Electrical Engineering: Ch 16: Laplace Transform (1 of 58) What is a Laplace Transform? Electrical Engineering: Ch 16: Laplace Transform (2 of 58) What is a Laplace Transform? Math Def Electrical Engineering: Ch 16: Laplace Transform (3 of 58) The Laplace Transform of f(t)=t Electrical Engineering: Ch 16: Laplace Transform (4 of 58) The Laplace Transform of f(t)=e^(at) Electrical Engineering: Ch 16: Laplace Transform (5 of 58) The Laplace Transform of f(t)=cos(wt) Electrical Engineering: Ch 16: Laplace Transform (6 of 58) The Laplace Transform of f(t)=sin(wt) Electrical Engineering: Ch 16: Laplace Transform (7 of 58) Laplace Transform of f(t)=cos(wt)e^(at) Electrical Engineering: Ch 16: Laplace Transform (8 of 58) s-Domain Equivalent of an Inductor Electrical Engineering: Ch 16: Laplace Transform (9 of 53) s-Domain Equivalent of a Capacitor Electrical Engineering: Ch 16: Laplace Transform (10 of 58) Analyzing a RCL Circuit in the s-Domain Electrical Engineering: Ch 16: Laplace Transform (11 of 58) The Laplace Transform Table Electrical Engineering: Ch 16: Laplace Transform (12 of 58) The Inverse of the Laplace Transform Electrical Engineering: Ch 16: Laplace Transform (13 of 58) The Inverse[Laplace Transf] Strategy 1 Electrical Engineering: Ch 16: Laplace Transform (14 of 58) The Inverse[Laplace Transf] Strategy 2 Electrical Engineering: Ch 16: Laplace Transform (15 of 58) The Inverse[Laplace Transf] Strategy 3 Electrical Engineering: Ch 16: Laplace Transform (16 of 58) The Residue Method Electrical Engineering: Ch 16: Laplace Transform (17 of 58) Linear Properties of the Laplace Transf Electrical Engineering: Ch 16: Laplace Transform (18 of 58) Translation Prop of the Laplace Transf Electrical Engineering: Ch 16: Laplace Transform (19 of 58) Shifting Prop. of the Laplace Transf Electrical Engineering: Ch 16: Laplace Transform (20 of 58) Laplace Transform of the 1st Derivative Electrical Engineering: Ch 16: Laplace Transform (21 of 58) Laplace Transf of the 1st Derivative: 1 Electrical Engineering: Ch 16: Laplace Transform (22 of 58) Laplace Transf of the 2nd Derivative Electrical Engineering: Ch 16: Laplace Transform (23 of 58) Laplace Transf of the 3rd Derivative Electrical Engineering: Ch 16: Laplace Transform (24 of 58) Solving a 2nd Order Differential Eqn Electrical Engineering: Ch 16: Laplace Transform (25 of 58) Inverse Laplace Transform=? Ex. 1 Electrical Engineering: Ch 16: Laplace Transform (26 of 58) Inverse Laplace Transform=? Ex. 2 Electrical Engineering: Ch 16: Laplace Transform (27 of 58) Inverse Laplace Transform=? Ex. 3 Electrical Engineering: Ch 16: Laplace Transform (28 of 58) Inverse Laplace Transform=? Ex. 4 Electrical Engineering: Ch 16: Laplace Transform (29 of 58) Inverse Laplace Transform=? Ex. 5 Electrical Engineering: Ch 16: Laplace Transform (30 of 58) Solving Differential Equation Ex. 1 Electrical Engineering: Ch 16: Laplace Transform (31 of 58) Solving Differential Equation Ex. 2 Electrical Engineering: Ch 16: Laplace Transform (32 of 58) Solving Differential Equation Ex. 3 Electrical Engineering: Ch 16: Laplace Transform (33 of 58) Solving Differential Equation Ex. 4 Electrical Engineering: Ch 16: Laplace Transform (34 of 58) Shifting on the s-Domain Revisited Electrical Engineering: Ch 16: Laplace Transform (35 of 58) Shifting on the t-Axis Revisited Electrical Engineering: Ch 16: Laplace Transform (36 of 58) Find the Laplace Transform Electrical Engineering: Ch 16: Laplace Transform (37 of 58) Response to an RC Circuit Electrical Engineering: Ch 16: Laplace Transform (38 of 58) Response to an Undamped System 1 Electrical Engineering: Ch 16: Laplace Transform (39 of 58) Response to a Damped System 2 Electrical Engineering: Ch 16: Laplace Transform (40 of 58) Laplace Transform of the Integral Electrical Engineering: Ch 16: Laplace Transform (41 of 58) Laplace Transform of the Integral Ex. Electrical Engineering: Ch 16: Laplace Transform (42 of 58) Solving a Non-Homogeneous Diff. Eqn. 1 Electrical Engineering: Ch 16: Laplace Transform (43 of 58) Solving a Non-Homogeneous Diff. Eqn. 2 Electrical Engineering: Ch 16: Laplace Transform (44 of 58) What is Convolution? Def. 1 Electrical Engineering: Ch 16: Laplace Transform (45 of 58) What is Convolution? Def. 1: Ex. Electrical Engineering: Ch 16: Laplace Transform (46 of 58) What is Convolution? Def. 1: Ex. Electrical Engineering: Ch 16: Laplace Transform (47 of 58) What is Convolution? Def. 2: Graph 1 Electrical Engineering: Ch 16: Laplace Transform (48 of 58) What is Convolution? Def. 2: Graph 2 Electrical Engineering: Ch 16: Laplace Transform (49 of 58) What is Convolution? Example 2 Electrical Engineering: Ch 16: Laplace Transform (50 of 58) What is Convolution? Example 3 Electrical Engineering: Ch 16: Laplace Transform (1 of 58) What is a Laplace Transform? Electrical Engineering: Ch 16: Laplace Transform (2 of 58) What is a Laplace Transform? Math Def Electrical Engineering: Ch 16: Laplace Transform (3 of 58) The Laplace Transform of f(t)=t Electrical Engineering: Ch 16: Laplace Transform (4 of 58) The Laplace Transform of f(t)=e^(at) Electrical Engineering: Ch 16: Laplace Transform (5 of 58) The Laplace Transform of f(t)=cos(wt) Electrical Engineering: Ch 16: Laplace Transform (6 of 58) The Laplace Transform of f(t)=sin(wt) Electrical Engineering: Ch 16: Laplace Transform (7 of 58) Laplace Transform of f(t)=cos(wt)e^(at) Electrical Engineering: Ch 16: Laplace Transform (8 of 58) s-Domain Equivalent of an Inductor