Advanced Engineering Mathematics with MATLAB

Advanced Engineering Mathematics with MATLAB

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Resoundingly popular in its first edition, Dean Duffy's Advanced Engineering Mathematics has been updated, expanded, and now more than ever provides the solid mathematics background required throughout the engineering disciplines. Melding the author's expertise as a practitioner and his years of teaching engineering mathematics, this text stands clearly apart from the many others available. Relevant, insightful examples follow nearly every concept introduced and demonstrate its practical application. This edition includes two new chapters on differential equations, another on Hilbert transforms, and many new examples, problems, and projects that help build problem-solving skills. Most importantly, the book now incorporates the use of MATLAB throughout the presentation to reinforce the concepts presented. MATLAB code is included so readers can take an analytic result, fully explore it graphically, and gain valuable experience with this industry-standard more

Product details

  • Hardback | 840 pages
  • 162.56 x 233.68 x 50.8mm | 1,292.73g
  • Taylor & Francis Inc
  • CRC Press Inc
  • Bosa Roca, United States
  • English
  • Revised
  • 2nd Revised edition
  • 204 black & white illustrations, 15 black & white tables
  • 1584883499
  • 9781584883494

Table of contents

_ _____ COMPLEX VARIABLES Complex Numbers Finding Roots The Derivative in the Complex Plane: The Cauchy-Riemann Equations Line Integrals Cauchy-Goursat Theorem Cauchy's Integral Formula Taylor and Laurent Expansions and Singularities Theory of Residues Evaluation of Real Definite Integrals Cauchy's Principal Value Integral FIRST-ORDER ORDINARY DIFFERENTIAL EQUATIONS Classification of Differential Equations Separation of Variables Homogeneous Equations Exact Equations Linear Equations Graphical Solutions Numerical Methods HIGHER-ORDER ORDINARY DIFFERENTIAL EQUATIONS Homogeneous Linear Equations with Constant Coefficients Simple Harmonic Motion Damped Harmonic Motion Method of Undetermined Coefficients Forced Harmonic Motion Variation of Parameters Euler-Cauchy Equation Phase Diagrams Numerical Methods FOURIER SERIES Fourier Series Properties of Fourier Series Half-Range Expansions Fourier Series with Phase Angles Complex Fourier Series The Use of Fourier Series in the Solution of Ordinary Differential Equations Finite Fourier Series THE FOURIER TRANSFORM Fourier Transforms Fourier Transforms Containing the Delta Function Properties of Fourier Transforms Inversion of Fourier Transforms Convolution Solution of Ordinary Differential Equations by Fourier Transforms THE LAPLACE TRANSFORM Definition and Elementary Properties The Heaviside Step and Dirac Delta Functions Some Useful Theorems The Laplace Transform of a Periodic Function Inversion by Partial Fractions: Heaviside's Expansion Theorem Convolution Integral Equations Solution of Linear Differential Equations with Constant Coefficients Transfer Functions, Green's Function, and Indicial Admittance Inversion by Contour Integration THE Z-TRANSFORM The Relationship of the Z-Transform to the Laplace Transform Some Useful Properties Inverse Z-Transforms Solution of Difference Equations Stability of Discrete-Time Systems THE HILBERT TRANSFORM Definition Some Useful Properties Analytic Signals Causality: The Kramer-Kronig Relationship THE STURM-LIOUVILLE PROBLEM Eigenvalues and Eigenfunctions Orthogonality of Eigenfunctions Expansion in Series of Eigenfunctions A Singular Sturm-Liouville Problem: Legendre's Equation Another Singular Sturm-Liouville Problem: Bessel's Equation THE WAVE EQUATION The Vibrating String Initial Conditions: Cauchy Problem Separation of Variables D'Alembert's Formula The Laplace Transform Method Numerical Solution of the Wave Equation THE HEAT EQUATION Derivation of the Heat Equation Initial and Boundary Conditions Separation of Variables The Laplace Transform Method The Fourier Transform Method The Superposition Integral Numerical Solution of the Heat Equation LAPLACE'S EQUATION Derivation of Laplace's Equation Boundary Conditions Separation of Variables The Solution of Laplace's Equation on the Upper Half-Plane Poisson's Equation on a Rectangle The Laplace Transform Method Numerical Solution of Laplace's Equation VECTOR CALCULUS Review Divergence and Curl Line Integrals The Potential Function Surface Integrals Green's Lemma Stokes' Theorem Divergence Theorem LINEAR ALGEBRA Fundamentals of Linear Algebra Determinants Cramer's Rule Row Echelon Form and Gaussian Elimination Eigenvalues and Eigenvectors Systems of Linear Differential Equations ANSWERS TO THE ODD-NUMBERED PROBLEMS INDEXshow more

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