Study guide for exam 1, math 20d, Fall 2010
Hint: Best way to study is to go over as many problems as you can in the book. Both my notes (L) and
BoyceDiPrima (BD).
Correspondence is:
L 0.2 is BD chapter 1
L chapter 1 (1.1,1.2,1.3,1.4,1.6) is BD chapter 2
L chapter 2 (2.1,2.2,2.3,2.4) is BD chapter 3
Here’s the summary.
L 0.2: What is a diﬀerential equation and what is a mathematical model. Key terms:
diﬀerential equation
,
initial value problem
,
initial condition(s)
,
the general solution
,
particular solution
.
L 1.1: Solution by integration, i.e.
y
0
=
f
(
x
) or
y
0
=
f
(
y
).
L 1.2: Slope ﬁelds and Solution curves. Be able to sketch slope ﬁelds, solution curves. Note the existence
and uniqueness theorem.
L 1.3: Separable equations:
y
0
=
f
(
x
)
g
(
y
). New key terms:
implicit solution
.
L 1.4: Linear ﬁrst order ODE. Know how to solve using the
integrating factor
. Study the mixture problem.
L 1.6: Autonomous equations. Long term behaviour of solutions to autonomous equations. Key terms:
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This note was uploaded on 09/07/2011 for the course MATH 20D taught by Professor Mohanty during the Spring '06 term at UCSD.
 Spring '06
 Mohanty
 Math, Differential Equations, Equations

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