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Calculus (6) - Khan Academy: High School level Intro to Differential Equations (45) - 7h

  • Lecture 1
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  • 2. Separable Differential Equations
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  • 3. Separable differential equations 2
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  • 4. Exact Equations Intuition 1 (proofy)
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  • 5. Exact Equations Intuition 2 (proofy)
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  • 6. Exact Equations Example 1
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  • 7. Exact Equations Example 2
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  • 8. Exact Equations Example 3
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  • 9. Integrating factors 1
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  • 10. Integrating factors 2
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  • 11. First order homegenous equations
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  • 12. First order homogenous equations 2
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  • 13. 2nd Order Linear Homogeneous Differential Equations 1
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  • 14. 2nd Order Linear Homogeneous Differential Equations 2
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  • 15. 2nd Order Linear Homogeneous Differential Equations 3
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  • 16. 2nd Order Linear Homogeneous Differential Equations 4
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  • 17. Complex roots of the characteristic equations 1
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  • 18. Complex roots of the characteristic equations 2
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  • 19. Complex roots of the characteristic equations 3
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  • 20. Repeated roots of the characteristic equation
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  • 21. Repeated roots of the characterisitic equations part 2
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  • 22. Undetermined Coefficients 1
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  • 23. Undetermined Coefficients 2
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  • 24. Undetermined Coefficients 3
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  • 25. Undetermined Coefficients 4
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  • 26. Laplace Transform 1
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  • 27. Laplace Transform 2
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  • 28. Laplace Transform 3
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  • 29. Laplace Transform 4
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  • 30. Laplace Transform 5
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  • 31. Laplace Transform 6
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  • 32. Laplace Transform to solve an equation
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  • 33. Laplace Transform solves an equation 2
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  • 34.More Laplace Transform tools
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  • 35. Using the Laplace Transform to solve a nonhomogenous eq
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  • 36. Laplace Transform of : L{t}
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  • 37. Laplace Transform of t^n: L{t^n}
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  • 38. Laplace Transform of the Unit Step Function
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  • 39. Inverse Laplace Examples
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  • 40. Laplace&Step Function Differential Equation
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  • 41. Dirac Delta Function
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  • 42. Laplace Transform of the Dirac Delta Function
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  • 43. Introduction to the Convolution
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  • 44. The Convolution and the Laplace Transform
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  • 45.Using the Convolution Theorem to Solve an Initial Value Prob
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Description

 (Source: Wikipedia)

differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. Differential equations play a prominent role in engineeringphysicseconomics, and other disciplines.

Differential equations arise in many areas of science and technology: whenever a deterministic relationship involving some continuously varying quantities (modelled by functions) and their rates of change in space and/or time (expressed as derivatives) is known or postulated. This is illustrated in classical mechanics, where the motion of a body is described by its position and velocity as the time varies. Newton's Laws allow one to relate the position, velocity, acceleration and various forces acting on the body and state this relation as a differential equation for the unknown position of the body as a function of time. In some cases, this differential equation (called an equation of motion) may be solved explicitly.

 


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More Reading

 http://tutorial.math.lamar.edu/classes/de/de.aspx

http://user.mendelu.cz/marik/maw/index.php?lang=en&form=ode

http://www.hedengren.net/research/models.htm

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