Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 1: Introduction
Definitions: Differential Equation Mathematical Model Direction (Slope) Field Equilibrium Solution Rate (growth) constant Initial Condition
Math 23 - Fall 2014
Homework 8
Due Wednesday, 12 Nov. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and DiPrima 10th
Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indi
Math 23 - Fall 2014
Homework 5
Due Wednesday, 22 Oct. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and
DiPrima 10th Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indi
Math 23 - Fall 2014
Homework 1
Due Wednesday, 24 Sep. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and
DiPrima 10th Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indi
Math 23 - Fall 2013
Homework 2
Due Wednesday, 1 Oct. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and DiPrima 10th
Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indic
Math 23 - Fall 2014 - Corrected
Homework 7
Due Wednesday, 5 Nov. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and
DiPrima 10th Edition.
Please show all of your work (writing a list of answers is not sucient).
Math 23 Fall 2014
Dierential Equations
Exam 1
Friday, October 10, 4:00PM - 6:00PM
Your name (please print):
SOLUTION
Instructor (circle one): Olivia Prosper, Min Hyung Cho
Instructions: This is a closed book, closed notes exam. The use of calculators is n
Short Answer Questions - Work will not be graded
1. (10 Points) Match the dierential equation with the corresponding direction eld.
y 0 = y 2 (2
y)
(a)
dv
dt
=t
2v
dz
dt
=
1
z(z 1)
(b)
dP
dt
= et dx = 2x + 1
dt
(c)
(d)
(e)
Answer: -(c), -(a), -(d), -(e)
Short Answer Questions - Work will not be graded
1. Find all the equilibrium solutions of
dy
= (y + 2)(y 2
dt
16)2
and determined whether it is stable, unstable, or semi-stable.
y = 4(semi-stable),
y = 2(unstable),
y = 4(semi-stable)
2. Find the longest i
Work will not be graded in this page
1. Short Answer Questions (a) (e)-Work will not be graded
(a)(2 pts) Find the equilibrium solutions to
dy
= (y + 2)(y 2
dt
16)2
and determine whether they are stable, unstable or semistable.
Answer: y =
(b) (2 pts) Fin
Short Answer Questions - Work will not be graded
1. Determine a lower bound for the radius of convergence (|x
about each given x0 .
(5 Points) ex y 00 + ty 0
x0 | < ) of series solution
5y = 0, x0 = 0
Answer: = 1
(5 Points) p00 +
1
p0
(x 2)(x+2)
+
x
p
(
Short Answer Questions - Work will not be graded
1. (10 Points) Match the dierential equation with the corresponding direction eld.
y = y 2 (2 y)
dv
dt
= t 2v
(a)
dz
dt
=
1
z(z1)
dP
dt
= et dx = 2x + 1
dt
(b)
(c)
(d)
Answer:
(e)
,
,
1
,
,
Short Answer
Short Answer Questions - Work will not be graded
1. Determine a lower bound for the radius of convergence (|x
about each given x0 .
(5 Points) et y 00 + ty 0
x0 | < ) of series solution
5y = 0, x0 = 0
Answer: =
(5 Points) p00 +
1
p0
(x2 4)
+
x
p
(x+2)(x
Math 23 - Fall 2014
Homework 6
Due Wednesday, 29 Oct. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and DiPrima 10th
Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indi
Math 23 - Fall 2014
Homework 3
Due Wednesday, 8 Oct. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and
DiPrima 10th Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indic
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 2: First Order Differential Equations
Definitions: First Order Ordinary Differential Equation Integrating Factor, Integral Curves Variation of parameters (
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 3: Second Order Linear Equations
Definitions: Linear and nonlinear Homogeneous, Nonhomogeneous Characteristic Equation Wronskian General Solution, Fundamen
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 4: Higher Order Linear Equations
Definitions: n th Order Linear ODE Fundamental Set of Solutions, General Solution Homogeneous and nonhomogeneous equation
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 5: Series Solutions of Second Order Equations
Definitions: Radius of Convergence, Interval of Convergence Analytic Recurrence Relation Ordinary Point, Sing
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 6: The Laplace Transformation
Definitions: Integral Transforms, Kernel Improper Integral Piecewise Continuous Exponential Order Unit Step Function (Heavisi
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 7: Systems of First Order Linear Equations
Definitions: Systems of ODE's Linear vs. Nonlinear Systems Solution Prey-predator system Homogenous and Nonhomog
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 8: Numerical Methods
Definitions and Algorithms: Convergence Global truncation error Local truncation error Round-off error Euler method, backward Euler m
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 10: Partial Differential Equations and Fourier Series
Definitions: Boundary Conditions, Two-Point Boundary Value Problem (BVP) homogeneous, Nonhomogeneous
Chapter Review Sheets for
Elementary Differential Equations and Boundary Value Problems, 8e
Chapter 11: Boundary Value Problems and Sturm-Liouville Theory
Definitions: Eigenvalues and Eigenfunctions Separated Boundary Conditions Lagrange's Identity Othogo
Math 23 - Fall 2014
Homework 2
Due Wednesday, 15 Oct. 2014.
Note:
Except for problems that are stated explicitly, all problems are from Boyce and DiPrima 10th
Edition.
Please show all of your work (writing a list of answers is not sucient).
Please indi
Math 23 - Fall 2014
Homework 9
Note:
Except for problems that are stated explicitly, all problems are from Boyce and
DiPrima 10th Edition.
Please show all of your work (writing a list of answers is not sucient).
1. Section 10.3 #3, #4, #5
2. Section 10.
Math 23 Fall 2014
Dierential Equations
Exam 2
Friday, October 31, 4:00PM - 6:00PM
Your name (please print): SOLUTION
Instructor (circle one): Olivia Prosper, Min Hyung Cho
Instructions: This is a closed book, closed notes exam. The use of calculators is n