This preview shows pages 1–2. Sign up to view the full content.
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, Fundamental Set of Solutions
•
Principle of superposition (p. 145)
•
Linear Independence
•
Particular Solution
•
Method of undetermined solutions
•
Period, Natural Frequency, Amplitude, Phase
•
Overdamped, Critically Damped, Underdamped
•
Resonance
•
Transient Solution, SteadyState Solution or Forced Response
Theorems:
•
Theorem 3.2.1:
Existence and uniqueness of solutions to )'"+ p(l) y.+q(t)y ~ g(t) Y(to)
= Ya Y"(to } = Yo
•
Theorem 3.2.2:
Principle of superposition. If Yi and Y2 are solutions to so is C, Y, + c2 Y2 for any
constants c' and c2 .
•
Theorem 3.2.3:
Finding solutions to Eq. (2) an Eq. (3), using the Wronskian at the initial
conditions.
•
Theorem 3.2.4:
Representing general solutions to second order linear homogeneous GDE's
•
Theorem 3.2.5:
Existence of a fundamental set of solutions.
•
Theorem 3.3.1:
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.
This note was uploaded on 02/22/2010 for the course MATH 23 taught by Professor Dorothywallace during the Spring '10 term at Dartmouth.
 Spring '10
 DorothyWallace
 Differential Equations, Linear Equations, Equations

Click to edit the document details