Differential Equations Files

Review Sessions:

· Syllabus

Homework 2008

· Homework Assignments (Mathematica Format)

· Homework Assignments (PDF format)

Homework Solutions

· Homework 1 Vector Fields, Order, Solutions

· Homework 2 First order linear equations

· Homework 3 Exact Equations, Applications

· Homework 4 Valied Intervals, Bernoulli Equation, Applications

· Homework 5 Euler’s Method, Picard’s Method

· Homework 6 Linear second order equations with constant coefficients

· Homework 7 Complex roots of characteristic polynomial, Reduction of Order

· Homework 8 Undetermined Coefficients, Reduction of Order

· Homework 9 Vibrations

· Homework 10 Higher Order Linear Equations

· Homework 11 Undetermined Coefficients, Variation of Parameters

· Homework 12 Ordinary Points

· Homework 13 Euler's Equation, Regular Singular Points

· Homework 14 Logarithmic Solution, Bessel Equation

· Homework 15 Laplace Transform

Mathematica Homework

· Homework 1 Vector Fields

· Homework 1 Vector Fields Solutions

· Homework 2 Euler’s Method

· Euler and Modified Euler Functions for Homework 2

· Homework 3 Method of Annihilators

Handouts

·

• Existence Theorem
• Comparison Theorem
• Integrating Factors
• Reduction of Order
• Green’s Function
• Green’s Function Constant Coefficients
• Vibrations
• Regular Singular Points Logarithmic Solutions
• Regular Singular Points
• Regular Singular Points Examples of Logarithmic Solutions
• Bessel Functions
• Bessel Functions of Order 3/2
• Different Forms of the Bessel Equation
• Green's Function from the Laplace Tranform
• Dirac Delta Function and Laplace Transform
• Abel’s Equation for Order n
• Green’s Function for Order n equations
• Higher Derivatives of Products