Homework 1, due August 31, 2016

Post by **goodwine** » Fri Aug 26, 2016 4:26 pm

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:

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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Post by **goodwine** » Sat Aug 27, 2016 7:16 pm

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.

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