Applied Laplace Transforms and z-Transforms for Scientists and Engineers

1 Laplace Transformation.- 1.1 The One-Sided Laplace Transform.- 1.2 The Two-Sided Laplace Transform.- 1.3 Ordinary Linear Differential Equations.- 2 z-Transformation.- 2.1 z-Transforms and Inverse z-Transforms.- 2.2 Difference Equations.- 3 Laplace Transforms with the Package.- 3.1 Basics.- 3.2 The Use of Transformation Rules.- 3.3 The Finite Laplace Transform.- 3.4 Special Functions.- 3.5 Inverse Laplace Transformation.- 3.6 Differential Equations.- 4 z-Transformation with the Package.- 4.1 Basics.- 4.2 Use of Transformation Rules.- 4.3 Difference Equations.- 5 Applications To Automatic Control.- 5.1 Controller Configurations.- 5.2 State-Variable Analysis.- 5.3 Second Order Differential Systems.- 5.4 Stability.- 5.5 Frequency Analysis.- 5.6 Sampled-Data Control Systems.- 6 Laplace Transformation: Further Topics.- 6.1 The Complex Inversion Formula.- 6.2 Laplace Transforms and Asymptotics.- 6.3 Differential Equations.- 7 z-Transformation: Further Topics.- 7.1 The Advanced z-Transformation.- 7.2 Applications.- 7.3 Use of the Package.- 8 Examples from Electricity.- 8.1 Transmission Lines.- 8.2 Electrical Networks.- 9 Examples from Control Engineering.- 9.1 Control of an Inverted Pendulum.- 9.2 Controling a Seesaw-Pendulum.- 9.3 Control of a DC Motor.- 9.4 A Magnetic-Ball-Suspension-System.- 9.5 A Sampled-Data State-Variable Control System.- 10 Heat Conduction and Vibration Problems.- 10.1 Flow of Heat.- 10.2 Waves and Vibrations in Elastic Solids.- 11 Further Techniques.- 11.1 Duhamel’s Formulas.- 11.2 Green’s Functions.- 11.3 Fundamental Solutions.- 11.4 Finite Fourier Transforms.- 12 Numerical Inversion of Laplace Transforms.- 12.1 Inversion by the Use of Laguerre Functions.- 12.2 Inversion by Use of Fourier Analysis.- 12.3 The Use of Gaussian Quadrature Formulas.- 12.4 The Method of Gaver and Stehfest.- 12.5 Example.- Appendix: Package Commands.