Monthly Archives: February 2014

Checking something is a solution

Consider the ODE \(y” – 3y’ -4y = t^2 +2\). In class we came up with a particular solution: \( Y(t) = -1/4*t + 2/8*t – 29/32\). Here’s how you can get Sage to check quickly that you are correct.

t = var('t');
Y = -1/4*t^2 + 3/8*t - 29/32;
Y.diff(2) - 3*Y.diff() -4*Y

If you enter this in Sage, your output will be \(t^2 + 2\), which means \(Y(t)\) is a solution to the ODE given above.

Assignment 6

Note: this assignment is now complete.

Due 4th of March, 2014.

  • Read Sections 3.4 – 3.6
  • Read especially Section 3.5 example 5
  • Do the WeBWorK for Sections 3.4 – 3.6
  • Do these written problems:
    • Section 3.4 problems 11, 12, 16. Additional instructions: on 16, state explicitly what this “special” solution is, and discuss its long-term behavior.
    • Section 3.5 problems 5, 16, 19
    • Section 3.6 problems 3, 7, 13

edit: Let me clarify “special” above. The book asks you to find some critical value of \(b\). This value of \(b\) gives you an (one) IVP, and I call this IVP’s solution the “special solution”. So I want this solution, and its limit as \(t\to\infty\) .

Assignment 5

This assignment will be due on Thursday, Februaury 20. Note: the first midterm exam is on February 18.

  • Read sections 3.2 and 3.3 in the book.
  • Complete the WeBWorK for section 3.3
  • Complete the written problems:
    • 2, 7 and 24 of Section 3.2, and
    • 1, 7, and 17 of Section 3.3

Study sheet for Exam 1

The first midterm exam is February 18. I’ve created a study sheet that lists the sections and topics covered and the skills you need to know for the exam. The first two bullet points under skills are calculus 1, 2, and 3 skills. Keep in mind that solutions to all homeworks and quizzes are in BlackBoard.

Assignment 4

Due Tuesday, February 11.

  • Read Sections 2.6 and 3.1
  • Do WeBWorK for Sections 2.6 and 3.1
  • Complete these problems from the book
    • Section 2.6 problems 1, 9, 19, 26
    • Section 3.1 problems 1, 9, 10, 20