Laplace Transform of f(t) = t sin(2t) 
Laplace Transform of f(t) = t sin(2t)
by Robert Donley
Video Lecture 29 of 41
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Date Added: March 14, 2015

Lecture Description

ODEs: Find the Laplace Transform of f(t) = t sin(2t). We use the derivative formula for the Laplace Transform: L(y') = sL(y) - y(0) instead of the definition. This method also finds the Laplace transform of g(t) = t cos(2t). We verify the answer by finding the IVP with f(t) as the unique solution.

Course Index

  1. General Solution of y' + xy = 0
  2. Verifying the Solution of an ODE
  3. The Logistic Function 1: Solving The ODE
  4. The Logistic Function 2: Sketching The S-Curve
  5. General Solution to y' - 3y = b(x)
  6. Example of Population Growth 1
  7. Example of Population Growth 2
  8. Example of Radioactive Decay 1
  9. Example of Radioactive Decay 2
  10. General Solution to y" - 6y' + 9y = 0
  11. Complex Numbers for ODEs (1 of 4)
  12. Complex Numbers for ODEs (2 of 4)
  13. Complex Numbers for ODEs (3 of 4)
  14. Complex Numbers for ODEs (4 of 4)
  15. General Solution to y" - 6y' +25y = 0
  16. Antiderivative of e^{3x} cos(4x) (ODE Solution)
  17. Antiderivative of x^2 e^x (ODE Solution)
  18. General Solution of y'''-4y''+5y'-2y=0
  19. Wronskian for {e^{3x}, e^{-x}, 2}
  20. Linear Dependence of {x^2-1, x^2+x, x+1} Using Wronskian
  21. Annihilator Method 1: Real Linear Factors
  22. Example of Annihilator Method: y"-y = sin(2x)
  23. Power Series Solution for y"-2y'+y=x, y(0)=0, y'(0)=1
  24. Mass-Spring Systems 1: Undamped Motion
  25. Mass-Spring Systems 2: Underdamped Motion
  26. Mass-Spring Systems 3: Critically Damped Motion
  27. Laplace Transform of f(t) = 2t-1
  28. Laplace Transform of f(t) = sin(2t)
  29. Laplace Transform of f(t) = t sin(2t)
  30. Laplace Transform of f(t) = e^{3t}cos(4t)
  31. Laplace Transform of f(t) = t^2 e^{2t} cos(3t)
  32. Inverse Laplace Transform of (s-1)/s^2(s^2+4)
  33. Laplace Transform Solution of y'-3y=e^{2t}, y(0)=2
  34. Laplace Transform Solution of y"-2y'-3y=e^t, y(0) = 0, y'(0) = 1
  35. Laplace Transform of f(t) = 2 on the Interval (1,2)
  36. Second Shift Formula for a Piecewise-defined Function
  37. Laplace Transform Solution of y'-y=f(t) (Piecewise-Defined)
  38. Example of Convolution Theorem: f(t)=t, g(t)=sin(t)
  39. Convolution Theorem for y'-2y=e^t, y(0)=0
  40. Fourier Series: Example of Orthonormal Set of Functions
  41. Fourier Series: Example of Parseval's Identity

Course Description

Dr. Bob explains ordinary differential equations, offering various examples of first and second order equations, higher order differential equations using the Wronskian determinant, Laplace transforms, and more.

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