Review Sheet for Exam 1
MAP 4341
When: In-class portion: October 14, Take-home portion: October 14-21.
Material: 1.1-1.2, 2.1-2.5, 2.8, 3.1, 3.3-3.6, 3.8
In-Class:
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For the in-class portion of the exam, you may bring in a calculator (any type) and a
writing instrument. While I am allowing calculators of any type, I need to see all work
on the integrals – only giving me the output from your calculator will not be acceptable.
You will be provided the integral page from the last page in your text book, along with a
formula page. You will be provided with the following formulas:
o Fourier series with arbitrary period (Theorem 1, page 39)
o Half-range expansions (Theorem 1, page 50)
o Parseval’s Identity (Equation 6, page 56)
o Solution to wave equation (boxed, page 119)
o D’Alembert’s solution (Equations 4, page 126)
o Solution to the heat equation with zero boundaries (boxed, page 138)
o Solution to the heat equation with insulated ends (Equations 4 and 5 on page
147)
o Solution to the Laplace equation on a rectangle (boxed, page 168)
The following are a list of problems that I would consider acceptable for an in-class
exam, along with the length of time I was consider reasonable.
o Classifying a PDE (homogeneous, linear, order, elliptic/hyperbolic/parabolic) (2
or 3 minutes, assuming I ask for elliptic/hyperbolic/parabolic).
o Testing a solution for a PDE (5 minutes tops).
o Solving a PDE with initial conditions (15-20 minutes, depending on how many
shortcuts you can take)
o Calculating d’Alembert’s solution to the wave equation (10 minutes)
o Deriving a solution to a PDE with certain initial conditions and boundary
conditions (20 mintues)
o Calculating the Fourier expansion or half-range expansion of a function (15-20
minutes, depending on how many shortcuts you can take)
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You will only be asked to find a solution to a PDE from the text, not from the homework
(for instance, the damped wave or the heated ring are off limits)
I consider the following derivations to be fair game for the exam:
o Wave equation
o Heat equation with zero boundary
o Heat equation with insulated boundaries
o Laplace equation on a rectangle with three zero boundaries
o Heat equation on a circle
Take-Home:
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In addition to the in-class portion of the exam, you will have a take-home portion.
You may use any non-human source for this exam. You may use Maple/calculators for
the computations, just make sure you let me know what you did (DO NOT just give me
an answer: justify it).
You may NOT talk about this exam with ANYONE except for me. Nothing. No words at
all. No talking. Shush.
Everything from this class is fair game for the take-home portion.
You should think of this as a homework assignment that covers the entire first portion of
the course.