Math 320 Linear Algebra and Differential Equations (Fall 2010 Lec 002)

Lectures

Syllabus

Textbook

Discussion Sections and TAs

Examinations, Homework, and Final Grade

• HW #1: Due Friday, Sep. 10:
  1. Section 1.1: 7, 10, 21, 25.
  2. Section 1.2: 6, 28.
• HW #2: Due Friday, Sep. 17:
  1. Section 1.3: 22.
  2. Section 1.4: 3, 12, 22, 48.
  3. Section 1.5: 8, 14, 16, 31, 32, 37.
• HW #3: Due Friday, Sep. 24:
  1. Section 1.6: 6, 10, 18, 22, 34, 36, 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. 1:
  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 2.4: 4, 7.
  3. Section 3.1: 4, 14, 23.
• HW #5: Due Friday, October 8:
  1. Section 3.2: 12, 18, 24.
  2. Section 3.3: 7, 14, 32, 35.
• HW #6: Due Friday, October 15:
  1. Section 3.4: 3, 8, 10, 31, 32.
  2. Section 3.5: 6, 8, 14, 18, 30, 36.
• HW #7: Due Friday, October 22:
  1. Section 3.6: 3, 10, 14, 25, 28, 36, 38, 52.
  2. Section 4.1: 11, 16, 20, 22, 28, 32, 35.
• HW #8: Due Friday, October 29:
  1. Section 4.2: 6, 11, 12, 16, 20, 30.
  2. Section 4.3: 12, 14, 15, 18, 20.
• HW #9: Due Friday, November 5:
  1. Section 4.4: 2, 8, 14, 20, 24.
  2. Section 4.5: 2, 8, 13, 15.
  3. Section 4.6: 2, 15, 19, 23.
• HW #10: Due Friday, November 12:
  1. Section 5.1: 10, 12, 26, 34, 40, 46.
  2. Section 5.2: 8, 14, 24
• HW #11: Due Friday, November 19:
  1. Section 5.3: 6, 9, 12, 16, 23, 26, 33, 40, 41.
• HW #12: Due Friday, December 3:
  1. Section 5.4: 4, 13, 14.
  2. Section 5.5: 4, 6, 8, 10, 32, 34, 35.
  3. Section 6.1: 10, 20, 30.
• HW #13: Due THURSDAY, December 9, IN CLASS:
  1. Section 7.3: 2, 3, 9, 12, 15 (solve and plot by hand using method from class, and label type of critical point).
  2. Section 7.3: 18, 19.
  3. Section 7.5: 4 (no plot).
• Practice Problems (do not need to hand in)
  1. Section 8.1: 2,3,4,14,22,24.

Topics covered

Brief lecture outline

• Lecture 1: Thursday, September 2
  
  1. Syllabus and introduction.
• Lecture 2: Tuesday, September 7
  
  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 9
  
  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.
• Lecture 4: Tuesday, September 14
  
  1. Section 1.4: Cooling and heating.
  2. Section 1.5: Linear first order equations.
  3. Integrating factors.
  4. Mixture problems.
• Lecture 5: Thursday, September 16
  
  1. Section 1.6: Linear substitutions.
  2. Homogeneous equations.
  3. Bernoulli equations.
  4. Exact equations.
  5. Reducible second order equations.
• Lecture 6: Tuesday, September 21
  
  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 23
  
  1. Section 2.2: Harvesting and stocking.
  2. Bifurcation and dependence on parameters.
  3. Section 2.4: Euler's method.
• Lecture 8: Tuesday, September 28
  
  1. Section 3.1: Introduction to linear systems.
  2. Examples of 3x3 linear systems.
• Lecture 9: Thursday, September 30
  
  1. Section 3.2: Matrices and elementary row operations.
  2. Section 3.2: Gaussian elimination.
  3. Section 3.3: Reduced row-echelon matrices.
• Lecture 10: Tuesday, October 5
  
  1. Section 3.4: Matrix operations.
  2. Exam review.
• Thursday, October 7
  
  1. Exam I. 11:00-12:15, Location: Van Vleck B239.
  2. RESULTS.
• Lecture 11: Tuesday, October 12
  
  1. Section 3.5: Inverses of Matrices.
• Lecture 12: Thursday, October 14
  
  1. Section 3.6: Determinants.
• Lecture 13: Tuesday, October 19
  
  1. Section 4.1: The vector space R^3.
• Lecture 14: Thursday, October 21
  
  1. Section 4.2: The vector space R^n and subspaces.
• Lecture 15: Tuesday, October 26
  
  1. Section 4.3: Linear combinations and independence of vectors.
  2. Section 4.4: Bases and dimension for vector spaces (first part).
• Lecture 16: Thursday, October 28
  
  1. Section 4.4: Bases and dimension for vector spaces cont'd.
  2. Section 4.5: Row spaces and column spaces.
• Lecture 17: Tuesday, November 2
  
  1. Section 4.5: Rank of a matrix.
  2. Non-homogeneous equations.
  3. Section 4.6: Orthogonal vectors in R^n.
  4. Cauchy-Schwarz inequality and triangle inequality.
  5. Orthogonal complements.
  6. Row space = orthogonal complement to Null Space.
• Lecture 18: Thursday, November 4
  
  1. Section 5.1: Second order linear equations.
• Lecture 19: Tuesday, November 9
  
  1. Section 5.2: Higher order linear equations.
  2. Exam Review.
• Thursday, November 11
  
  1. Exam II. 11:00-12:15, Location: Van Vleck B239.
  2. RESULTS.
• Lecture 20: Tuesday, November 16
  
  1. Section 5.3: Constant coefficient equations.
  2. Section 5.3: Complex numbers.
  3. Repeated imaginary roots.
• Lecture 21: Thursday, November 18
  
  1. Section 5.4: Mechanical Vibrations.
  2. Overdamped, critically damped, and underdamped systems.
• Lecture 22: Tuesday, November 23
  
  1. Section 5.5: Nonhomogeneous equations and undetermined coefficients.
• Thursday, November 25
  
  Thanksgiving vacation.
• Lecture 23: Tuesday, November 30
  
  1. Section 6.1: Introduction to eigenvalues.
  2. Section 6.2: Diagonalization of matrices.
• Lecture 24: Thursday, 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: Tuesday, December 7
  
  1. Section 7.3: The eigenvalue method for linear systems cont'd.
  2. Section 7.5: Multiple eigenvalue solutions.
• Lecture 26: Thursday, December 9
  
  1. Section 8.1: Matrix Exponentials.
  2. Remarks on final exam.
  3. Course evaluations.
• Lecture 27: Tuesday, December 14
  
  1. Exam III. 11:00-12:15, Location: Van Vleck B239.
  2. RESULTS TBA.

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