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Textbook

Discussion Sections

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 in-class 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 in-class 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 20-23
  1. Section 1.1: Examples of ODEs.
     Newton's law of cooling.
     Population equation.
     Problems: 7, 11, 22, 25.
  2. 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 26-Feb 30
  1. Section 1.4: Separable equations.
     Implicit solutions.
     Cooling and heating.
     Problems: 4, 13, 26, 49.
  2. Section 1.5: Linear first order equations.
     Integrating factors.
     Mixture problems.
     Problems: 9, 13, 17, 31, 32, 36.
  3. 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 2-Feb 6
  1. Section 2.1: Population models.
     Logistic equation.
     Peak Oil. (Not in the text)
     The phase line (= phase diagram see figure 2.2.9).
     Explosion-extinction.
     Problems: 5, 9, 28.
  2. 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.
  3. Section 2.3: Acceleration Velocity Models
     Problems: 10.
• Week 4: Feb 9 - Feb 13
  1. Section 3.1: Introduction to linear systems.
     Problems: 4, 14, 24.
  2. Exam Review
  3. Exam I. Friday Feb 13, 09:55-10:45. Locations TBA
• Week 5: Feb 16 - Feb 20
  1. Section 3.2: Matrices and Gaussian elimination.
     Problems: 12, 17, 24.
  2. Section 3.3: Reduced row-echelon matrices.
     Problems: 7, 13, 32, 35.
  3. Section 3.4: Matrix operations.
     Problems: 3, 8, 10, 32.
• Week 6: Feb 23 - Feb 27
  1. Section 3.5: Inverses of Matrices.
     Problems: 2, 6, 11, 30, 36.
  2. Section 3.6: Determinants.
     Problems: 4, 8, 13, 26, 27, 34, 38, 52.
  3. Section 4.1: The vector space R^3.
     Problems: 11, 16, 20, 22, 28, 32, 35.

• Week 7: Mar 2 - Mar 6
  1. Section 4.2: The vector space R^n and subspaces.
     Problems: 6, 11, 16, 20, 30.
  2. Section 4.3: Linear combinations and independence of vectors.
     Problems: 13, 15, 19, 21.
  3. Section 4.4: Bases and dimension for vector spaces.
     Problems: 2, 7, 14, 21, 24.
• Week 8: Mar 9 - Mar 13
  1. Section 4.5: Row spaces and column spaces.
     Rank of a matrix.
     Problems: 2, 8, 13, 15.
  2. Section 4.6: Orthogonal vectors in R^n.
     Cauchy-Schwarz inequality and triangle inequality.
     Orthogonal complements.
     Row space = orthogonal complement to Null Space.
     Problems: 1, 15, 19, 23.

• Week 9: Mar 23 - Mar 27
  1. Section 4.7. Problems 1-12.
  2. Exam review.
  3. Exam II. Friday Mar 27, 09:55-10:45. Locations TBA
• Week 10: Mar 30 - Apr 3
  1. Section 5.1: Second order linear equations.
     Problems: 9, 12, 26, 34, 39, 46.
  2. Section 5.2: Higher order linear equations.
     Problems: 8, 14, 24.
  3. 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
  1. Section 5.4: Mechanical Vibrations.
     Overdamped, critically damped, and underdamped systems.
     Problems: 4, 13, 14.
  2. Section 5.5: Nonhomogeneous equations and undetermined coefficients.
     Problems: 4, 10, 32, 33.
  3. Section 5.6: Forced oscillations and resonance.
     Problems: 5, 6.
• Week 12: Apr 13 - Apr 17
  1. Section 6.1: Introduction to eigenvalues.
     Problems: 10, 20, 30.
  2. Section 6.2: Diagonalization.
     Problems: 3,4,9,13,34.
  3. Section 7.1: First order systems and applications.
     Problems: 1, 10, 11, 12, 22, 24, 27.
• Week 13: Apr 20 - Apr 24
  1. Section 7.2: Matrices and linear systems.
     Problems: 9, 19, 28.
  2. 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).
  3. Section 7.4: Second order systems and mechanical applications.
     Problems: 1, 3
• Week 14: Apr 27 - May 1
  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.
  2. Section 8.2: Nonhomogeneous linear systems.
     Problems: 17, 18.
• Week 15: May 4 - May 8
  Review and catch up