## Mathematical Methods in Electrical EngineeringIn this volume, the author covers the mathematical methods appropriate to both linear-systems theory and signal processing. The text deals with a number of topics usually found in introductory linear-systems courses, such as complex numbers and Laplace transforms, and addresses additional topics such as complex variable theory and Fourier series and transforms. Although the discussion is mathematically self-contained, it assumes that the reader has a firm background in calculus and differential equations. Each chapter contains a number of worked examples plus exercises designed to allow the student to put concepts into practice. The author writes in a mathematically elegant yet relaxed and readable style, and provides interesting historical notes along the way. Undergraduate students of electrical engineering, applied mathematics, and related disciplines - and their teachers - will welcome this book. |

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### Contents

Laplace transforms | 13 |

Linear systems | 49 |

Fourier series | 97 |

Functions of a complex variable | 133 |

Fourier transforms | 205 |

Laplace transform revisited | 256 |

Answers to Selected Exercises | 265 |

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analytic function analytic inside application argz Cauchy-Riemann equations Cauchy's integral circle closed contour coefficients complex number complex plane complex variable consider convolution theorem cosine defined definition denote derivatives Determine differential equation domain equivalent input Evaluate example Exercise exist expansion exponential expression f f(z)dz finite number Fourier series Fourier transform Fourier-series representation frequency spectrum function f(t gives half-plane Hence implying impulse function impulse response initial values initially at rest input f(t integral formula inverse transform jump discontinuity Laurent linear systems mathematical multivalued function necessary obtained odd function operation output path closure periodic function piecewise-continuous piecewise-smooth pole polynomial problem Proof proper rational function properties radius rational function real axis real numbers real variable result right-hand satisfied Section series converges shown in Fig signal Similarly sine singularity solution stable system steady-state response step response theory transfer function unique unit-step function zero