Author Archives: Peter Horn

About Peter Horn

I'm an assistant professor in the Department of Mathematics at Syracuse University.

Totally Bonus Assignments

These two assignments are worth extra points. The problems cover repeated eigenvalues in Section 7.8. These are optional. While 7.8 is not on the Final Exam, these problems require you to find eigenvalues and eigenvectors, so the exercises will help you prepare for the Final.

1. Do book problems from Section 7.8: 1, 2, 3. Due at the Final Exam. I will add up to 18 points to your written homework score for the semester.

2. Do the WeBWorK for Section 7.8. Due at the Final Exam. I will add up to 16 points to your online homework score for the semester.

Also, don’t forget about the Library’s archive of past final exams. I won’t give any extra credit for completing these, but they will be useful guides to study for our final exam.

Assignment 13

Due in class on Tuesday, April 29.

For the written homework, you are required to generate phase portraits (aka direction fields) for the systems. See this relevant post for how to generate the phase portraits.

Read Sections 7.5 and 7.6 in the book.

Do the WeBWorK for 7.5 and 7.6.

Complete these written problems:

  • Section 7.5 problems 1, 7, 24.
  • Section 7.6 problems 1, 7, 11.

Direction fields for 2×2 systems

Here is the Sage code to produce a direction field for a 2×2 system of ODEs.


# v' = Av, A is 2x2 matrix
A = matrix([[-1/2,1],[-1,-1/2]]);
print 'You entered: A = ';
print A;
x,y = var('x,y');
intermediate_step = (A*vector([x,y])).normalized();
v_prime(x,y) = (intermediate_step[0],intermediate_step[1]);
plot_vector_field(v_prime(x,y), (x,-2,2), (y,-2,2))

If you haven’t already, go to sagenb.org, log in (you might should click the Google or Yahoo icon), open a new worksheet, copy paste this into a cell, and click “evaluate”. You should get a beautiful direction field.

Note, I’m finding that sagenb.org isn’t working the way it used to. If having trouble, you might try https://cloud.sagemath.com/ and create a new project and create a new Sage worksheet, then copy, paste, and run the code.

Assignment 11

Due Tuesday, April 15, in class

Read Sections 6.5, 7.1, and 7.2

Do the WeBWorK for Sections 6.5, 7.1, 7.2

Do the written problems:

  • Section 6.5 problems 1, 5, 17
  • Section 7.1 problems 1, 5, 22
  • Section 7.2 problems 1, 22, 25

Assignment 9

This assignment is due Thursday, April 3, in class. Recall the exam is Tuesday, April 1. There will be no quiz that week.

1. Read Sections 6.3 and 6.4.
2. Do WeBWorK for Sections 6.3 and 6.4.
3. Do written problems Section 6.3 #22, 36, Section 6.4 #1, 14.

Assignment 8

Due March 25

  • Read Sections 6.1, 6.2
  • Do WeBWork for Sections 6.1 and 6.2
  • Do book problems:
    • Section 6.1 problems 5, 8, 24
    • Section 6.2 problems 11, 21, 24