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0. Laplace transform brief table
1. Representation of complex numbers
2. The concept of complex variable functions, poles and zeros
3. Definition of Laplace Transform
3.1 Determine whether Laplace exists
4. Laplace transform of a typical time function
4.1 Unit Step Function
4.2 Unit pulse function
4.3 Unit speed function (unit ramp function)
4..4 Exponential functions
4.5 Sinusoidal Signal Function
4.6 Cosine Signal Function
5. The basic properties of Laplace transform
5.1 Linearity theorem
5.2 Translation theorem
5.3 Differentiation Theorem
5.4 The Differential Theorem (extended to order n)
5.5 Integral theorem
5.6 Integral theorem (n-fold integration)
5.7 Final Value Theorem
5.8 Initial Value Theorem
6. Inverse Laplace Transform