Advanced engineering mathematics with MATLAB. (2010)

• Record Type: Book
• Further Information: Note: By Dean G. Duffy.
• Other Names: Duffy, Dean G
• 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; 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 Kramers–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; Finite Element Method 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; Finite Element Solution of Laplace’s Equation GREEN’S FUNCTIONS; What Is a Green’s Function?; Ordinary Differential Equations; Joint Transform Method; Wave Equation; Heat Equation; Helmholtz’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; Matrix Exponential PROBABILITY ; Review of Set Theory; Classic Probability; Discrete Random Variables; Continuous Random Variables; Mean and Variance; Some Commonly Used Distributions; Joint Distributions RANDOM PROCESSES ; Fundamental Concepts; Power Spectrum; Differential Equations Forced by Random Forcing; Two-State Markov Chains; Birth and Death Processes; Poisson Processes; Random Walk ANSWERS TO THE ODD-NUMBERED PROBLEMS INDEX
• Edition: 3rd ed
• Publisher Details: Place of publication not identified : CRC Press
• Publication Date: 2010
• Extent: 1 online resource (1105 pages), (302 illustrations)
• Subjects: 620.00285; Engineering mathematics -- Data processing
• Languages: English
• ISBNs: 9781439894644; 1439894647
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.