Math 3280 Differential Equations and Linear Algebra Syllabus, Fall 2017

This page will be updated throughout the semester.

Practice tests    Worksheets     Homework     Labs     Resources

Instructor:

Dr. Marshall Hampton

Office: 172 SCC

Email: mhampton at d.umn.edu (preferred contact method)

Telephone: 726-6329

Office hours: 12:00 - 1:30 Monday, Tuesday, and Wednesday.

Class homepage:
http://www.d.umn.edu/~mhampton/m3280f17.html (this page)

Lecture Times:
Section 007: 11:00 P.M. - 11:50 P.M., M, W, Th, F (8/28/2017 - 12/8/2017), SCC 21.

Lab (008) Times:
11:00 P.M. - 11:50 P.M., Tu, MonH 209

Lab TA: Richa Rawat
SCC 152, OH: 1:30-3:30 Tu, 9:30-11:30 MF.

Prerequisites:
Math 1297 (Calculus II) or equivalent. Examples of expected knowledge and avoidable errors.

Student Conduct Code:
see the full description at http://regents.umn.edu/sites/default/files/policies/Student_Conduct_Code.pdf.
Note that while collaborating on homework and lab assignments is encouraged, it is not acceptable to simply copy another person's work.

Textbook:
Differential Equations and Linear Algebra, 2nd, 3rd, or 4th Edition, Edwards and Penney, Prentice-Hall, is our primary textbook. It does not matter which edition of the text you have.

Topics:
This course will build on your knowledge of calculus, extending it to differential equations. In addition to their intrinsic mathematical interest, differential equations are applied in a wide variety of fields. In order to understand systems of linear differential equations, we will also learn some basic linear algebra. We will try to cover some sections from every chapter of the book, although more attention will be given to chapters 1 through 7. These will be covered at a pace of roughly one chapter per week.

Primary topic outline by section (subject to revision and adjustment):
Week 1: Introduction, slope fields and separable ODES Ch 1.1 - 1.3
Week 2: 1st order ODEs and numerical methods Ch 1.4-1.6, 2.4-2.6
Week 3: Autonomous ODEs, 1D equilibria, compartment models Ch 2.1 - 2.4, 3.1-3.3
Week 4: Matrix Algebra: row reduction, inversion 3.1 - 3.5
Week 5: Determinants, Vector Spaces 3.6 - 4.1
Week 6: Vector Spaces: bases, linear independence, subspaces, spans 4.1 - 4.6
Week 7: 2nd order ODEs and review 5.1 - 5.2
Week 8: Higher order ODEs, numerics 5.3 - 5.6
Week 9: Eigenvectors and eigenvalues 6.1 - 6.3
Week 10: Systems of differential equations 7.1 - 7.5
Week 11: Review
Week 13: Laplace Transform 10.1 - 10.5
Week 14: Nonlinear Systems 9.1 - 9.4
Week 15: Review

In the learning objectives below, W=worksheet, H=homework, L = labs, A=midterm 1, B=midterm 2, and F = final.
Primary Learning Objectives Required by the Higher Learning Commission.
  1. Recognize and solve linear and separable ODEs. (H,W,A,F)
  2. Use linear ODEs to model physical phenomena. (H,W,A,F)
  3. Apply the existence and uniqueness theorem to first order ODES. (H,W,A,F)
  4. Approximate solutions of initial value problems using numerical methods such as Euler's method and the fourth-order Runge-Kutta method. (H,W,L,A,F)
  5. Compute the location and stability of equilibria of autonomous ODEs. (H,W,A,F)
  6. Use numerical methods to model 2nd order ODEs, such as nonlinear air resistance models.(H,W,A,F)
  7. Use row reduction of matrices to solve linear systems, invert matrices, determine linear independence of vectors, and efficiently compute determinants.(H,W,A,F)
  8. Compute matrix products.(H,W,L,A,F)
  9. Recognize whether or not a given subset of a vector space is a vector subspace.(H,W,B,F)
  10. Use the Wronskian of a set of functions to determine whether or not they are linearly dependent.(H,W,B,F)
  11. Solve higher order homogeneous linear initial value problems by factoring their characteristic polynomials.(H,W,B,F)
  12. Solve linear nonhomogeneous ODEs using the method of undetermined coefficients.(H,W,B,F)
  13. Interpret linear ODEs in the context of mechanical oscillations.(H,W,L,B,F)
  14. Rewrite a linear system of ODEs as an equivalent first order system.(H,W,B,F)
  15. Use eigenvalues and eigenvectors to solve linear systems of ODEs.(H,W,F)
  16. Diagonalize a matrix using its eigenvectors and eigenvalues.(H,W,F)
  17. Use numerical methods to approximate systems of ODEs.(H,W,L,F)
  18. Use the Laplace transform to solve initial value problems.(H,W,F)
  19. Compute the linearization of nonlinear ODEs around their equilibria, and compute their stability.(H,W,F)

Exams:
There will be two midterms (10/6 and 11/10) and a final exam (12/13, 10-12 am). A calculator and sheet of notes is allowed on each exam. For the final you can use two pages of notes.

Practice exams:
Practice tests for the midterms and final will be posted here 1 week before the relevant exam.

Practice midterm 1

Practice midterm 1 solutions

Practice midterm 2

Practice midterm 2 solutions

Practice final

Practice final solutions


Calculator Policy:
Calculators are allowed during exams (note: an internet-capable device is not considered a calculator). However, you are expected to show the steps that justify your answers, and to give exact answers whenever possible. This also applies to homework unless the question specifically instructs you to use a computer or calculator. On a test, any step on which you use a calculator must be clearly indicated (just write "CALCULATOR" or "CALC").

Grading:
Grades will be based on your understanding of the material as demonstrated by class participation (mainly worksheets), office hours, homework, labs, and exams. The homework assignments will be weighted equally, with the lowest score dropped. The lowest lab score will also be dropped. The lowest three worksheet scores will be dropped. The approximate weighting is homework is 20%, each midterm 15%, labs 10%, worksheets 15%, and the final exam is 25%. Note that I do not use traditional grading percentages, although generally a score of around 90% of the total is sufficent for an A.


Worksheets:
W 1 Some calculus review.
W 2 Separable ODEs.
W 3 Existence and uniqueness of ODES.
W 4 Slope fields.
W 5 Linear ODEs.
W 6 Compartment modeling.
W 7 Euler's Method.
W 8 Improved Euler and Runge-Kutta.
W 9 Equilibria.
W 10 Bifurcation analysis.
W 11 Linear air resistance.
W 12 Linear systems.
W 13 RREF.
W 14 Matrix multiplication.
W 15 Matrix inversion.
W 16 Determinants.
W 17 Determinants part II.
W 18 Curve-fitting.
W 19 Vector spaces.
W 20 Linear dependence.
W 21 Review.
Review.
W 22 Solution bases.
W 23 2nd order ODEs.
W 24 more 2nd order ODEs.
W 25 Nonhomogeneous 2nd order ODEs.
W 26 More nonhomogeneous 2nd order ODEs.
W 27 Nth order odes to n first order systems.
W 28 The Wronskian.
W 29 Eigenvectors and eigenvalues.
W 30 Forced damped oscillators.
W 31 Complex eigenvectors and eigenvalues.
W 32 1st order linear systems.
W 33 Linear algebra review.
Midterm 2 review .
Midterm 2 review solutions .
W 34 Oscillating first order system.
W 35 Vectorial Euler's method.
W 36 Three tanks.
W 37 Oscillator systems.
W 38 The Laplace transform.
W 39 Laplace transforms for IVPs.
W 40 Periodic Laplace transforms.
W 41 Laplace transform for systems.
W 42 Linearizing 2D systems.
W 43 Trace, det, 2d linear systems.
W 44 Of Wolves and Moose.
W 45 IVP/numerics review.
W 46 Review.
W 46 Review solutions.

Homework:
Late homework is not accepted without a prior arrangement. Your answers should include intermediate steps - it is not acceptable to only write down an answer.

Assignment 1 (due Friday, September 1st).

Assignment 2 (due Friday, September 8th).

Assignment 3 (due Friday, September 15th).

Assignment 4 (due Friday, September 22nd).

Assignment 5 (due Friday, September 29th).

Assignment 6 (due Monday October 23rd).

Assignment 7 (due Monday October 30th).

Assignment 8 (due Monday November 6th).

Assignment 9 (due Wednesday November 15th).

Assignment 10 (due Wednesday November 22nd).

Assignment 11 (due Friday December 1st).

Labs:

We will use the computer algebra system Sage for our labs. Sage can be accessed through a browser at CoCalc or https://sage2.d.umn.edu:8008/

The two servers are not synchronized so if you wish to switch, you need to make accounts separately on each, and download/upload your lab. On the sage2 server, worksheets are stored as ".sws" files, while on CoCalc they are ".sagews" files. If you upload and open a sws file on CoCalc, it will automatically convert it to the sagews file type.

Lab 1 on sage2 server (due Tuesday, September 21st).

Lab 2 on sage2 server (due Tuesday, September 26th).

Lab 3 on sage2 server (due Tuesday, October 3rd).

Lab 4 on sage2 server (due Tuesday, October 10th).

Lab 5 on sage2 server (due Tuesday, October 24th).

Lab 6 on sage2 server (due Tuesday, November 14th).

Lab 7 on sage2 server (due Tuesday, November 28th).

Optional lab (extra credit) on sage2 server (due Tuesday, December 5th).

Lab 8 on sage2 server(due Tuesday, December 5th).

It may be helpful to read this introduction, written by professor Gregory Bard of UW Stout. There is also another interesting book on Sage which is currently under development.

Other resources:

Highly Recommended!:The Essence of Linear Algebra, an excellent set of videos by Grant Sanderson (3Blue1Brown).

Interactive introduction to Python. This might be easier to use than the CodeAcademy site.

MIT ODE lectures online. This course is somewhat different from ours but there is significant overlap.

Code Academy's brief intro to Python. A good interactive tutorial on the basics of the Python language.

Policy statement:
The University of Minnesota is committed to the policy that all persons shall have equal access to its programs, facilities, and employment without regard to race, religion, color, sex, national origin, handicap, age, veteran status, or sexual orientation.

Disabilities:
An individual who has a disability, either permanent or temporary, which might affect his/her ability to perform in this class should contact the instructor as soon as possible so that he can adapt methods, materials and/or tests as needed to provide for equitable participation.