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Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped
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Classroom Contents
Ordinary Differential Equations
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- 1 What is a DIFFERENTIAL EQUATION?? **Intro to my full ODE course**
- 2 The Key Definitions of Differential Equations: ODE, order, solution, initial condition, IVP
- 3 Separation of Variables // Differential Equations
- 4 Newton's Law of Cooling // Separable ODE Example
- 5 The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines
- 6 The Big Theorem of Differential Equations: Existence & Uniqueness
- 7 Linear Differential Equations & the Method of Integrating Factors
- 8 The Method of Integrating Factors for Linear 1st Order ODEs **full example**
- 9 The Bernoulli Equation // Substitutions in Differential Equations
- 10 Autonomous Equations, Equilibrium Solutions, and Stability
- 11 The Logistic Growth Differential Equation
- 12 The Theory of 2nd Order ODEs // Existence & Uniqueness, Superposition, & Linear Independence
- 13 How to Solve Constant Coefficient Homogeneous Differential Equations
- 14 Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair
- 15 Higher Order Constant Coefficient Differential Equations: y'''+y'=0 and y''''-3y'''+3y''-y'=0
- 16 Linear Independence of Functions & The Wronskian
- 17 The Theory of Higher Order Differential Equations
- 18 Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion
- 19 Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped
- 20 Undetermined Coefficients: Solving non-homogeneous ODEs
- 21 Variation of Parameters || How to solve non-homogeneous ODEs
- 22 How to solve ODEs with infinite series | Intro & Easiest Example: y'=y
- 23 When can you use Series to solve ODEs? Ordinary vs Singular Points
- 24 How to use SERIES to solve DIFFERENTIAL EQUATIONS example: Airy's Equation y''-xy=0
