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Scientific computing with Matlab / Dingyü Xue, YangQuan Chen

Author
Xue, Dingyü
Published
Boca Raton, FL : CRC Press, 2016.
Edition
Second edition.
Physical Description
xvii, 586 pages : illustrations ; 27 cm
Additional Creators
Chen, YangQuan, 1966-

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Contents
Machine generated contents note: 1.1.Computer Solutions to Mathematics Problems -- 1.1.1.Why should we study computer mathematics language? -- 1.1.2.Analytical solutions versus numerical solutions -- 1.1.3.Mathematics software packages: an overview -- 1.1.4.Limitations of conventional computer languages -- 1.2.Summary of Computer Mathematics Languages -- 1.2.1.A brief historic review of MATLAB -- 1.2.2.Three widely used computer mathematics languages -- 1.2.3.Introduction to free scientific open-source softwares -- 1.3.Outline of the Book -- 1.3.1.The organization of the book -- 1.3.2.How to learn and use MATLAB -- 1.3.3.The three-phase solution methodology -- Exercises -- Bibliography -- 2.1.Essentials in MATLAB Programming -- 2.1.1.Variables and constants in MATLAB -- 2.1.2.Data structures -- 2.1.3.Basic statement structures of MATLAB -- 2.1.4.Colon expressions and sub-matrices extraction -- 2.2.Fundamental Mathematical Calculations -- 2.2.1.Algebraic operations of matrices -- 2.2.2.Logic operations of matrices -- 2.2.3.Relationship operations of matrices -- 2.2.4.Simplifications and presentations of analytical results -- 2.2.5.Basic number theory computations -- 2.3.Flow Control Structures of MATLAB Language -- 2.3.1.Loop control structures -- 2.3.2.Conditional control structures -- 2.3.3.Switch structure -- 2.3.4.Trial structure -- 2.4.Writing and Debugging MATLAB Functions -- 2.4.1.Basic structure of MATLAB functions -- 2.4.2.Programming of functions with variable numbers of arguments in inputs and outputs -- 2.4.3.Inline functions and anonymous functions -- 2.4.4.Pseudo code and source code protection -- 2.5.Two-dimensional Graphics -- 2.5.1.Basic statements of two-dimensional plotting -- 2.5.2.Plotting with multiple horizontal or vertical axes -- 2.5.3.Other two-dimensional plotting functions -- 2.5.4.Plots of implicit functions -- 2.5.5.Graphics decorations -- 2.5.6.Data file access with MATLAB -- 2.6.Three-dimensional Graphics -- 2.6.1.Plotting of three-dimensional curves -- 2.6.2.Plotting of three-dimensional surfaces -- 2.6.3.Viewpoint settings in 3D graphs -- 2.6.4.Surface plots of parametric equations -- 2.6.5.Spheres and cylinders -- 2.6.6.Drawing 2D and 3D contours -- 2.6.7.Drawing 3D implicit functions -- 2.7.Four-dimensional Visualization -- Exercises -- Bibliography -- 3.1.Analytical Solutions to Limit Problems -- 3.1.1.Limits of univariate functions -- 3.1.2.Limits of interval functions -- 3.1.3.Limits of multivariate functions -- 3.2.Analytical Solutions to Derivative Problems -- 3.2.1.Derivatives and high-order derivatives -- 3.2.2.Partial derivatives of multivariate functions -- 3.2.3.Jacobian matrix of multivariate functions -- 3.2.4.Hessian partial derivative matrix -- 3.2.5.Partial derivatives of implicit functions -- 3.2.6.Derivatives of parametric equations -- 3.2.7.Gradients, divergences and curls of fields -- 3.3.Analytical Solutions to Integral Problems -- 3.3.1.Indefinite integrals -- 3.3.2.Computing definite, infinite and improper integrals -- 3.3.3.Computing multiple Integrals -- 3.4.Series Expansions and Finite-term Series Approximations -- 3.4.1.Taylor series expansion -- 3.4.2.Fourier series expansion -- 3.5.Infinite Series and Products -- 3.5.1.Series -- 3.5.2.Product of sequences -- 3.5.3.Convergence test of infinite series -- 3.6.Path Integrals and Line Integrals -- 3.6.1.Path integrals -- 3.6.2.Line integrals -- 3.7.Surface Integrals -- 3.7.1.Scalar surface integrals -- 3.7.2.Vector surface integrals -- 3.8.Numerical Differentiation -- 3.8.1.Numerical differentiation algorithms -- 3.8.2.Central-point difference algorithm with MATLAB implementation -- 3.8.3.Gradient computations of functions with two variables -- 3.9.Numerical Integration Problems -- 3.9.1.Numerical integration from given data using trapezoidal method -- 3.9.2.Numerical integration of univariate functions -- 3.9.3.Numerical infinite integrals -- 3.9.4.Evaluating integral functions -- 3.9.5.Numerical solutions to double integrals -- 3.9.6.Numerical solutions to triple integrals -- 3.9.7.Multiple integral evaluations -- Exercises -- Bibliography -- 4.1.Inputting Special Matrices -- 4.1.1.Numerical matrix input -- 4.1.2.Defining symbolic matrices -- 4.1.3.Sparse matrix input -- 4.2.Fundamental Matrix Operations -- 4.2.1.Basic concepts and properties of matrices -- 4.2.2.Matrix inversion -- 4.2.3.Generalized matrix inverse -- 4.2.4.Matrix eigenvalue problems -- 4.3.Fundamental Matrix Transformations -- 4.3.1.Similarity transformations and orthogonal matrices -- 4.3.2.Triangular and Cholesky factorizations -- 4.3.3.Companion, diagonal and Jordan transformations -- 4.3.4.Singular value decompositions -- 4.4.Solving Matrix Equations -- 4.4.1.Solutions to linear algebraic equations -- 4.4.2.Solutions to Lyapunov equations -- 4.4.3.Solutions to Sylvester equations -- 4.4.4.Solutions of Diophantine equations -- 4.4.5.Solutions to Riccati equations -- 4.5.Nonlinear Functions and Matrix Function Evaluations -- 4.5.1.Element-by-element computations -- 4.5.2.Computations of matrix exponentials -- 4.5.3.Trigonometric functions of matrices -- 4.5.4.General matrix functions -- 4.5.5.Power of a matrix -- Exercises -- Bibliography -- 5.1.Laplace Transforms and Their Inverses -- 5.1.1.Definitions and properties -- 5.1.2.Computer solution to Laplace transform problems -- 5.1.3.Numerical solutions of Laplace transforms -- 5.2.Fourier Transforms and Their Inverses -- 5.2.1.Definitions and properties -- 5.2.2.Solving Fourier transform problems -- 5.2.3.Fourier sinusoidal and cosine transforms -- 5.2.4.Discrete Fourier sine, cosine transforms -- 5.2.5.Fast Fourier transforms -- 5.3.Other Integral Trasforms -- 5.3.1.Mellin transform -- 5.3.2.Hankel transform solutions -- 5.4.z Transforms and Their Inverses -- 5.4.1.Definitions and properties of z transforms and inverses -- 5.4.2.Computations of z transform -- 5.4.3.Bilateral z transforms -- 5.4.4.Numerical inverse z transform of rational functions -- 5.5.Essentials of Complex-valued Functions -- 5.5.1.Complex matrices and their manipulations -- 5.5.2.Mapping of complex-valued functions -- 5.5.3.Riemann surfaces -- 5.6.Solving Complex-valued Function Problems -- 5.6.1.Concept and computation of poles and residues -- 5.6.2.Partial fraction expansion for rational functions -- 5.6.3.Inverse Laplace transform using PFEs -- 5.6.4.Laurent series expansions -- 5.6.5.Computing closed-path integrals -- 5.7.Solutions of Difference Equations -- 5.7.1.Analytical solutions of linear difference equations -- 5.7.2.Numerical solutions of linear time varying difference equations -- 5.7.3.Solutions of linear time-invariant difference equations -- 5.7.4.Numerical solutions of nonlinear difference equations -- Exercises -- Bibliography -- 6.1.Nonlinear Algebraic Equations -- 6.1.1.Graphical method for solving nonlinear equations -- 6.1.2.Quasi-analytic solutions to polynomial-type equations -- 6.1.3.Numerical solutions to general nonlinear equations -- 6.2.Nonlinear Equations with Multiple Solutions -- 6.2.1.Numerical solutions -- 6.2.2.Finding high-precision solutions -- 6.2.3.Solutions of underdetermined equations -- 6.3.Unconstrained Optimization Problems -- 6.3.1.Analytical solutions and graphical solution methods -- 6.3.2.Solution of unconstrained optimization using MATLAB -- 6.3.3.Global minimum and local minima -- 6.3.4.Solving optimization problems with gradient information -- 6.4.Constrained Optimization Problems -- 6.4.1.Constraints and feasibility regions -- 6.4.2.Solving linear programming problems -- 6.4.3.Solving quadratic programming problems -- 6.4.4.Solving general nonlinear programming problems -- 6.5.Mixed Integer Programming Problems -- 6.5.1.Enumerate method in integer programming problems -- 6.5.2.Solutions of linear integer programming problems -- 6.5.3.Solutions of nonlinear integer programming problems -- 6.5.4.Solving binary programming problems -- 6.5.5.Assignment problems -- 6.6.Linear Matrix Inequalities -- 6.6.1.A general introduction to LMIs -- 6.6.2.Lyapunov inequalities -- 6.6.3.Classification of LMI problems -- 6.6.4.LMI problem solutions with MATLAB -- 6.6.5.Optimization of LMI problems by YALMIP Toolbox -- 6.7.Solutions of Multi-objective Programming Problems -- 6.7.1.Multi-objective optimization model -- 6.7.2.Least squares solutions of unconstrained multi-objective programming problems -- 6.7.3.Converting multi-objective problems into single-objective ones -- 6.7.4.Pareto front of multi-objective programming problems -- 6.7.5.Solutions of minimax problems -- 6.7.6.Solutions of multi-objective goal attainment problems -- 6.8.Dynamic Programming and Shortest Path Planning -- 6.8.1.Matrix representation of graphs -- 6.8.2.Optimal path planning of oriented graphs -- 6.8.3.Optimal path planning of undigraphs -- 6.8.4.Optimal path planning for graphs described by coordinates -- Exercises -- Bibliography -- 7.1.Analytical Solution Methods for Some Ordinary Differential Equations -- 7.1.1.Linear time-invariant ordinary differential equations -- 7.1.2.Analytical solution with MATLAB -- 7.1.3.Analytical solutions of linear state space equations -- 7.1.4.Analytical solutions to special nonlinear differential equations. -- 7.2.Numerical Solutions to Ordinary Differential Equations -- 7.2.1.Overview of numerical solution algorithms -- 7.2.2.Fixed-step Runge-Kutta algorithm and its MATLAB implementation -- 7.2.3.Numerical solution to first-order vector ODEs -- 7.3.Transforms to Standard Differential Equations -- 7.3.1.Manipulating a single high-order ODE -- 7.3.2.Manipulating multiple high-order ODEs -- 7.3.3.Validation of numerical solutions to ODEs -- 7.3.4.Transformation of differential matrix equations -- 7.4.Solutions to Special Ordinary Differential Equations -- 7.4.1.Solutions of stiff ordinary differential equations -- 7.4.2.Solutions of implicit differential equations -- 7.4.3.Solutions to differential algebraic equations -- and Contents note continued: 7.4.4.Solutions of switching differential equations -- 7.4.5.Solutions to linear stochastic differential equations -- 7.5.Solutions to Delay Differential Equations -- 7.5.1.Solutions of typical delay differential equations -- 7.5.2.Solutions of differential equations with variable delays -- 7.5.3.Solutions of neutral-type delay differential equations -- 7.6.Solving Boundary Value Problems -- 7.6.1.Shooting algorithm for linear equations -- 7.6.2.Boundary value problems of nonlinear equations -- 7.6.3.Solutions to general boundary value problems -- 7.7.Introduction to Partial Differential Equations -- 7.7.1.Solving a set of one-dimensional partial differential equations -- 7.7.2.Mathematical description to two-dimensional PDEs -- 7.7.3.The GUI for the PDE Toolbox - an introduction -- 7.8.Solving ODEs with Block Diagrams in Simulink -- 7.8.1.A brief introduction to Simulink -- 7.8.2.Simulink - relevant blocks -- 7.8.3.Using Simulink for modeling and simulation of ODEs -- Exercises -- Bibliography -- 8.1.Interpolation and Data Fitting -- 8.1.1.One-dimensional data interpolation -- 8.1.2.Definite integral evaluation from given samples -- 8.1.3.Two-dimensional grid data interpolation -- 8.1.4.Two-dimensional scattered data interpolation -- 8.1.5.Optimization problems based on scattered sample data -- 8.1.6.High-dimensional data interpolations -- 8.2.Spline Interpolation and Numerical Calculus -- 8.2.1.Spline interpolation in MATLAB -- 8.2.2.Numerical differentiation and integration with splines -- 8.3.Fitting Mathematical Models from Data -- 8.3.1.Polynomial fitting -- 8.3.2.Curve fitting by linear combination of basis functions -- 8.3.3.Least squares curve fitting -- 8.3.4.Least squares fitting of multivariate functions -- 8.4.Rational Function Approximations -- 8.4.1.Approximation by continued fraction expansions -- 8.4.2.Pade rational approximations -- 8.4.3.Special approximation polynomials -- 8.5.Special Functions and Their Plots -- 8.5.1.Gamma functions -- 8.5.2.Beta functions -- 8.5.3.Legendre functions -- 8.5.4.Bessel functions -- 8.5.5.Mittag-Leffler functions -- 8.6.Signal Analysis and Digital Signal Processing -- 8.6.1.Correlation analysis -- 8.6.2.Power spectral analysis -- 8.6.3.Filtering techniques and filter design -- Exercises -- Bibliography -- 9.1.Probability Distributions and Pseudorandom Numbers -- 9.1.1.Introduction to probability density functions and cumulative distribution functions -- 9.1.2.Probability density functions and cumulative distribution functions of commonly used distributions -- 9.1.3.Random numbers and pseudorandom numbers -- 9.2.Solving Probability Problems -- 9.2.1.Histogram and pie representation of discrete numbers -- 9.2.2.Probability computation of continuous functions -- 9.2.3.Monte Carlo solutions to mathematical problems -- 9.2.4.Simulation of random walk processes -- 9.3.Fundamental Statistical Analysis -- 9.3.1.Mean and variance of stochastic variables -- 9.3.2.Moments of stochastic variables -- 9.3.3.Covariance analysis of multivariate stochastic variables -- 9.3.4.Joint PDFs and CDFs of multivariate normal distributions -- 9.3.5.Outliers, quartiles and box plots -- 9.4.Statistical Estimations -- 9.4.1.Parametric estimation and interval estimation -- 9.4.2.Multivariate linear regression and interval estimation -- 9.4.3.Nonlinear least squares parametric and interval estimations -- 9.4.4.Maximum likelihood estimations -- 9.5.Statistical Hypothesis Tests -- 9.5.1.Concept and procedures for statistic hypothesis test -- 9.5.2.Hypothesis tests for distributions -- 9.6.Analysis of Variance -- 9.6.1.One-way ANOVA -- 9.6.2.Two-way ANOVA -- 9.6.3.n-way ANOVA -- 9.7.Principal Component Analysis -- Exercises -- Bibliography -- 10.1.Fuzzy Logic and Fuzzy Inference -- 10.1.1.MATLAB solutions to classical set problems -- 10.1.2.Fuzzy sets and membership functions -- 10.1.3.Fuzzy rules and fuzzy inference -- 10.2.Rough Set Theory and Its Applications -- 10.2.1.Introduction to rough set theory -- 10.2.2.Data processing problem solutions using rough sets -- 10.3.Neural Network and Applications in Data Fitting Problems -- 10.3.1.Fundamentals of neural networks -- 10.3.2.Feedforward neural network -- 10.3.3.Radial basis neural networks and applications -- 10.3.4.Graphical user interface for neural networks -- 10.4.Evolutionary Computing and Global Optimization Problem Solutions -- 10.4.1.Basic idea of genetic algorithms -- 10.4.2.Solutions to optimization problems with genetic algorithms -- 10.4.3.Solving constrained problems -- 10.4.4.Solving optimization problems with Global Optimization Toolbox -- 10.4.5.Towards accurate global minimum solutions -- 10.5.Wavelet Transform and Its Applications in Data Processing -- 10.5.1.Wavelet transform and waveforms of wavelet bases -- 10.5.2.Wavelet transform in signal processing problems -- 10.5.3.Graphical user interface in wavelets -- 10.6.Fractional-order Calculus -- 10.6.1.Definitions of fractional-order calculus -- 10.6.2.Properties and relationship of various fractional-order differentiation definitions -- 10.6.3.Evaluating fractional-order differentiation -- 10.6.4.Solving fractional-order differential equations -- 10.6.5.Block diagram based solutions of nonlinear fractional-order ordinary differential equations -- 10.6.6.Object-oriented modeling and analysis of linear fractional-order systems -- Exercises -- Bibliography.
Subject(s)
ISBN
9781498757775
1498757774
Note
A chapman & Hall Book.
Bibliography Note
Includes bibliographical references and index.
Source of Acquisition
Purchased with funds from the James and Joyce Gettys Libraries Endowment in the Math Library and in the School of Information Sciences and Technology; 2015
Endowment Note
James and Joyce Gettys Libraries Endowment in the Math Library and in the School of Information Sciences and Technology
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