高等应用数学问题的MATLAB求解05.ppt

Slide 1 (of 11) Chapter 5Integral Transforms and Complex Variable Functions Chapter 5 Integral Transforms and Complex Variable Functions Laplace Transforms and Their Inverses Fourier Transforms and Their Inverses Other Integral Transforms Z Transforms and Their Inverses Solving Complex Variable Function Problems Chapter summary 5.1 Laplace Transforms and Their Inverses Definitions and properties Computer solutions to Laplace transform problems 5.1.1 Definitions and properties Mathematical definition of the one-sided Laplace transform Properties of Laplace transform: Linear property where and are scalars. Time-domain shift -domain property Differentiation property The nth order derivative when initial values are 0, then, Integration property Zero initial conditions: the multiple integral: Initial value property Final value property If has no pole with non-negative real part Convolution property where the convolution operator is defined as Other properties Inverse Laplace transform: where is greater than the real part of the poles of function 5.1.2 Computer solutions to Laplace transform problems Problem solution procedures for Laplace transform: Define a symbolic variable such as t , and define time-domain function Directly call Laplace() function or Call pretty() or latex() function to further process the obtained symbolic results Inverse Laplace transform: The syntax: default variable is specify the domain variables and Example 5.1 Given perform its Laplace transform MATLAB solutions: Simplify the answer Result: Example 5.2 Given obtain its Laplace and inverse Laplace transforms Laplace transform: Inverse Laplace transform: Example 5.3 Solve the inverse Laplace transform: Direct solution: High precision numerical solution: Example 5.4 Given , derive the