Lecture Notes
Overview of Differential Equations & Terminology
Introduction / .pdf file
First Order Differential Equations & Solution Techniques
Separable Differential Equations / .pdf file
Linear First Order Differential Equations / .pdf file
Exact Differential Equations and Integrating Factors / .pdf file
Exact Differential Equations and Integrating Factors (Part 2) / .pdf file
Bernoulli Equations / .pdf file
Existence and Uniqueness of Solutions to Differential Equations / .pdf file
Existence and Uniqueness of Solutions to Differential Equations (part 2) / .pdf file
Applications of First Order Differential Equations / .pdf file
Linear First Order Differential Equations / .pdf file
Exact Differential Equations and Integrating Factors / .pdf file
Exact Differential Equations and Integrating Factors (Part 2) / .pdf file
Bernoulli Equations / .pdf file
Existence and Uniqueness of Solutions to Differential Equations / .pdf file
Existence and Uniqueness of Solutions to Differential Equations (part 2) / .pdf file
Applications of First Order Differential Equations / .pdf file
Second Order Linear Differential Equations
Second Order Homogeneous Constant Coefficient ODEs / .pdf file
Linear Independence and the Wronskian / .pdf file
Second Order Abel's Theorem + Repeated Roots / .pdf file
Second Order Complex Roots / .pdf file
Second Order Linear, Constant Coefficient, Homogeneous, ODEs Summary / .pdf file
Second Order Method of Undetermined Coefficients / .pdf file
Second Order Variation of Parameters / .pdf file
Challenge Problem / pdf file
Linear Independence and the Wronskian / .pdf file
Second Order Abel's Theorem + Repeated Roots / .pdf file
Second Order Complex Roots / .pdf file
Second Order Linear, Constant Coefficient, Homogeneous, ODEs Summary / .pdf file
Second Order Method of Undetermined Coefficients / .pdf file
Second Order Variation of Parameters / .pdf file
Challenge Problem / pdf file
Applications
Second Order Mass, Spring, Damper Systems / .pdf file
Forced Mass, Spring, Damper System / .pdf file
Forced Mass, Spring, Damper System / .pdf file
The Laplace Transform
The Laplace Transform / Introduction / Definition / .pdf file
The Laplace Transform / Why the Laplace Transform is SOOO rad! / .pdf file
The Laplace Transform / The Unit Step Function / .pdf file The Laplace Transform / Examples / .pdf file
The Laplace Transform / Dirac Function / .pdf file
The Laplace Transform / Why the Laplace Transform is SOOO rad! / .pdf file
The Laplace Transform / The Unit Step Function / .pdf file The Laplace Transform / Examples / .pdf file
The Laplace Transform / Dirac Function / .pdf file
Series Solutions
Numerical Methods
Numerical Methods / .pdf file
Systems of Differential Equations
Linear Algebra Review / .pdf file
Systems of Differential Equations / Overview & Notation / .pdf file
Systems of Differential Equations / Unique Roots / .pdf file
Systems of Differential Equations / Unique Roots and Parametric Plots / .pdf file
Systems of Differential Equations / 3 x 3 Example / .pdf file
Systems of Differential Equations / Complex Roots / .pdf file
Repeated Roots / .pdf file
Repeated Roots Additional Examples / 2 x 2 Example / 3 x 3 example
The Fundamental Matrix / .pdf file
Non-Homogeneous Systems / .pdf file / (Example LT) / (Example VOP)
Non-Homogeneous Last Day / .pptx file / .pdf file
Choose the Method / .pdf file / solutions
Systems of Differential Equations / Overview & Notation / .pdf file
Systems of Differential Equations / Unique Roots / .pdf file
Systems of Differential Equations / Unique Roots and Parametric Plots / .pdf file
Systems of Differential Equations / 3 x 3 Example / .pdf file
Systems of Differential Equations / Complex Roots / .pdf file
Repeated Roots / .pdf file
Repeated Roots Additional Examples / 2 x 2 Example / 3 x 3 example
The Fundamental Matrix / .pdf file
Non-Homogeneous Systems / .pdf file / (Example LT) / (Example VOP)
Non-Homogeneous Last Day / .pptx file / .pdf file
Choose the Method / .pdf file / solutions
Additional Materials / Commonly Used Tables
General Review
Laplace Transforms / Tabular Integration by Parts .pdf file
Partial Fractions Review by Paul Dawkins @ Lamar University / HIGHLY RECOMMENDED, AWESOME GENERAL RESOURCE!!! (external link)
Oregon State University ODE Web Study Guide (website)
Review of Integration Techniques .pdf file
Partial Fractions Review by Paul Dawkins @ Lamar University / HIGHLY RECOMMENDED, AWESOME GENERAL RESOURCE!!! (external link)
Oregon State University ODE Web Study Guide (website)
Review of Integration Techniques .pdf file
Tables of Integrals and Various Identities
Table of Commonly Used Integrals .pdf file
External Links
WIKI site for WebWorks (website)
Tacoma Narrows Bridge Collapse (youTube link)
Fireflies in Sync (youTube link)
London Millenium Bridge / People in Sync (youTube link)
Tacoma Narrows Bridge Collapse (youTube link)
Fireflies in Sync (youTube link)
London Millenium Bridge / People in Sync (youTube link)
Useful Code/Computing References
Matlab Code
Direction Field and Phase Plane Java App / From Rice University (click here)
Direction Field and Phase Plane Matlab Code / From Rice University (click here)
Direction Field and Phase Plane Matlab Code / From Rice University (click here)
Accessing Matlab from Home
0. If home is off the SU network, please install the Cisco anyConnect client first.
1. Navigate to vlab.seattleu.edu
2. Install the appropriate view client for your operating system
3. Run the VMWare program.
4. Log in by with your SU username and password to vlab.seattleu.edu. Please make sure that you choose the option "Math Applications" for better Mathematica/Matlab support.
1. Navigate to vlab.seattleu.edu
2. Install the appropriate view client for your operating system
3. Run the VMWare program.
4. Log in by with your SU username and password to vlab.seattleu.edu. Please make sure that you choose the option "Math Applications" for better Mathematica/Matlab support.