Chapter Review Sheets for Elementary Differential Equations and Boundary Value Problems, 8e Chapter 6: The Laplace Transformation Definitions: • Integral Transforms, Kernel • Improper Integral Piecewise • Continuous Exponential • Order • Unit Step Function (Heaviside Function) • Unit Impulse Function, Delta Function • Convolution • Transfer Function, Impulse Response Theorems: • Theorem 6.1.1: Comparison Test for Improper Integrals • Theorem 6.1.2: Existence of the Laplace Transform, F(s) • Theorem 6.2.1: Laplace Transform of f'(t) • Corollary 6.2.2: Laplace Transform of f(t) • Theorem 6.3.1: Transform of the unit step function, u(1), times a shifted function, f(t) • Theorem 6,3.2: First Translation Theorem; Inverse Transforming F(s - c) • Theorem 6.6.1: Second Translation Theorem; Convolution Result Important Skills: • The Laplace transformation is defined through an improper integral. You must be comfortable evaluating them. Hence you should review this topic in any calculus book.
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