Math 319: Techniques in Ordinary Differential Equations (Spring 2017)

Lectures

• Section 319-001 meets on MWF at 12:05-12:55 PM in Van Vleck B130.
• Section 319-003 meets on MWF at 09:55-10:45 AM in Van Vleck B239.

Some important information:

• I will have office hours on Mondays and Wednesdays in Van Vleck 803 from 11:00-11:55 AM.
• If you email me, please always put the number 319 in the subject line, or I might miss your email.
• If anyone is spotted browsing the internet or sending text messages during lectures, their computer or cell phone will be confiscated for the remainder of the lecture (the TAs *do* attend the lectures, and they will be watching carefully). However, taking notes on a tablet PC, or briefly using a computer to look up a formula is acceptable (except on an exam of course).
• Cheating is not allowed, and will result in very serious consequences if you are caught.

Textbook

Discussion Sections and TAs

SECTION	LECTURE	TIME	LOCATION	TEACHING ASSISTANT
301	1	T 12:05--12:55PM	Van Vleck B337	Bingyang Hu
302	1	R 12:05--12:55PM	Van Vleck B337	Bingyang Hu
303	1	T 1:20--2:10PM	Van Vleck B139	Bingyang Hu
344	3	R 9:55--10:45AM	Van Vleck B333	Cullen McDonald
345	3	T 11:00--11:50AM	Van Vleck B333	Cullen McDonald
346	3	R 11:00--11:50AM	Van Vleck B333	Cullen McDonald

Bingyang Hu may be reached at bhu32 "at" wisc.edu. His office hours are on Mondays 3:30-5:30PM in Van Vleck 101-4A.

Cullen McDonald may be reached at crmcdonald2 "at" wisc.edu. His office hours are on Mondays 2:00-3:00 PM and Wednesdays 4:00-5:00 PM in Van Vleck 722.

Examinations, Homework, and Final Grade

• There will be weekly homework assignments, 3 in-class exams, 4 quizzes in discussion, and no final exam.
• The homework will be 100 points total, each exam will be worth 100 points, and each quiz will be worth 25 points, for a grand total of 500 points. Cutoff for A = 450, cutoff for B = 400, cutoff for C = 350, cutoff for D = 300, and below 250 is failing.
• The in-class exams are scheduled for March 3, April 21, and May 3. Exams may not be missed or rescheduled, except with a note from the dean.
• Homework is due at the beginning of lecture on Fridays, unless otherwise noted. No late homework will be accepted.

• HW #1: Due Friday, January 27:
  1. Section 2.1: 13, 14, 16, 18, 33.
  2. Section 2.2: 2, 3, 6, 7 , 8.
• HW #2: Due Friday, February 3:
  1. Section 2.3: 3, 4, 5, 16.
  2. Section 2.5: 3, 9, 10, 12.
• HW #3: Due Friday, February 10:
  1. Section 2.6: 3, 6, 9, 10, 12.
  2. Section 2.7: 1abd, 2abd.
• HW #4: Due Friday, February 17:
  1. Section 3.1: 4 , 5, 10 (no sketch), 11 (no sketch).
  2. Section 3.3: 10, 11, 12, 18 (no sketch), 19 (no sketch).
  3. Section 3.4: 4, 9, 11 (no sketch), 14 (no sketch).
• HW #5: Due Friday, February 24:
  1. Section 3.5: 5, 6, 7, 10, 16, 20.
  2. Section 3.7: 2, 4, 7, 10.
• HW #6: Due Friday, March 10:
  1. Section 6.1: 5ab, 7, 10, 15, 16.
• HW #7: Due Friday, March 17:
  1. Section 6.2: 8, 13, 16.
  2. Section 6.3: 17, 19, 21.
  3. Section 6.4: 1a, 3a, 5a, 9a.
• HW #8: Due Friday, March 31:
  1. Section 6.5: 3a, 5a, 11a.
  2. Section 7.1: 2, 5, 8ab, 11ab.
  3. Section 7.2: 1, 10, 12.
• HW #9: Due Friday, April 7:
  1. Section 7.2: 14, 16.
  2. Section 7.3: 1, 2, 6, 7, 8, 16, 17, 23.
• HW #10: Due Friday, April 14:
  1. Section 7.3: 22, 25.
  2. Section 7.5: 2ab, 4ab, 12, 15.
  3. Section 7.6: 1ab, 3ab, 7, 9.
  4. Note: In part b of the above problems, use the method from class to sketch trajectories.
• HW #11: Due Friday, April 28:
  1. Section 7.7: 4, 5.
  2. Section 7.8: 2c, 3c, 7a.

Topics covered

Brief lecture outline

• Week 1: January 18, 20.
  
  1. Wednesday: Introduction, syllabus, and course overview.
  2. Friday: First and second order ODEs and initial value problems.
  3. Section 2.1: Linear first order equations and integrating factors.
• Week 2: January 23, 25, 27.
  
  1. Monday: Slope fields and integral curves, existence and uniqueness.
  2. Section 2.2, Separable equations.
  3. Wednesday: 2 more examples of separation of variables.
  4. Section 2.3, modeling with first order equations.
  5. Newton's law of cooling.
  6. Friday: Mixture problems.
  7. Begin Chapter 2.5: Autonomous equations and population dynamics.
  8. Population models and logistic equation, solution of logistic equation.
• Week 3: January 31, February 1, 3.
  
  1. Monday: Solutions of logistic and explosion-extinction equations.
  2. Autonomous equations, stable and unstable critical points.
  3. Wednesday: Harvesting a logistic population.
  4. Further examples of autonomous equations.
  5. Friday: Section 2.6, Exact equations (omit integrating factors).
• Week 4: February 6, 8, 10.
  
  1. Monday: Section 2.7, Numerical approximations: Euler's method.
  2. Wednesday: Begin Chapter 3, Second order linear equations.
  3. Principle of superposition.
  4. Equations f'' + f = 0 and f'' - f = 0.
  5. Friday: Section 3.2, linear independence and the Wronskian.
  6. Section 3.1: Constant coefficient equations.
  7. Distinct real roots (Section 3.1) and repeated roots (Section 3.4) of characteristic equation.
• Week 5: February 13, 15, 17.
  
  1. Monday: Review of complex numbers.
  2. Section 3.3: Complex roots of the characteristic equation.
  3. Wednesday: Section 3.5, nonhomogeneous equations; method of undetermined coefficients.
  4. Friday: General method of undetermined coefficients.
• Week 6: February 20, 22, 24.
  
  1. Section 3.7: Mechanical and electrical vibrations.
  2. Monday: Simple pendulum, Electric circuits, undamped motion.
  3. Wednesday: Undamped example.
  4. 3 cases with damping: overdamped, critically damped and underdamped.
  5. Underdamped example.
  6. Friday: Section 3.8, forced vibrations and resonance.
• Week 7: February 27, March 1, 3.
  
  1. Monday: Exam Review.
  2. Wednesday: Section 6.1, The Laplace Transform.
  3. Exam I: Friday, March 3, in-class.
• Week 8: March 6, 8, 10.
  
  1. Section 6.2: Solution of initial value problems using the Laplace Transform.
  2. Section 6.3: Step functions.
• Week 9: March 13, 15, 17.
  
  1. Section 6.4: ODEs with discontinuous forcing functions.
  2. Section 6.5: Impulse functions.
• Week 10: Spring Break, no class.
  
• Week 11: March 27, 29, 31.
  
  1. Begin Chapter 7: Systems of first order linear equations.
  2. Section 7.1: Introduction.
  3. Section 7.2: Review of Matrices.
  4. Determinants.
  5. Transpose, minors, cofactors.
  6. Formula for inverse of a matrix.
• Week 12: April 3, 5, 7.
  
  1. Monday: Section 7.3. Systems of linear equations.
  2. Linear independence.
  3. Wednesday. Eigenvalues and eigenvectors.
  4. Friday: Section 7.4. Basic theory of first order linear equations.
• Week 13: April 10, 12, 14.
  
  1. Monday: Section 7.5. Homogeneous linear systems with constant coefficients.
  2. Wednesday: Section 7.6. Complex eigenvalues.
  3. Friday: Exam review.
• Week 14: April 17, 19, 21.
  
  1. Monday: Section 7.7. Fundamental matrices and matrix exponentials.
  2. Wednesday: Section 7.8. Repeated eigenvalues.
  3. Exam II: Friday, April 21, in-class.
• Week 15: April 24, 26, 28.
  
  1. Chapter 9: Nonlinear differential equations and stability.
• Week 16: May 1, 3.
  
  1. Exam III, Wednesday, May 3, in-class..

Contact Information

Dr. Jeff Viaclovsky
Department of Mathematics
University of Wisconsin
480 Lincoln Drive
Madison, WI 53706

Office: 803 Van Vleck
Office phone: 608-263-1161
e-mail: jeffv@math.wisc.edu