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Section	Content	Suggested Problems
Section 4.1	Definition of Improper Integral Basic Definition of Laplace Transform Transforms of Basic Functions (Theorem 4.1) Exponential Order Theorem 4.1 Sufficient Condition for Existence Laplace Transform of Piece-wise Continuous Function	3, 5, 9, 13, 21, 24, 27, 31,
Section 4.2	Inverse Transforms Theorem 4.3 Partial Fraction Expansions and Linearity Transforms of Derivatives Solving linear initial-value problems Procedure Diagram Solve First Order Linear IVPs Solve Second Order Linear IVPs	3, 4, 8, 15, 17, 20, 23, 26, 27, 32, 34, 36
Section 4.3	Translation on the s-axis First translation/shifting theorem (Theorem 4.6) Unit step function Piece-wise Defined Functions Translation on the t-axis Second translation/shifting theorem (Theorem 4.7) Alternative Version of Theorem 4.7 Solving linear initial-value problems	3, 6, 9, 10, 11, 14, 16, 18, 19, 22, 24, 26, 29, 37, 41, 43, 44, 47, 63, 65, 68
Section 4.4	Derivatives of Transforms (Theorem 4.8) Transforms of Integrals Convolution Theorem (Theorem 4.9) Transform of a Period Function (Theorem 4.10) Solving linear initial-value problems	3, 6, 9, 11, 13, 21, 23, 50, 51
Section 4.5	Unit Impulse Function Dirac Delta Function Solving linear initial-value problems	1, 3, 6, 9