Differential Equation - Laplace Transform (English)

   Monday, November 30, 2020   

Starting a new Lecture Notes Series on Differential Equation - Laplace Transform 

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Differential Equation - Laplace Transform
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Lecture Description of this above Topic:

Lecture 1: What is a Laplace Transform?

Lecture 2: What is a Laplace Transform? Math Def

Lecture 3: The Laplace Transform of f(t)=t

Lecture 4: The Laplace Transform of f(t)=e^(at)

Lecture 5: The Laplace Transform of f(t)=cos(wt)

Lecture 6: The Laplace Transform of f(t)=sin(wt)

Lecture 7: Laplace Transform of f(t)=cos(wt)e^(at)

Lecture 8: s-Domain Equivalent of an Inductor

Lecture 9: Analyzing a RCL Circuit in the s-Domain

Lecture 10: The Laplace Transform Table

Lecture 11: The Inverse of the Laplace Transform

Lecture 12: The Inverse[Laplace Transf] Strategy 1

Lecture 13: The Inverse[Laplace Transf] Strategy 2

Lecture 14: The Inverse[Laplace Transf] Strategy 3

Lecture 15: The Residue Method

Lecture 16: Linear Properties of the Laplace Transf

Lecture 17: Translation Prop of the Laplace Transf

Lecture 18: Shifting Prop. of the Laplace Transf

Lecture 19: Laplace Transform of the 1st Derivative

Lecture 20: Laplace Transf of the 1st Derivative: 1

Lecture 21: Laplace Transf of the 2nd Derivative

Lecture 22: Laplace Transf of the 3rd Derivative

Lecture 23: Solving a 2nd Order Differential Eqn

Lecture 24: Inverse Laplace Transform=? Ex. 1

Lecture 25: Inverse Laplace Transform=? Ex. 2

Lecture 26: Inverse Laplace Transform=? Ex. 3

Lecture 27: Inverse Laplace Transform=? Ex. 4

Lecture 28: Inverse Laplace Transform=? Ex. 5

Lecture 29: Solving Differential Equation Ex. 1

Lecture 30: Solving Differential Equation Ex. 2

Lecture 31: Solving Differential Equation Ex. 3

Lecture 32: Solving Differential Equation Ex. 4

Lecture 33: Shifting on the s-Domain Revisited

Lecture 34: Shifting on the t-Axis Revisited

Lecture 35: Find the Laplace Transform

Lecture 36: Response to an RC Circuit

Lecture 37: Response to an Undamped System 1

Lecture 38: Response to a Damped System 2

Lecture 39: Laplace Transform of the Integral

Lecture 40: Laplace Transform of the Integral Ex.

Lecture 41: Solving a Non-Homogeneous Diff. Eqn. 1

Lecture 42: Solving a Non-Homogeneous Diff. Eqn. 2

Lecture 43: What is Convolution? Def. 1

Lecture 44: What is Convolution? Def. 1: Ex.

Lecture 45: What is Convolution? Def. 1: Ex.

Lecture 46: What is Convolution? Def. 2: Graph 1

Lecture 47: What is Convolution? Def. 2: Graph 2

Lecture 48: What is Convolution? Example 2

Lecture 49: What is Convolution? Example 3

Lecture 50: What is Convolution? Example 4

Lecture 51: What is Convolution? Circuit Ex.

Lecture 52: Laplace Transform of Periodic Fct.

Lecture 53: Laplace Transform of Periodic Function

Lecture 54: Laplace Transform of Periodic Fct. Sum.

Lecture 55: Undamped System with a Spring

Lecture 56: Convolution Example

Lecture 57: Solve the Integrodifferential Equation