MathEng 351 (Fall, 2004)
Study tips
.
To achieve minimal competency (C) you must be able to do, without hesitation,
the first 3 problems from the exercises in the book of the sections we covered.
To achieve prof
ficiency (B), you must be able to know how to apply the tools we have explored to problems
involving multistep (four or more) conceptual calculations. To achieve excellence (A) you must
be able to synthesize and interpret the information provided from multistep calculations in order
to reach meaningful analytical conclusions. So, do every answered part of the first 3 problems of:
Chapter 2 sections 25, Chapter 3 sections 28, Chapter 8 sections 23, Chapter 9 sections 210,
Chapter 10 sections 26, Chapter 11 sections 25.
Beyond that, make sure you can do without
hesitation all the problems on the midterms. Then review the rest of your homework assignments.
Stick to the problems that have answers in the back so you can check your work. I will be available
to help with the questions that don’t have answers in the back.
Topics
(1) Chapters 13: ODE’s
(a) Classification:
n’th order, (non)linear, (non)homogeneous, (non)constant co
e
ﬃ
cients, separable equations, exact equations, CauchyEuler equation, sys
tems of ODE’s
.
(b) Solution techniques:
•
exact equations
(for certain firstorder ODEs),
•
separation of variables
, (for first order separable equations),
•
variation of parameters
(for first or second order, nonhomogeneous linear
ODE’s),
•
reduction of order
,
•
secondorder linear homogeneous ODE’s with constant coe
ﬃ
cients
(know what to do with the characteristic polynomial/equation and repeated
roots, know what linear independence of general solutions means and how to
test for/generate linearly independent solutions, know how many linearly inde
pendent solutions to expect for a general
n
th order ODE, know the di
ff
erence
between the general solution expressed as a linear combination of
n
linearly in
dependent functions (
Theorem 3.3.2
) and an exact solution satisfying given
initial/boundary conditions),
•
method of undetermined coe
ﬃ
cients
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Staff
 Math, Linear Algebra, Ode, linearly independent solutions, linear homogeneous ODE

Click to edit the document details