friday, December 4:
  1. Section 5.4: 4, 13, 14.
  2. Section 5.5: 4, 6, 8, 10, 32, 34, 35.
- HW #12: Due Monday, December 14:
  1. Section 6.1: 10, 20, 30.
  2. Section 7.3: 2, 3, 9, 12, 15 (solve and plot by hand using method from class, and label type of critical point).
  3. Section 7.3: 18, 19.
  4. Section 7.5: 4 (no plot).
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 6: Section 1.
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: Thursday, September 3
  1. Syllabus and introduction.
- Lecture 2: Tuesday, September 8
  1. Section 1.1: Examples of ODEs.
  2. Newton's law of cooling.
  3. Population equation.
  4. Section 1.2: ODE dy/dx = f(x), solved by integration.
  5. Second order ODEs.
  6. Section 1.2: Vertical motion with gravitational acceleration.
- Lecture 3: Thursday, September 10
  1. Section 1.3: Slope fields and solutions curves.
  2. Isocline = curve of constant slope.
  3. Existence and uniqueness theorem.
  4. Section 1.4: Separable equations.
  5. Implicit solutions.
  6. Section 1.4: Cooling and heating.
- Lecture 4: Tuesday, September 15
  1. Section 1.5: Linear first order equations.
  2. Integrating factors.
  3. Mixture problems.
- Lecture 5: Thursday, September 17
  1. Section 1.6: Linear substitutions.
  2. Homogeneous equations.
  3. Bernoulli equations.
  4. Exact equations.
  5. Reducible second order equations.
- Lecture 6: Tuesday, September 22
  1. Section 2.1: Population models.
  2. Logistic equation.
  3. Explosion-extinction.
  4. Autonomous equations: isoclines are horizontal lines.
  5. Section 2.2: Equilibrium solutions and stability.
- Lecture 7: Thursday, September 24
  1. Section 2.2: Harvesting and stocking.
  2. Bifurcation and dependence on parameters.
  3. Section 2.3: Air resistance.
  4. Gravitational acceleration.
- Lecture 8: Tuesday, September 29
  1. Section 2.4: Euler's method.
  2. Section 3.1: Introduction to linear systems.
- Lecture 9: Thursday, October 1
  1. Section 3.1: Examples of 3x3 linear systems.
  2. Section 3.2: Matrices and elementary row operations.
- Lecture 10: Tuesday, October 6
  1. Section 3.2: Gaussian elimination.
  2. Exam review.
- Thursday, October 8
- Lecture 11: Tuesday, October 13
  1. Section 3.3: Reduced row-echelon matrices.
  2. Section 3.4: Matrix operations.
- Lecture 12: Thursday, October 15
  1. Section 3.5: Inverses of Matrices.
- Lecture 13: Tuesday, October 20
  1. Section 3.6: Determinants.
- Lecture 14: Thursday, October 22
  1. Section 4.1: The vector space R^3.
- Lecture 15: Tuesday, October 27
  1. Section 4.2: The vector space R^n and subspaces.
- Lecture 16: Thursday, October 29
  1. Section 4.3: Linear combinations and independence of vectors.
  2. Section 4.4: Bases and dimension for vector spaces (first couple of pages).
- Lecture 17: Tuesday, November 3
  1. Section 4.4: Bases and dimension for vector spaces cont'd.
  2. Section 4.5: Row spaces and column spaces.
  3. Rank of a matrix.
- Lecture 18: Thursday, November 5
  1. Section 4.6: Orthogonal vectors in R^n.
  2. Cauchy-Schwarz inequality and triangle inequality.
  3. Orthogonal complements.
  4. Row space = orthogonal complement to Null Space.
- Lecture 19: Tuesday, November 10
  1. TBA.
  2. Exam Review.
- Thursday, November 12
- Lecture 20: Tuesday, November 17
  1. Section 5.1: Second order linear equations.
- Lecture 21: Thursday, November 19
  1. Section 5.2: Higher order linear equations.
  2. Section 5.3: Constant coefficient equations.
  3. Section 5.3: Complex numbers.
- Lecture 22: Tuesday, November 24
  1. Section 5.3: Repeated imaginary roots.
  2. Section 5.4: Mechanical Vibrations.
  3. Section 5.4: Overdamped, critically damped, and underdamped systems.
- Thursday, November 26
- Lecture 23: Tuesday, December 1
  1. Section 5.5: Nonhomogeneous equations and undetermined coefficients.
- Lecture 24: Thursday, December 3
  1. Section 6.1: Introduction to eigenvalues.
- Lecture 25: Tuesday, December 8
  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 26: Thursday, December 10
  1. Section 7.3: The eigenvalue method for linear systems cont'd.
  2. Section 7.5: Multiple eigenvalue solutions.
- Lecture 27: Tuesday, December 15
  1. Section 8.1: Matrix Exponentials.
  2. Remarks on final exam.
- Sunday, December 20
Contact Information

Math 320 Linear Algebra and Differential Equations (Fall 2009 Lec 002)

Lectures

Syllabus

Textbook

Discussion Sections and TAs

Examinations, Homework, and Final Grade

Topics covered

Brief lecture outline

Contact Information