An Introduction to Laplace Transforms and Fourier Series

摘要: 1. The Laplace Transform.- 1.1 Introduction.- 1.2 1.3 Elementary Properties.- 1.4 Exercises.- 2. Further Properties of the 2.1 Real Functions.- 2.2 Derivative Property 2.3 Heaviside's Unit Step Function.- 2.4 Inverse 2.5 Limiting Theorems.- 2.6 Impulse 2.7 Periodic 2.8 3. Convolution and Solution Ordinary Differential Equations.- 3.1 3.2 Convolution.- 3.3 3.3.1 Second Order 3.3.2 Simultaneous 3.4 Using 3.5 Integral 3.6 4. Fourier Series.- 4.1 4.2 Definition a 4.3 Odd Even 4.4 Complex 4.5 Half Range 4.6 4.7 5. Partial 5.1 5.2 Classification 5.3 Separation Variables.- 5.4 Transforms to Solve PDEs.- 5.5 Boundary Conditions Asymptotics.- 5.6 6. Transforms.- 6.1 6.2 Deriving 6.3 Basic 6.4 6.5 Signal Processing.- 6.6 7. Variables 7.1 7.2 Rudiments Analysis.- 7.3 Integration.- 7.4 Branch Points.- 7.5 7.6 Inversion Formula in 7.7 A. Solutions B. Table C. Linear Spaces.- C.1 Algebra.- C.2 Gramm-Schmidt Orthonormalisation Process.