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Basic Terminology
Qualitative Analysis: Direction Field of y' = f(t, y)
Existence and Uniqueness of Solutions to First Order Linear IVP
Solving First Order Linear Homogeneous DE
Solving First Order Linear Non Homogeneous DE: The Method of Integrating Factor
Modeling with First Order Linear Differential Equations
Additional Applications: Mixing Problems and Cooling Problems
Existence and Uniqueness of Solutions to the IVP y'= f(t,y), y(t0)=y0
Separable Differential Equations
Exact Differential Equations
Substitution Techniques: Bernoulli and Ricatti Equations
Applications of First Order Nonlinear Equations: The Logistic Population Model
Applications of First Order Nonlinear Equations: One-Dimensional Motion with Air Resistance
One-Dimensional Dynamics: Velocity as Function of Position
Second Order Linear Differential Equations: Existence and Uniqueness Results
The General Solution of Homogeneous Equations
Existence of Many Fundamental Sets
Second Order Linear Homogeneous Equations with Constant Coefficients
Characteristic Equations with Repeated Roots
Characteristic Equations with Complex Roots
Applications of Homogeneous Second Order Linear Differential Equations: Unforced Mechanical Vibrations
The Structure of the General Solution of Linear Nonhomogeneous Equations
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Applications of Nonhomogeneous Second Order Linear Differential Equations: Forced Mechanical Vibrations