Elementary SignalsSignals Described in Math Form.1-1The Unit Step Function ...1-2The Unit Ramp Function ...1-10The Delta Function 1-12Sampling Property of the Delta Function1-12Sifting Property of the Delta Function.1-13Higher Order Delta Functions...1-15Summary...1-19Exercises...1-20Solutions to Exercises 1-21Chapter 2The Laplace TransformationDefinition of the Laplace Transformation. 2-1Properties of the Laplace Transform..2-2The Laplace Transform of Common Functions of Time .2-12The Laplace Transform of Common Waveforms..2-23Summary...2-29Exercises...2-34Solutions to Exercises 2-37Chapter 3The Inverse Laplace TransformationThe Inverse Laplace Transform Integral3-1Partial Fraction Expansion ...3-1Case where is Improper Rational Function ( )... 3-13Alternate Method of Partial Fraction Expansion... 3-15Summary.. 3-18Exercises ..3-20Solutions to Exercises3-22Chapter 4Circuit Analysis with Laplace TransformsCircuit Transformation from Time to Complex Frequency... 4-1Complex Impedance ...4-8Complex Admittance 4-10Transfer Functions .4-13Summary ..4-16Exercises ..4-18Solutions to Exercises4-21Chapter 5State Variables and State EquationsExpressing Differential Equations in State Equation Form...5-1Solution of Single State Equations..5-7The State Transition Matrix .5-9Computation of the State Transition Matrix...5-11Eigenvectors 5-18Circuit Analysis with State Variables 5-22Relationship between State Equations and Laplace Transform...5-28Summary ..5-35Exercises ..5-39Solutions to Exercises5-41Chapter 6The Impulse Response and ConvolutionThe Impulse Response in Time Domain...6-1Even and Odd Functions of Time..6-5Convolution...6-7Graphical Evaluation of the Convolution Integral ..6-8Circuit Analysis with the Convolution Integral.. 6-18Summary . 6-20