Basic Concepts
First Order
Linear – i
Linear – ii
Separable Equations – i
Separable Equations – ii
Exact – i
Exact – ii
Bernoulli
Substitutions
Intervals of Validity
Modeling – i
Modeling – ii
Equilibrium Solutions
Euler’s Method
Second Order
Basic Concepts
Real & Distinct Roots
Complex Roots
Repeated Roots
Reduction of Order
Fundamental Sets of Solutions
Wronskian Applications
Non-homogeneous
Undetermined Coefficients – i
Undetermined Coefficients – ii
Undetermined Coefficients – iii
Variation of Parameters – i
Variation of Parameters – ii
Mechanical Vibrations – i
Mechanical Vibrations – ii
Laplace Transforms
Definition
Examples
Inverse – i
Inverse – ii
Step Functions – i
Step Functions – ii
Step Functions – iii
Solving Initial Value Problems – i
Solving Initial Value Problems – ii
Nonconstant Coefficient IVP’s
IVP’s With Step Functions – i
IVP’s With Step Functions – ii
Dirac Delta Function
Convolution Integrals
Table
Systems
Equations
Matrices & Vectors – i
Matrices & Vectors – ii
Matrices & Vectors – iii
Eigenvalues & Eigenvectors – i
Eigenvalues & Eigenvectors – ii
Examples
Solutions
Phase Plane
Real Eigenvalues – i
Real Eigenvalues – ii
Complex Eigenvalues
Repeated Eigenvalues – i
Repeated Eigenvalues – ii
Non-homogeneous
Laplace Transforms
Modeling
Series Solutions
Power Series – i
Power Series – ii
Taylor
Examples – i
Examples – ii
Examples – iii
Examples – iv
Euler Equations
Robert Karamagi 