WeBWorK 6: What are these “basic solutions” in part c) of the questions??

Posted on March 20, 2015 by | 1 comment

Hi everyone,

Just a quick note about part c) in problems like these:

Screen Shot 2015-03-20 at 1.12.05 AM

 

The “basic solutions” refer to the two solutions that come from plugging the roots of the characteristic equation into our “best guess” formula y=e^{rt}.

For example, if the two roots are r=3, r=-5, then the basic solutions would be:

e^{3t}, e^{-5t}

Let me know if you have any followup questions  (or questions about anything else in the current WeBWorK assignment).

Regards,
Prof. Reitz

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OpenLab #2: Differential Equations Study Guide (part 1 – topic selection)

Posted on March 18, 2015 by | 1 comment

Hi everyone,

This is the beginning of a multi-part OpenLab assignment focussed on building resources for you and your fellow students.  Our ultimate goal will be to create a study guide for this course, with videos and other resources for each topic.

Assignment (Due next Thursday, 3/26).  Your first assignment is to choose a topic to work on.  Fill in the form below, selecting THREE different topics that you would be interested in researching for our Study Guide (you will be assigned one of your three choices).  Feel free to choose a topic that we have not yet studied (you will be given ample time to work on your portion of the Study Guide after we cover the topic in class).

You must be logged in to the OpenLab to complete this form. Having trouble with your account? Look here for help and resources: https://openlab.citytech.cuny.edu/2015-spring-mat-2680-reitz/?p=39

 

 

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Office hours cancelled today (Thursday, 3/19)

Posted on March 18, 2015 by | Leave a comment

Hi everyone,

My office hours are cancelled today (Thursday, 3/19) as I will be observing another class.  I will be available directly after class for brief questions – if you want to meet with me for a longer period please let me know.

Best,
Prof. Reitz

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Second order ordinary homogeneous differential equations with constant coefficients

Posted on March 17, 2015 by | Leave a comment

Here are some video resources showing complete examples (from Khan Academy).  I hope they help!

-Prof. Reitz

Example 1 — in which the characteristic equation has two distinct real roots.

 

Example 2 — in which the characteristic equation has one repeated (real) root.

 

Example 3 — in which the characteristic equation has complex roots.

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Euler’s Method Exercises

Posted on March 13, 2015 by | 1 comment

Hi everyone,

Here are some examples of Euler’s Method problems for you to try.  These are for practice only, they will not be collected.
NOTE: The first example is the one we solved in class on Thursday – I’m including it here for your reference.

Questions? Problems? Leave a comment on this post and I’ll respond here.

Example 1.  Given the initial value problem \frac{dy}{dt} = 3-2t-0.5y with y(0)=1, approximate the value of y(1).  Use 5 steps.

Example 2.  Consider y' = y \sin{t} -1.  Suppose y(0)=2.  What is y(3)?  Use a step size of h=0.5.

Example 3. If y'=\frac{x-4}{x-y+1}, use Euler’s method with 4 steps to approximate y(8) for the particular solution satisfying y(3)=3

Example 4.  Given \frac{dy}{dt}=e^\frac{t^2}{y^2+1} - y with y(-0.82)=0.97, estimate the value of y(1.28) using 6 steps.

Solutions to these examples are provided here for your reference – if you notice an error, please let me know by leaving a comment below (or sending an email).

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Office Hours rescheduled Thursday 3/11/15

Posted on March 11, 2015 by | Leave a comment

Hi everyone,

I will be observing another class from 9-10am this Thursday 3/11, so my office hours will take place:
12:30pm – 1:30pm, on Thursday 3/11, in N707

Best regards,
Prof. Reitz

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Office Hours rescheduled today (2/26)

Posted on February 25, 2015 by | Leave a comment

Hi everyone,

I was running a workshop from 8:30 – 10:00am today (Thursday, 2/26), so my office hours will take place directly after class, 11:15-12:15, instead of before class.

Sorry for any inconvenience,

Prof. Reitz

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Exam 1 Review is posted

Posted on February 21, 2015 by | 2 comments

Hi everyone,

Exam #1 will take place on Thursday, March 5th, during class.  The review sheet for Exam #1 has been posted on the “Handouts” page.  Let me know if you have any questions.

Regards,
Prof. Reitz

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WeBWorK – how to enter infinity

Posted on February 17, 2015 by | 1 comment

Hi everyone,

It seems that entering “infinity” in WeBWorK can vary from problem to problem – but the most common versions are:

infty, -infty

infinity, -infinity

Inf, -Inf

I think the problems in this set prefer “infinity” and “-infinity”.

I was unaware of these variations – my apologies!  Let me know if you are still having trouble.

Regards,
Prof. Reitz

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OpenLab #1: Advice from the Past

Posted on February 10, 2015 by | 67 comments

Last Spring I taught this same course for the first time.   At the end of the semester, I gave my students the following assignment:

Imagine that you are invited to speak on the first day of MAT 2680, to give advice to entering students. Write at least three sentences … describing what you would tell them.

To see the assignment and the students’ responses, follow this link.

Your assignment, due on Thursday 2/19 at the start of class, is to:

  1. Read through ALL the responses (there are 53 of them – many are quite short).
  2. Write a reply to this post (150 words minimum, not including quotations) responding to all of the following:
    1. What advice seemed most relevant to you personally? Why? (you can copy/paste a short statement, or put it in your own words)
    2. Based on this advice, what changes can you make right now to help you with this course?

Extra Credit. For extra credit, write a response to one of your classmates’ comments.  Do you have any advice?  Be kind.

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