Comprehensive final exam will include some material from review
sheets 1, 2, and 3 in addition to the material below. The best way to prepare
for a final is to review homework problems, examples, definitions, and theorems
from the textbook and class notes. Make sure that you can solve problems in a
reasonable amount of time without reference to the textbook or class notes. It
is important that on the final you show all your work and explain your answers.
Just answers (especially wrong ones!) without any explanation will earn you no
credit.
List of major topics covered in
class.
1. Sections 4.1 and 4.2. Forced harmonic oscillators (pp.
382-408). Extended linearity principle (p. 384), forced response, steady-state
response, natural or free response Method of Undetermined Coefficients. # 6, 8,
16, 18, 36, 38 on pp. 394-396; 6, 8, 12, 14, 16, 17 on pp. 406-408.
2. Section 6.1. Definition of the
Laplace transform, Laplace transform of exponential function, Laplace transform
of a derivative, linearity of Laplace transform, inverse Laplace transforms,
Laplace transform of a power function. #1, 3, 9, 13, 14, 15,
16, 20, 22 after 6.1.
3. Section 6.2. Discontinuous
functions. Heaviside function and its Laplace transform. Differential equations
with discontinuity - see examples from 6.2 and from class. Formula
on page 576. # 4, 6, 7, 8, 9, 10, 11 after 6.2.
5. Section 6.3. Solving
second-order equations. Laplace transform of exponential and trigonometric functions.
Examples of solutions using Laplace transform from class and from section 6.3.
Please see homework for this section as well.
Additional practice problems: 1,
3, 7, 15-22, 23 on pp.443-445;
1-6, 11, 18-22, 24-28 on pp.
621-623.
GOOD LUCK!