Math 320 Linear Algebra and Differential Equations (Fall 2015 Lec 002)

Lectures

Syllabus

Textbook

Discussion Sections and TAs

Examinations, Homework, and Final Grade

• HW #1: Due Friday, Sep. 11:
  1. Section 1.1: 7, 10, 21, 25 (graphing not necessary on 21 and 25).
  2. Section 1.2: 6, 28.
• HW #2: Due Friday, Sep. 18:
  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. 25:
  1. Section 1.6: 6, 10, 18, 22, 34, 36, 37.
• HW #4: Due Friday, Oct. 2:
  1. 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).
  2. 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).
  3. Section 2.4: 4, 7.
• HW #5: Due Friday, October 16:
  1. Section 3.1: 4, 14, 23.
  2. Section 3.2: 12, 18, 24.
  3. Section 3.3: 7, 14, 32, 35.
• HW #6: Due Friday, October 23:
  1. Section 3.4: 3, 8, 10, 31, 32.
  2. Section 3.5: 6, 8, 14, 18, 30, 36.
• HW #7: Due Friday, October 30:
  1. Section 3.6: 3, 10, 14, 28, 36.
  2. Section 4.2: 6, 11, 12, 16, 20.
  3. Section 4.3: 12, 14, 15, 18, 20.
• HW #8: Due Friday, November 6:
  1. Section 4.4: 8, 14, 20, 24.
  2. Section 4.5: 2, 8, 13, 15.
  3. Section 4.6: 2, 15, 19.
• HW #9: Due Friday, November 20:
  1. Section 5.1: 34, 40, 46.
  2. Section 5.2: 14, 24.
  3. Section 5.3: 6, 9, 12, 16, 23, 26, 40, 41.
• HW #10: Due Friday, December 4:
  1. Section 5.5: 4, 6, 8, 10, 32, 34, 35.
  2. Section 6.1: 9, 10, 18, 19, 20, 30, 31.
• HW #11: (do not need to hand in):
  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: 1, 4 (no plot necessary).
  4. Section 8.1: 2,3,4,14,22,24.

Topics covered

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.
• Lecture 3: Thursday, September 10
  
  1. Section 1.2: Vertical motion with gravitational acceleration.
  2. Section 1.3: Slope fields and solutions curves.
  3. Isocline = curve of constant slope.
  4. Existence and uniqueness theorem.
  5. Section 1.4: Separable equations.
  6. Implicit solutions.
• Lecture 4: Tuesday, September 15
  
  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 17
  
  1. Section 1.6: Linear substitutions.
  2. Homogeneous equations.
  3. Bernoulli equations.
  4. Exact equations.
• Lecture 6: Tuesday, September 22
  
  1. Exact equations continued.
  2. Reducible second order equations.
• Lecture 7: Thursday, September 24
  
  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 8: Tuesday, September 29
  
  1. Section 2.2: Harvesting and stocking.
  2. Bifurcation and dependence on parameters.
  3. Section 2.4: Euler's method.
• Lecture 9: Thursday, October 1
  
  1. Euler's method continued.
  2. If convex, then Euler undershoots, if concave, then Euler overshoots.
  3. Section 2.3: Air resistance and terminal velocity, gravitation and escape velocity.
  4. Section 3.1: Introduction to linear systems.
• Lecture 10: Tuesday, October 6
  
  1. Examples of 3x3 linear systems.
  2. Applications to the initial value problem for ODEs.
  3. Exam Review.
• Thursday, October 8
  
  1. Exam I. 11:00-12:15, Location: Van Vleck B130.
• Lecture 11: Tuesday, October 13
  
  1. Section 3.2: Matrices and elementary row operations.
  2. Section 3.2: Gaussian elimination.
  3. Section 3.3: Reduced row-echelon matrices.
• Lecture 12: Thursday, October 15
  
  1. Section 3.4: Matrix operations.
  2. Section 3.5: Inverses of Matrices.
• Lecture 13: Tuesday, October 20
  
  1. Section 3.5 continued.
  2. Section 3.6: Determinants.
• Lecture 14: Thursday, October 22
  
  1. Section 3.6 continued.
  2. Inverse of matrix = transponse of cofactor matrix divided by the determinant.
  3. Gaussian reduction much more efficient.
• Lecture 15: Tuesday, October 27
  
  1. Section 4.1: The vector space R^3.
  2. Section 4.2: The vector space R^n and subspaces.
  3. Section 4.3: Linear combinations and independence of vectors.
• Lecture 16: Thursday, October 29
  
  1. Section 4.3 continued.
  2. Section 4.4: Bases and dimension for vector spaces.
• Lecture 17: Tuesday, November 3
  
  1. Section 4.5: Row spaces and column spaces.
  2. Section 4.5: Rank of a matrix.
  3. Non-homogeneous equations.
  4. Section 4.6: Orthogonal vectors in R^n.
  5. Cauchy-Schwarz inequality and triangle inequality.
• Lecture 18: Thursday, November 5
  
  1. Section 4.6 continued.
  2. Orthogonal complements.
  3. Row space = orthogonal complement to Null Space.
  4. Exam Review.
• Lecture 19: Tuesday, November 10
  
  1. Section 5.1: Second order linear equations.
• Thursday, November 12
  
  1. Exam II. 11:00-12:15, Location: Van Vleck B130.
• Lecture 20: Tuesday, November 17
  
  1. Section 5.2: Higher order linear equations.
  2. Section 5.3: Constant coefficient equations.
  3. Section 5.3: Complex numbers.
• Lecture 21: Thursday, November 19
  
  1. Section 5.3: Repeated imaginary roots.
  2. Section 5.5: Nonhomogeneous equations and undetermined coefficients.
• Lecture 22: Tuesday, November 24
  
  1. Section 6.1: Introduction to eigenvalues.
  2. Section 6.2: Diagonalization of matrices.
• Thursday, November 26
  
  Thanksgiving vacation.
• Lecture 23: Tuesday, December 1
  
  1. Section 7.1: First order systems and applications.
  2. Section 7.2: Matrices and linear systems.
• Lecture 24: Thursday, December 3
  
  1. Section 7.3: The eigenvalue method for linear systems.
  2. Phase plots and types of critical points (terminology from Section 9.1 and 9.2).
• Lecture 25: Tuesday, December 8
  
  1. Section 7.5: Multiple eigenvalue solutions.
  2. Section 8.1: Matrix exponentials.
• Lecture 26: Thursday, December 10
  
  1. Review for Exam III.
  2. Course evaluations.
• Tuesday, December 15
  
  1. Exam III. 11:00-12:15, Location: Van Vleck B130.

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