Finan M. A First Course in Elementary Differential Equations

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Finan M. A First Course in Elementary Differential Equations

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Textbook in PDF format 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