Differential Equations (Math 2214) | Mathematics

Archive for March, 2010

Quiz 6

Wednesday, March 31st, 2010

Hi,
I was trying to work through calculating the cube roots of 1 + Root3 * i

I got my radius as 2, my original angle as pi/3, but then my new radius is the cubed root of 2, and my new angles are pi/9, 7pi/9, and 13pi/9.

Did I do something wrong or is it just an ugly problem?

Thank you

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Quiz 6:

Wednesday, March 31st, 2010

Quiz 6 will cover sections 3.11 and 3.12:

Use synthetic division to factor a characteristic polynomial. (Example: Find the roots of $k^3 -k^2 - 5k - 3$ )
Find the general solution to a homogeneous differential equation of order > 2. (Example: Solve $y''' - y'' - 5y' - 3y = 0$ )
Test a set of three functions to see if they form a fundamental set or not.
Be able to write the general solution to a homogeneous differential equation with repeated complex roots. (Example: Solve $y'''' - 8y''' + 42y'' - 104y' +169y = 0$ using the fact that the characteristic polynomial factors as $(k - 2 - 3i)^2(k - 2 + 3i)^2$ .)
Calculate the nth roots of a complex number (such as the cube roots of $1 + \sqrt{3}i$ ).

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In Class Quiz on Thursday April 1st..

Wednesday, March 31st, 2010

Do we have an In-Class Quiz on thursday April 1st? Just double checking because you have not made an announcement about it so i wanted to ask you or everyone else?

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Homework 9

Monday, March 29th, 2010

Is homework 9 due on Thursday as the schedule says?

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p 151. #5

Wednesday, March 24th, 2010

I could not figure out how to solve for the initial velocity? i even went to the math tutoring lab and they couldn’t figure it out either? how do you set this one up?

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Homework 8 is posted + Quiz 5 details

Friday, March 19th, 2010

Homework 8 is posted.

Quiz 5 will take place on Thursday in class. The quiz will cover sections 3.6-3.8 and may include questions on these topics:

Set up a spring problem involving unforced vibrations (example: an object weighing 9 pounds stretches a spring 6 inches at equilibrium. Write the differential equation modelling the motion of the spring.)
Given an already-set up spring problem, identify whether the motion is overdamped, critically damped, or underdamped.
Given a spring problem with initial conditions; find the solution equation in amplitude/phase-shift form.
Use the equation $y = y_C + y_P$ to identify the parts of a solution to a nonhomogeneous differential equation.
Use the Method of Undetermined Coefficients to identify the form of a particular solution to a nonhomogeneous differential equation.
Solve a nonhomogeneous differential equation using the Method of Undetermined Coefficients.

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Course Notes 3.10

Thursday, March 18th, 2010

Dear Professor,

I just wanted to let you know that the link to “Course Notes 3.10″ for Thursday March 18th isn’t working and was wondering if you would be able to fix the problem?

Thanks

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Quiz 5 was scheduled for this Thursday (March 18), and no quiz was scheduled for the following Thursday (March 25). I’m moving Quiz 5 until March 25 to give folks a chance to work with the material and ask questions on it.

I’ll post more information about the quiz along with the next homework assignment.

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math empo quiz question

Monday, March 15th, 2010

I had this question on my quiz asking for amplitude and period.
5cos(2t)+sin(2t)
I had gotten the amplitude correctly as sqrt(26) and the phase shift wrong. I was sure that it is arctan(c2/c1)
and the arctan of 1/5, the answer the quiz had was pi as the answer and that does not make sense or seem correct?

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