Syllabus
(PDF Format)
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Integration
Facts (PDF File)
Series Handouts (PDF file)
Introduction to Series
The
Integral Test and Estimates of
Sums
The
Comparison Tests
Alternating Series
Absolute
Convergence and the Ratio and Root Tests
Representations
of Functions as Power Series
POWER
POINT PRESENTATIONS
NOTE: Note these PowerPoint presentations are PDF files.
Chapter 1: Introduction to Differential Equations
Section 1:
Basic Definitions and Terminology
Section 2:
Some Mathematical Models
Chapter 2: First-Order Differential Equations
Section 1:
Preliminary Theory
Section 2:
Separation of Variables
Section 3:
Homogeneous Equations
Handout for Integrating Factors
Section 4:
Exact Equations
Section 5:
Linear Equations
Section 6:
Equations of Bernoulli, Ricatti, and Clairnaut
Section 7:
Substitutions
Chapter 3:
Applications of First-Order Differential Equations
Section 1:
Orthogonal Trajectories
Section 2:
Applications of Linear Equations
Section 3:
Applications of Nonlinear Equations
Chapter 4:
Linear Differential Equations of Higher Order
Section 1:
Preliminary Theory
Section 2:
Constructing a Second Solution from a Known Solution
Section 3:
Homogeneous Linear Equations with Constant Coefficients
Section 4:
Undetermined Coefficients--Superposition Approach
Section 5:
Differential Operators
Section 6:
Undetermined Coefficients--Annihilator Approach
Section 7:
Variation of Parameters
Chapter 5: Applications of
Second-Order Differential Equations: Vibrational Models
Section 1:
Simple Harmonic Motion
Section 2:
Damped Motion
Section
3: Forces Motion
Chapter 6:
Differential Equations with Variable Coefficients
Section 1:
Cauchy-Euler Equation
Section 2:
Review of Power Series; Power Series Solutions
Section 3:
Solutions about Ordinary Points
Chapter 7:
Laplace Transform
Section 1:
Laplace Transform
Section 2:
Inverse Transform
Section 3:
Translation Theorems and Derivatives of Transforms
Section 4:
Transforms of Derivatives, Integrals, and Periodic Functions
Section 5:
Applications
Chapter 9: Numerical Methods for
Ordinary Differential Equations
Section 1:
Direction Fields
Section 2:
The Euler Methods
Excel Spreadsheet
Section 3:
The Three-Term Taylor Method
Chapter 8: Systems of Linear
Differential Equations
Section
1: Operator Method
Section
2: Laplace Transform Method