Advanced modern engineering mathematics / / Glyn James [and six others]

• Autore: James Glyn
• Pubblicazione: Harlow, England : , : Prentice Hall, is an imprint of Pearson, , 2011
• Edizione: Fourth edition.
• Descrizione fisica: 1 online resource (1,065 pages) : illustrations
• Disciplina: 620.001/51
• Soggetto topico: Engineering mathematics
• Note generali: Includes index.
• Nota di contenuto: Cover -- Advanced Modern Engineering Mathematics -- Contents -- Preface -- About the Authors -- Publisher's Acknowledgements -- Matrix Analysis -- Introduction -- Review of matrix algebra -- Definitions -- Basic operations on matrices -- Determinants -- Adjoint and inverse matrices -- Linear equations -- Rank of a matrix -- Vector spaces -- Linear independence -- Transformations between bases -- Exercises (1-4) -- The eigenvalue problem -- The characteristic equation -- Eigenvalues and eigenvectors -- Exercises (5-6) -- Repeated eigenvalues -- Exercises (7-9) -- Some useful properties of eigenvalues -- Symmetric matrices -- Exercises (10-13) -- Numerical methods -- The power method -- Gerschgorin circles -- Exercises (14-19) -- Reduction to canonical form -- Reduction to diagonal form -- The Jordan canonical form -- Exercises (20-27) -- Quadratic forms -- Exercises (28-34) -- Functions of a matrix -- Exercises (35-42) -- Singular value decomposition -- Singular values -- Singular value decomposition (SVD) -- Pseudo inverse -- Exercises (43-50) -- State-space representation -- Single-input-single-output (SISO) systems -- Multi-input-multi-output (MIMO) systems -- Exercises (51-55) -- Solution of the state equation -- Direct form of the solution -- The transition matrix -- Evaluating the transition matrix -- Exercises (56-61) -- Spectral representation of response -- Canonical representation -- Exercises (62-68) -- Engineering application: Lyapunov stability analysis -- Exercises (69-73) -- Engineering application: capacitor microphone -- Review exercises (1-20) -- Numerical Solution of Ordinary Differential Equations -- Introduction -- Engineering application: motion in a viscous fluid -- Numerical solution of first-order ordinary differential equations -- A simple solution method: Euler's method -- Analysing Euler's method. ; Using numerical methods to solve engineering problems -- Exercises (1-7) -- More accurate solution methods: multistep methods -- Local and global truncation errors -- More accurate solution methods: predictor-corrector methods -- More accurate solution methods: Runge-Kutta methods -- Exercises (8-17) -- Stiff equations -- Computer software libraries and the `state of the art' -- Numerical solution of second- and higher-order differential equations -- Numerical solution of coupled first-order equations -- State-space representation of higher-order systems -- Exercises (18-23) -- Boundary-value problems -- The method of shooting -- Function approximation methods -- Engineering application: oscillations of a pendulum -- Engineering application: heating of an electrical fuse -- Review exercises (1-12) -- Vector Calculus -- Introduction -- Basic concepts -- Exercises (1-10) -- Transformations -- Exercises (11-17) -- The total differential -- Exercises (18-20) -- Derivatives of a scalar point function -- The gradient of a scalar point function -- Exercises (21-30) -- Derivatives of a vector point function -- Divergence of a vector field -- Exercises (31-37) -- Curl of a vector field -- Exercises (38-45) -- Further properties of the vector operator ∇ -- Exercises (46-55) -- Topics in integration -- Line integrals -- Exercises (56-64) -- Double integrals -- Exercises (65-76) -- Green's theorem in a plane -- Exercises (77-82) -- Surface integrals -- Exercises (83-91) -- Volume integrals -- Exercises (92-102) -- Gauss's divergence theorem -- Stokes' theorem -- Exercises (103-112) -- Engineering application: streamlines in fluid dynamics -- Engineering application: heat transfer -- Review exercises (1-21) -- Functions of a Complex Variable -- Introduction -- Complex functions and mappings -- Linear mappings -- Exercises (1-8) -- Inversion -- Bilinear mappings. ; Exercises (9-19) -- The mapping w = z2 -- Exercises (20-23) -- Complex differentiation -- Cauchy-Riemann equations -- Conjugate and harmonic functions -- Exercises (24-32) -- Mappings revisited -- Exercises (33-37) -- Complex series -- Power series -- Exercises (38-39) -- Taylor series -- Exercises (40-43) -- Laurent series -- Exercises (44-46) -- Singularities, zeros and residues -- Singularities and zeros -- Exercises (47-49) -- Residues -- Exercises (50-52) -- Contour integration -- Contour integrals -- Cauchy's theorem -- Exercises (53-59) -- The residue theorem -- Evaluation of definite real integrals -- Exercises (60-65) -- Engineering application: analysing AC circuits -- Engineering application: use of harmonic functions -- A heat transfer problem -- Current in a field-effect transistor -- Exercises (66-72) -- Review exercises (1-24) -- Laplace Transforms -- Introduction -- The Laplace transform -- Definition and notation -- Transforms of simple functions -- Existence of the Laplace transform -- Properties of the Laplace transform -- Table of Laplace transforms -- Exercises (1-3) -- The inverse transform -- Evaluation of inverse transforms -- Inversion using the first shift theorem -- Exercise (4) -- Solution of differential equations -- Transforms of derivatives -- Transforms of integrals -- Ordinary differential equations -- Simultaneous differential equations -- Exercises (5-6) -- Engineering applications: electrical circuits and mechanical vibrations -- Electrical circuits -- Mechanical vibrations -- Exercises (7-12) -- Step and impulse functions -- The Heaviside step function -- Laplace transform of unit step function -- The second shift theorem -- Inversion using the second shift theorem -- Differential equations -- Periodic functions -- Exercises (13-24) -- The impulse function -- The sifting property. ; Laplace transforms of impulse functions -- Relationship between Heaviside step and impulse functions -- Exercises (25-30) -- Bending of beams -- Exercises (31-33) -- Transfer functions -- Definitions -- Stability -- Impulse response -- Initial- and final-value theorems -- Exercises (34-47) -- Convolution -- System response to an arbitrary input -- Exercises (48-52) -- Solution of state-space equations -- SISO systems -- Exercises (53-61) -- MIMO systems -- Exercises (62-64) -- Engineering application: frequency response -- Engineering application: pole placement -- Poles and eigenvalues -- The pole placement or eigenvalue location technique -- Exercises (65-70) -- Review exercises (1-34) -- The z Transform -- Introduction -- The z transform -- Definition and notation -- Sampling: a first introduction -- Exercises (1-2) -- Properties of the z transform -- The linearity property -- The first shift property (delaying) -- The second shift property (advancing) -- Some further properties -- Table of z transforms -- Exercises (3-10) -- The inverse z transform -- Inverse techniques -- Exercises (11-13) -- Discrete-time systems and difference equations -- Difference equations -- The solution of difference equations -- Exercises (14-20) -- Discrete linear systems: characterization -- z transfer functions -- The impulse response -- Stability -- Convolution -- Exercises (21-29) -- The relationship between Laplace and z transforms -- Solution of discrete-time state-space equations -- State-space model -- Solution of the discrete-time state equation -- Exercises (30-33) -- Discretization of continuous-time state-space models -- Euler's method -- Step-invariant method -- Exercises (34-37) -- Engineering application: design of discrete-time systems -- Analogue filters -- Designing a digital replacement filter -- Possible developments. ; Engineering application: the delta operator and the D transform -- Introduction -- The q or shift operator and the δ operator -- Constructing a discrete-time system model -- Implementing the design -- The D transform -- Exercises (38-41) -- Review exercises (1-18) -- Fourier Series -- Introduction -- Fourier series expansion -- Periodic functions -- Fourier's theorem -- Functions of period 2π -- Even and odd functions -- Linearity property -- Exercises (1-7) -- Functions of period T -- Exercises (8-13) -- Convergence of the Fourier series -- Functions defined over a finite interval -- Full-range series -- Half-range cosine and sine series -- Exercises (14-23) -- Differentiation and integration of Fourier series -- Integration of a Fourier series -- Differentiation of a Fourier series -- Coefficients in terms of jumps at discontinuities -- Exercises (24-29) -- Engineering application: frequency response and oscillating systems -- Response to periodic input -- Exercises (30-33) -- Complex form of Fourier series -- Complex representation -- The multiplication theorem and Parseval's theorem -- Discrete frequency spectra -- Power spectrum -- Exercises (34-39) -- Orthogonal functions -- Definitions -- Generalized Fourier series -- Convergence of generalized Fourier series -- Exercises (40-46) -- Engineering application: describing functions -- Review exercises (1-20) -- The Fourier Transform -- Introduction -- The Fourier transform -- The Fourier integral -- The Fourier transform pair -- The continuous Fourier spectra -- Exercises (1-10) -- Properties of the Fourier transform -- The linearity property -- Time-differentiation property -- Time-shift property -- Frequency-shift property -- The symmetry property -- Exercises (11-16) -- The frequency response -- Relationship between Fourier and Laplace transforms -- The frequency response -- Exercises (17-21). ; Transforms of the step and impulse functions.
• Sommario/riassunto: Building on the foundations laid in the companion text Modern Engineering Mathematics, this book gives an extensive treatment of some of the advanced areas of mathematics that have applications in various fields of engineering, particularly as tools for computer-based system modelling, analysis and design. The philosophy of learning by doing helps students develop the ability to use mathematics with understanding to solve engineering problems. A wealth of engineering examples and the integration of MATLAB and MAPLE further support students.
• Titolo autorizzato: Advanced modern engineering mathematics
• ISBN: 1-283-05592-9; 9786613055927; 0-273-71927-0
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910150237903321
• Lo trovi qui: Univ. Federico II