Homework 1, due August 31, 2016

Due at the beginning of class on Wednesday, August 31, 2016.
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goodwine
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Homework 1, due August 31, 2016

Post by goodwine »

Reading:
  • Read sections 1.1 - 1.4 from the course text.
  • You are responsible for the material in section 1.5, but can read it at your convenience as long as it is before the end of September.
  • Reading for section 1.6 will be assigned separately.
Exercises:
  1. Exercise 1.8. In addition to identifying the attributes of the equation as required by the problem, also change one term in the equation in a manner that changes at least one of the attributes. Indicate which attribute(s) was changed. Also change one of the terms in a manner that does not change any of the attributes of the equation. Indicate the change and why it changed none of the attributes.

    By "attributes" I mean
    1. ordinary or partial
    2. order
    3. linear or nonlinear
    4. if linear, homogeneous or inhomogeneous
    5. if linear, constant or variable coefficient.
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    You must use an ND email address to register, but other than that you may choose any username or password you wish.
Bill Goodwine, 376 Fitzpatrick
goodwine
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Re: Homework 1, due August 31, 2016

Post by goodwine »

Someone asked me:
when we change a term in a manner that does not affect the attributes, how do we explain that none of the attributes changed?
Well, for example, if you change

x'' + 5 x^2 = cos(t)

to

x'' + 5 x^3 = cos(t)

you would say that you changed t^2 to t^3, but they are nonlinear in x, so that kept the equation nonlinear.
Bill Goodwine, 376 Fitzpatrick
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