Math 320 Linear Algebra and Differential Equations (Fall 2008)

Lectures

Syllabus

Textbook

Discussion Sections and TAs

Examinations, Homework, and Final Grade

• HW #1: Due Friday, Sep. 12:
  1. Section 1.1: 7, 11, 22, 25.
  2. Section 1.2: 6, 27.
  3. Section 1.3: 22.
  4. Section 1.4: 4, 13, 26, 49.
• HW #2: Due Friday, Sep. 19:
  1. Section 1.5: 9, 13, 17, 31, 32, 36.
  2. Section 1.6: 8, 18, 20, 34, 37.
• HW #3: Due Friday, Sep. 26:
  1. Section 2.1: 5, 9, 28.
  2. Section 2.2: 4, 9, 20, 29.
  3. NOTE: On problems 2.1:5 and 2.2:4,9 above, 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).
  4. Section 2.3: 10
  5. Section 2.4: 4, 8.
• HW #4: Due Friday, October 10:
  1. Section 3.1: 4, 14, 24.
  2. Section 3.2: 12, 17, 24.
  3. Section 3.3: 7, 13, 32, 35.
  4. Section 3.4: 3, 8, 10, 32.
• HW #5: Due Friday, October 17:
  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 24:
  1. Section 4.1: 11, 16, 20, 22, 28, 32, 35.
  2. Section 4.2: 6, 11, 16, 20, 30.
• HW #7: Due Friday, October 31:
  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 #8: Due Friday, November 14:
  1. Section 4.6: 1, 15, 19, 23.
  2. Section 5.1: 9, 12, 26, 34, 39, 46.
• HW #9: Due Friday, November 21:
  1. Section 5.2: 8, 14, 24.
  2. Section 5.3: 6, 9, 12, 16, 23, 26, 33, 40, 41.
• HW #10: Due Monday, December 1:
  1. Section 5.4: 4, 13, 14.
  2. Section 5.5: 4, 10, 32, 33.
  3. Section 5.6: 5, 6.
• HW #11: Due Friday, December 5
  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 Friday, December 12
  1. Section 7.3: 3, 8, 15, 16 (plot by hand using method from class, and label type of critical point).
  2. Section 7.3: 18 (no plot)
  3. Section 7.5: 4 (no plot).

Topics covered

Brief lecture outline

• Lecture 1: Tuesday, September 2
  
  1. Syllabus and introduction.
  2. Section 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 4
  
  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. Implicit solutions.
• Lecture 3: Tuesday, September 9
  
  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 11
  
  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 16
  
  1. Section 1.6: Exact equations.
  2. Reducible second order equations.
  3. Section 2.1: Population models.
  4. Logistic equation.
• Lecture 6: Thursday, September 18
  
  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 23
  
  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 25
  
  1. Euler's method continued.
  2. Section 3.1: Introduction to linear systems.
• Lecture 9: Tuesday, September 30
  
  1. Section 3.2: Matrices and Gaussian elimination.
  2. Review for Exam I.
• Thursday, October 2
  
  1. Exam I. 11:00-12:15. Students in Louis Deaett's discussion sections report to B239. Students in Hanjun Kim's discussion sections report to Chemistry B371.
  2. RESULTS.
• Lecture 10: Tuesday, October 7
  
  1. Section 3.3: Reduced row-echelon matrices.
  2. Section 3.4: Matrix operations.
• Lecture 11: Thursday, October 9
  
  1. Section 3.5: Inverses of Matrices.
• Lecture 12: Tuesday, October 14
  
  1. Section 3.6: Determinants.
• Lecture 13: Thursday, October 16
  
  1. Section 4.1: The vector space R^3.
• Lecture 14: Tuesday, October 21
  
  1. Section 4.2: The vector space R^n and subspaces.
• Lecture 15: Thursday, October 23
  
  1. Section 4.3: Linear combinations and independence of vectors.
• Lecture 16: Tuesday, October 28
  
  1. Section 4.4: Bases and dimension for vector spaces.
  2. Section 4.5: Row spaces and column spaces.
  3. Rank of a matrix.
• Lecture 17: Thursday, October 30
  
  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 18: Tuesday, November 4
  
  1. Exam review.
  2. Go vote!
• Thursday, November 6
  
  1. Exam II. 11:00-12:15. Students in Louis Deaett's discussion sections report to B239. Students in Hanjun Kim's discussion sections report to Chemistry B371.
  2. RESULTS.
• Lecture 19: Tuesday, November 11
  
  1. Section 5.1: Second order linear equations.
• Lecture 20: Thursday, November 13
  
  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 18
  
  1. Section 5.3: Repeated imaginary roots.
  2. Section 5.4: Mechanical Vibrations.
• Lecture 22: Thursday, November 20
  
  1. Section 5.4: Overdamped, critically damped, and underdamped systems.
  2. Section 5.5: Nonhomogeneous equations and undetermined coefficients.
• Lecture 23: Tuesday, November 25
  
  1. Section 5.6: Forced oscillations and resonance.
  2. Section 6.1: Introduction to eigenvalues.
• Thursday, November 27
  
  Thanksgiving vacation.
• Lecture 24: Tuesday, December 2
  
  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 4
  
  1. Section 7.4: Second order systems and mechanical applications.
  2. Section 7.5: Multiple eigenvalue solutions.
• Lecture 26: Tuesday, December 9
  
  1. Section 8.1: Matrix Exponentials.
  2. Section 9.1: Nonlinear Problems: critical points.
• Lecture 27: Thursday, December 11
  
  1. Section 9.2: The Jacobian matrix and linearization.
  2. Remarks on final exam.
  3. Course evaluations.
• Thursday, December 18
  
  Final Exam: 10:05AM - 12:05PM in Van Vleck B102.

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