October 5

section covered in text

4.2. Linear Differential Operators

objective

• to recognize second order linear differential equations
• to understand how to use differential operators
• to be able to find solutions to second order linear differential equations given initial conditions

• coefficients: variable and constant
• homogeneous and nonhomogeneous equations
• operators: differential and linear
• existence and uniqueness of solution

solved problems - using key ideas

• determining if an equation is linear with constant or variable coefficients or homogeneous, #1,3
• understanding differential operators, #9
• prove linearity of differential operators
• Lemma 1, #11   (nonlinear operator)
• prove Theorem 1 : linear combination of solutions
• finding solutions to equations with initial conditions, 13a
• D: differential operator notation, #23,33a,b
• Theorem 2:  existence and uniqueness of solutions, #15,16, 21

QUESTION OF THE DAY

Use the Fundamental Theorem of Calculus to find the derivative of

SOLUTION