Monthly Archives: February 2015

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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Homework Hints Week 2: Integrating Factors – A Shortcut

Posted on February 7, 2015 by | 2 comments

Shortcuts are dangerous things – they may save you time, but they usually don’t help you understand the problem.  Because of this, it’s usually important to have a thorough grasp of the basic idea of how to solve a problem before learning the shortcut.  Since you’ve had a few days to wrestle with the “Integrating Factors” problem, I wanted to share a standard shortcut (covered in the text, but not yet discussed in class) for solving these problems, which condenses much of the algebra into two formulas.  You are welcome to use it, or not, as you prefer.

Shortcut for solving Integrating Factors problems:

Step 1:  Rewrite the differential equation in the standard form:  

\frac{dy}{dt} + p(t)y = g(t)

In practice, this usually just means getting the y and \frac{dy}{dt} on the same side, and dividing to get rid of anything in front of the \frac{dy}{dt}.

Step 2:  Find \mu, by plugging in:

\mu = e^{\int p(t) dt}

That is, integrate the function in front of y, and then raise e to the power of the result.  This gives \mu.

Step 3:  Multiply both sides of the equation by \mu, and then integrate both sides.  Notice that the integral of the left side will always equal \mu\cdot y.

Step 4: Finally, solve the resulting equation for y.  You’re done!

Special Bonus Shortcut II:  The work of Steps 3 and 4 can be condensed into the following formula, which can be used to find y directly after completing Step 2:

y = \frac{1}{\mu(t)} \int \mu(t) g(t) dt + C

That is, multiply \mu by the function g(t) from the right hand side of the differential equation, integrate, and multiply the result by $\frac{1}{\mu}$.

NOTE: The standard form mentioned in Step 1 shows up a lot – in fact, even if you are not using the shortcut formulas above, it is considered “pretty standard” to rewrite your equation in standard form before solving the problem.

An example using the Shortcut: NOTE: In the video, he uses x as the independent variable, instead of t.

https://www.youtube.com/watch?v=Et4Y41ZNyao

 

Another example: NOTE: Towards the end of this example, when integrating the right-hand-side, he uses integral of \frac{1}{1+x^2}, which is \arctan x  — if this looks unfamiliar, you should review the derivatives of the inverse trig functions 

 

 

Happy shortcutting,
-Prof Reitz

 

 

 

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Homework Hints Week 2: Objects Falling near sea level

Posted on February 4, 2015 by | Leave a comment

Falling objects.  This video starts with some discussion of where the differential equation comes from, then carries out a problem from start to finish.  A couple of things to note:
1.  The problem uses U.S. Customary Units (feet, pounds, etc.) – in particular, acceleration due to gravity is 32 ft/sec^2  (instead of 9.8 m/sec^2).
2.  In solving the example, the differential equation is solved using the Integrating Factor method (which we will learn on Thursday).
3.  The “limiting velocity” is just another term for the terminal velocity.

 

 

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Calculus Review – some helpful hints for WeBWorK #1

Posted on February 1, 2015 by | 2 comments

EDIT 2/2/15: Added an example for finding the tangent line to a function.

Having trouble with the WeBWorK?  First, don’t panic – it’s a lot to remember!!  But do be prepared to put in some time re-learning stuff from Calculus I and II.  I’ve picked out a few video resources for you that hit some of the most important techniques  (I tried to find videos that were focussed on examples, rather than theory, since this is meant to be review).

Comments are welcome (just click the “leave a comment” button above).

  • Like a video? Leave comment and let me know.
  • Dislike a video (it wasn’t helpful/ it was confusing)? Let me know.
  • Need help with another topic (like the product rule, or equations of tangent lines, or something else)?  Let me know.
  • Have a video or other resource to suggest? Let me know!

Derivatives: Equation of the tangent line to a curve (similar to Problem 2):  This gives an example of finding the equation of a tangent line, starting with just the function and the x-value.  (NOTE: In the video, the function is an exponential function, so the numbers running around the answer all tend to have e in them – this will not be the case in the WeBWorK problem, where you will find more familiar numbers in your answer).

 

Derivatives: The Chain Rule (similar to Problem 4):  This video is short and sweet, a single example using the chain rule with a logarithmic function.

 

Integrals: U-Substitution (similar to Problems 5 & 6):

This video has three examples – the first two are most similar to what you will see in WeBWorK (the last one is a little trickier – but could be useful in the future):

https://www.youtube.com/watch?v=qclrs-1rpKI

 

Integration by Parts (similar to Problems 7 & 8)

This video also has a few examples – the first two will be most useful for the WeBWorK:

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