Section

Content

Suggested Problems

Section 3.1

 growth/decay linear models
 Newton's Law of Cooling/Heating
 dT/dt = k(TT_{m})
 ambient temperature
 Mixtures
 dx/dt = (input rate of salt)  (output rate of salt)
 inflow volume equals outflow volume
 inflow volume does not equal the outflow volume

3, 5, 11, 1415, 21, 25

Section 4.1

 InitialValue and Boundary Value Problems
 Existence and Uniqueness of IVP
 Potential NonExistence/NonUniqueness of BVP
 Homogeneous Equations
 Operator Notation
 Vector Space of Solutions of Homogeneous Equation
 Linear Independence of Solutions of Homogeneous Equation
 Theorem 3.3 Wronskian Test for Linear Independence
 Fundamental Set of Solutions
 Superpostion Principle  NonHomongenous Equations


Section 4.2

 Reduction of Order
 Standard Form
 y_{2} = u(x)y_{1}(x)


2, 6, 9 ,11

Section 4.3

 Linear, Constant Coefficient, Homogeneous
 Auxillary or Characteristic Equation
 Case I: Distinct Real Roots
 Case II: Repeated Real Roots
 Case III: Complex Conjuate Roots
 Special Cases
 y" + k^{2}y = 0
 y"  k^{2}y = 0

3, 5, 10, 13, 15, 18, 24, 31, 33, 34

Section 4.4

 Method of Undetermined Coefficients
 Particular Solution L(y) = f(x)
 f(x) = polynomial
 f(x) = exponential
 f(x) = cosine or sine
 Glitch in the Method
 InitialValue Problem

4, 8, 12, 16, 19, 23, 28, 31

Section 4.6

 Variation of Parameters
 Standard Form
 Construction Fundamental Set of Solutions for Homogeneous Problem
 Solution for u_{1}' and u_{2}'


1, 2, 6, 8, 11

Section 4.7

 CauchyEuler Equation
 Auxillary or Characteristic Equation
 Case I: Distinct Real Roots
 Case II: Repeated Real Roots
 Case III: Complex Conjuate Roots
 NonHomogeneous Equations

1, 4, 9, 11, 15, 19
