Math 320 Lecture 1 (Spring 2009)
Linear Algebra and Differential Equations
Professor Joel Robbin
MWF 09:5510:45, Van Vleck B239.
Contact Information
Lecturer:
Professor Joel Robbin
Email: robbin@math.wisc.edu
Office: 313 Van Vleck
Office phone: (608)2634698
Office hours: M 11 AM01 PM, W 11 AM12 PM, or by appointment.
TA: Myoungjean Bae
Email: bae(at)math(dot)wisc(dot)edu
Office: 522 Van Vleck
Office Phone: (608) 2637939
TA: Jonathan Mason
Email: mason(at)math(dot)wisc(dot)edu
Office: 718 Van Vleck
Office Phone: (608) 2620079
Textbook
Differential Equations and Linear Algebra by Edwards and Penney, Second Edition.
I like this textbook and I think that students should find it readable.
Learning to read a book is an important part of an undergraduate
education. You are responsible for all the material in the
assigned sections even if it was not expicitly
mentioned in the lectures.
Discussion Sections
SECTION 
TIME 
LOCATION 
TA 




301 
T 08:5009:40 
6228 Social Science 
Jonathan Mason 
302 
R 08:5009:40 
6228 Social Science 
Jonathan Mason 
303 
T 11:0010:50 
B215 Van Vleck 
Jonathan Mason 
304 
R 11:0011:50 
B215 Van Vleck 
Jonathan Mason 
305 
T 13:2014:10 
B231 Van Vleck 
Myoungjean Bae 
306 
R 13:2014:10 
B231 Van Vleck 
Myoungjean Bae 
Lecture Notes
A summary of the lectures on ODE
from the part of the course before the first exam.
A summary of the lectures on Linear Algebra
from the part of the course between the first and second exam.
This summary will be updated from time to time.
A summary of the lectures on Linear Systems
of Differential Equations
from the part of the course between the second exam and final exam.
This summary will be updated from time to time.
The answers to the first exam.
The answers to the second exam.
I'll post the answers to the final here when I find the time.
Here is the Final Curve
Examinations, Homework, and Final Grade
There will be weekly homework assignments, quizzes (both in lecture
and in the discussion section),
two inclass exams, and a final exam. The homework problems
are on WeBWorK. You can get there from
the Math Department Moodle Home Page.
The exam problems will be like
the examples and problems in the assigned
sections of the text and the WeBWorK problems.
You may also be asked to state definitions and theorems
correctly and provide simple proofs.
Any example or problem from the assigned sections of the text may be a question
on a test.
Exams may not be missed or rescheduled, except with a note from the dean.
For the final grade, the two inclass exams will each be worth 25 percent,
the final exam 40 percent, and
the homework + quizzes + discussion section is worth 10 percent.
Schedule of Lectures and Homework Problems
The problems listed below are representative of the course content.
 Week 1: Jan 2023
 Section 1.1: Examples of ODEs.
Newton's law of cooling.
Population equation.
Problems: 7, 11, 22, 25.
 Section 1.2: ODE dy/dx = f(x), solved by integration.
Vertical motion with gravitational acceleration.
Example of boat crossing a river.
Problems: 6, 27.
 Week 2: Jan 26Feb 30
 Section 1.4: Separable equations.
Implicit solutions.
Cooling and heating.
Problems: 4, 13, 26, 49.
 Section 1.5: Linear first order equations.
Integrating factors.
Mixture problems.
Problems: 9, 13, 17, 31, 32, 36.
 Section 1.6: Substitution methods and exact equations.
Linear substitutions.
Homogeneous equations.
Bernoulli equations.
Exact equations.
Reducible second order equations.
Problems: 8, 18, 20, 34, 37.
 Week 3: Feb 2Feb 6
 Section 2.1: Population models.
Logistic equation.
Peak Oil. (Not in the text)
The phase line (= phase diagram see figure 2.2.9).
Explosionextinction.
Problems: 5, 9, 28.
 Section 2.2: Equilibrium solutions and stability.
Phase diagram, bifurcation and dependence on parameters.
Harvesting and stocking.
Problems: 4, 9, 20, 29.
NOTE: On problems 2.1: 5 and 2.2: 4,9, 29 above,
you don't need to draw the slope field, and
you don't need to use a computer.
 Section 2.3: Acceleration Velocity Models
Problems: 10.
 Week 4: Feb 9  Feb 13
 Section 3.1: Introduction to linear systems.
Problems: 4, 14, 24.
 Exam Review
 Exam I. Friday Feb 13, 09:5510:45. Locations TBA
 Week 5: Feb 16  Feb 20
 Section 3.2: Matrices and Gaussian elimination.
Problems: 12, 17, 24.
 Section 3.3: Reduced rowechelon matrices.
Problems: 7, 13, 32, 35.
 Section 3.4: Matrix operations.
Problems: 3, 8, 10, 32.
 Week 6: Feb 23  Feb 27
 Section 3.5: Inverses of Matrices.
Problems: 2, 6, 11, 30, 36.
 Section 3.6: Determinants.
Problems: 4, 8, 13, 26, 27, 34, 38, 52.
 Section 4.1: The vector space R^3.
Problems: 11, 16, 20, 22, 28, 32, 35.
 Week 7: Mar 2  Mar 6
 Section 4.2: The vector space R^n and subspaces.
Problems: 6, 11, 16, 20, 30.
 Section 4.3: Linear combinations and independence of vectors.
Problems: 13, 15, 19, 21.
 Section 4.4: Bases and dimension for vector spaces.
Problems: 2, 7, 14, 21, 24.
 Week 8: Mar 9  Mar 13
 Section 4.5: Row spaces and column spaces.
Rank of a matrix.
Problems: 2, 8, 13, 15.
 Section 4.6: Orthogonal vectors in R^n.
CauchySchwarz inequality and triangle inequality.
Orthogonal complements.
Row space = orthogonal complement to Null Space.
Problems: 1, 15, 19, 23.
Spring recess Mar 1422 (SN)
 Week 9: Mar 23  Mar 27
 Section 4.7. Problems 112.
 Exam review.

Exam II. Friday Mar 27, 09:5510:45. Locations TBA
 Week 10: Mar 30  Apr 3
 Section 5.1: Second order linear equations.
Problems: 9, 12, 26, 34, 39, 46.
 Section 5.2: Higher order linear equations.
Problems: 8, 14, 24.
 Section 5.3: Constant coefficient equations.
Complex numbers.
Repeated imaginary roots.
Problems: 6, 9, 12, 16, 23, 26, 33, 40, 41.
 Week 11: Apr 6  Apr 10
 Section 5.4: Mechanical Vibrations.
Overdamped, critically damped, and underdamped systems.
Problems: 4, 13, 14.
 Section 5.5: Nonhomogeneous equations and undetermined coefficients.
Problems: 4, 10, 32, 33.
 Section 5.6: Forced oscillations and resonance.
Problems: 5, 6.
 Week 12: Apr 13  Apr 17
 Section 6.1: Introduction to eigenvalues.
Problems: 10, 20, 30.
 Section 6.2: Diagonalization.
Problems: 3,4,9,13,34.
 Section 7.1: First order systems and applications.
Problems: 1, 10, 11, 12, 22, 24, 27.
 Week 13: Apr 20  Apr 24
 Section 7.2: Matrices and linear systems.
Problems: 9, 19, 28.
 Section 7.3: The eigenvalue method for linear systems.
Problems: 2,3, 8, 9, 12, 15, 16, 18.
(Plot by hand and label type of critical point).
 Section 7.4: Second order systems and mechanical applications.
Problems: 1, 3
 Week 14: Apr 27  May 1
 Section 8.1: Matrix exponentials.
Problems: 4*, 5, 6, 9,10, 21.
Also find the exponentials of the matrices in 4, 5, 6.
WARNING: Problem 4 uses techniques which we haven't covered.
 Section 8.2: Nonhomogeneous linear systems.
Problems: 17, 18.
 Week 15: May 4  May 8
Review and catch up
Final Exam 07:45 A.M. THU. MAY 14 Location TBA