Author Archives: Peter Horn

About Peter Horn

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

Assignment 7

Due Tuesday, March 18.

  • WebWork for Sections 3.7 and 3.8
  • Read Sections 3.7 and 3.8
  • Book problems
    • Section 3.7 problems 3, 6, 11
    • Section 3.8 problems 5, 6, 10

Lecture supplement 3-6-14

We talked about forced spring vibrations. You can download a Sage worksheet that I used to generate the plots. Also, check out the disastrous consequences of resonance and the “beats” caused by amplitude modulation, both below.

(Note: for the sage worksheet to unpack properly, I had to use Stuffit Expander on a Mac. The build in archive utility didn’t work. You should get a .sws file after unzipping)

Resonance:

Beats:

Spring-mass systems (i.e. vibrations) bring this 90s gem to mind:

…And this older one:

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

Assignment 3

Due Tuesday, February 4. Written assignment due in class. Online assignment due at 11:59 PM.

Note: This was edited 1-30-14 at 10:20am.

  • Read sections 2.4 – 2.5
  • Do WeBWorK for 2.5
  • Complete these problems from the book:
    • Section 2.4 problems 8, 13
    • Section 2.5 problems 1, 5, 15, 19, 27

Am I spending too much time on homework?

A group of students asked me after class, “How much time do you intend for us to spend on homework?”

I didn’t know what to say to that. (See below for what I told them. In between you will read what I have thought about since they asked me the question).

I have never thought about homework from a time perspective. As a teacher, I make an assignment that covers a representative sample of the material (to make sure students know how to solve the different types of problems that will be on the quizzes and tests). I am a firm believer that you learn mathematics by doing mathematics.  If you sat in class and watched me solve problems without doing the homework, how would you do on a quiz? My answer to that question is “poor.” My philosophy is that each homework problem is a benefit to you because it prepares you for quizzes and exams, but also for your life later on. Homework is practice.

I read some online and see a general guideline that for every hour spent in lecture, a college student should expect to spend 2-3 hours studying. In a literature class, that 2-3 hours might be spent reading a novel. In math class, it might be spent solving problems.

Let’s take 2.5 hours of study to 1 hour of lecture as our ratio. The average student takes, say, 15 credit hours (this means 15 hours of lecture per week). So according to these guidelines, you sit in class for 15 hours per week and study for 38, for a total of 53 hours per week devoted to academics. Being a student is a full-time job, which makes 53 hours seem pretty reasonable. If this seems reasonable to you, then I hope you would agree that for a 3 credit hour class, 7.5 hours per week of study time (including homework) is reasonable.

(My answer to the students was 6-8 hours on ODE homework).