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About Differential Equations: From Slope Fields to Systems and Stability

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Master ordinary differential equations from first principles: classify equations, solve first-order equations by separation, integrating factors, and exactness, then conquer second-order linear equations, damping, resonance, and Laplace-transform methods. Finish with systems of ODEs via eigenvalues, phase-plane stability analysis, numerical solvers and their stiffness limits, and the separation-of-variables bridge to partial differential equations.

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What You'll Learn

Concepts:
Eigenvalue Method for Linear Systems of ODEs Existence and Uniqueness Theorem for ODEs Solving ODEs with the Laplace Transform Order and Linearity of a Differential Equation Integrating Factor Method Resonance in Forced Oscillations Characteristic Equation Method Damped Harmonic Oscillator Phase Plane Analysis Separation of Variables for PDEs Stiff Differential Equations Runge-Kutta Methods Variation of Parameters Method of Undetermined Coefficients Separable Differential Equations Exact Differential Equations

What you will learn

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