Ordinary Differential Equations

Ordinary Differential Equations

DrTreforBazett via YouTube Direct link

What is a DIFFERENTIAL EQUATION?? **Intro to my full ODE course**

1 of 24

1 of 24

What is a DIFFERENTIAL EQUATION?? **Intro to my full ODE course**

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Ordinary Differential Equations

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

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