Students should know the definition of the Laplace transform. They should be able to compute simple Laplace transforms "by hand" and should be able to use a table of Laplace transforms to solve initial value problems for constant coefficient ODE's. They should be able to write "rough" data in terms of Dirac and Heaviside functions. They should be able to recognize and use simple results regarding Laplace transforms.
Reality We covered sections 4.1-6. Sources for review material:
|Goals Students should know
principal definitions of linear algebra and recognize and work
with these ideas. Students should know how to
compute the rank of a matrix, the determinant of a matrix, and be able
to invert and diagonalize simple matrices "by hand".
Reality We covered sections 8.1-8.8, 8.10, and 8.12. Students should be able to state the principal definitions. Sources for review material:
Students should be able to compute the Fourier coefficients of
simple functions "by hand". They should know what orthogonality means
for functions. Given a function's graph on [0,A] they should be able to
graph the sum of the Fourier sine and cosine series on [-A,A]. They
should have some qualitative understanding of what partial sums of
Fourier series look like compared to the original function, including an
idea of the Gibbs phenomenon.
Reality Certainly we discussed the material in sections 12.1-12.3. I will not ask any questions about 12.4 (complex Fourier series). The ideas of 3.9 and 12.5 are essential in the last portion of the course. The specific content needed from section 12.5 is brief. Sources for review material:
|Boundary value problems for ODE's and PDE's|
Students should be able to solve simple boundary and initial value
problems for the classical PDE's using separation of variables
combined with the appropriate trigonometric series. They should also
understand some of the qualitative aspects of solutions (smoothness
for heat and possible shocks for wave), and simple asymptotics for
Reality Here the difference between what is declared in the syllabus and what I feel can realistically be covered is greater than in other parts of the semester. I think the exam should cover 13.1-5 and 13.8. I am writing this before the last week of the semester. I hope to cover in lecture some discussion of steady-state heat flows on a rectangular plate (Laplace's equation) and some discussion of vibrations on a rectangular plate. I haven't taught this before and I may need to revise my ambitions. Sources for review material:
I try to write and grade exams carefully. As you prepare for and work on the final exam, I hope that you will:
Formula sheets, etc.
I will hand out a formula sheet with Laplace transform information and with information about Fourier series and boundary value problems. If needed, I will likely also give you information about some matrices and their RREF's. You may not use any calculators or other notes during the exam. Although I can add more formulas, I would rather not make the formula sheet(s) unwieldy. Also, please keep in mind that if you have more formulas, legitimate test questions can be more difficult.
|Vocabulary of the day|
cumbersome, clumsy, or hard to manage, owing to size, shape, or weight
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