Verfügbarkeit: Numerical methods for chemical engineering

Numerical methods for chemical engineering: applications in MATLAB

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Bibliographische Detailangaben
1. Verfasser:	Beers, Kenneth J. (VerfasserIn)
Format:	Buch
Sprache:	English
Veröffentlicht:	Cambridge [u.a.] Cambridge Univ. Press 2007
Ausgabe:	1. publ.
Schlagworte:	MATLAB Ingeniería química - Matemáticas Mathematik Chemical engineering > Mathematics Chemische Verfahrenstechnik Numerisches Verfahren
Online-Zugang:	Inhaltsverzeichnis
Beschreibung:	XI, 474 S. Ill., graph. Darst.
ISBN:	0521859719 9780521859714

Internformat

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Datensatz im Suchindex

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adam_text	Contents Preface page ix 1 Linear algebra 1 Linear systems of algebraic equations 1 Review of scalar, vector, and matrix operations 3 Elimination methods for solving linear systems 10 Existence and uniqueness of solutions 23 The determinant 32 Matrix inversion 36 Matrix factorization 38 Matrix norm and rank 44 Submatrices and matrix partitions 44 Example. Modeling a separation system 45 Sparse and banded matrices 46 MATLAB summary 56 Problems 57 2 Nonlinear algebraic systems 61 Existence and uniqueness of solutions to a nonlinear algebraic equation 61 Iterative methods and the use of Taylor series 62 Newton s method for a single equation 63 The secant method 69 Bracketing and bisection methods 70 Finding complex solutions 70 Systems of multiple nonlinear algebraic equations 71 Newton s method for multiple nonlinear equations 72 Estimating the Jacobian and quasi-Newton methods 77 Robust reduced-step Newton method 79 The trust-region Newton method 81 Solving nonlinear algebraic systems in MATLAB 83 Example. 1 -D laminar flow of a shear-thinning polymer melt 85 Homotopy 88 Example. Steady-state modeling of a condensation polymerization reactor 89 v Bifurcation analysis 94 MATLAB summary 98 Problems 99 3 Matrix eigenvalue analysis 104 Orthogonal matrices 104 A specific example of an orthogonal matrix 105 Eigenvalues and eigenvectors defined 106 Eigenvalues/eigenvectors of a 2 x 2 real matrix 107 Multiplicity and formulas for the trace and determinant 109 Eigenvalues and the existence/uniqueness properties of linear systems 110 Estimating eigenvalues; Gershgorin s theorem 111 Applying Gershgorin s theorem to study the convergence of iterative linear solvers 114 Eigenvector matrix decomposition and basis sets 117 Numerical calculation of eigenvalues and eigenvectors in MATLAB 123 Computing extremal eigenvalues 126 The QR method for computing all eigenvalues 129 Normal mode analysis 134 Relaxing the assumption of equal masses 136 Eigenvalue problems in quantum mechanics 137 Single value decomposition SVD 141 Computing the roots of a polynomial 148 MATLAB summary 149 Problems 149 4 Initial value problems 154 Initial value problems of ordinary differential equations (ODE-IVPs) 155 Polynomial interpolation 156 Newton-Cotes integration 162 Gaussian quadrature 163 Multidimensional integrals 167 Linear ODE systems and dynamic stability 169 Overview of ODE-IVP solvers in MATLAB 176 Accuracy and stability of single-step methods 185 Stiff stability of BDF methods 192 Symplectic methods for classical mechanics 194 Differential-algebraic equation (DAE) systems 195 Parametric continuation 203 MATLAB summary 207 Problems 208 5 Numerical optimization 212 Local methods for unconstrained optimization problems 212 The simplex method 213 Gradient methods 213 Newton line search methods 223 Trust-region Newton method 225 Newton methods for large problems 227 Unconstrained minimizer fminunc in MATLAB 228 Example. Fitting a kinetic rate law to time-dependent data 230 Lagrangian methods for constrained optimization 231 Constrained minimizer fmincon in MATLAB 242 Optimal control 246 MATLAB summary 252 Problems 252 6 Boundary value problems 258 BVPs from conservation principles 258 Real-space vs. function-space BVP methods 260 The finite difference method applied to a 2-D BVP 260 Extending the finite difference method 264 Chemical reaction and diffusion in a spherical catalyst pellet 265 Finite differences for a convection/diffusion equation 270 Modeling a tubular chemical reactor with dispersion; treating multiple fields 279 Numerical issues for discretized PDEs with more than two spatial dimensions 282 The MATLAB 1-D parabolic and elliptic solver pdepe 294 Finite differences in complex geometries 294 The finite volume method 297 The finite element method (FEM) 299 FEM in MATLAB 309 Further study in the numerical solution of BVPs 311 MATLAB summary 311 Problems 312 7 Probability theory and stochastic simulation 317 The theory of probability 317 Important probability distributions 325 Random vectors and multivariate distributions 336 Brownian dynamics and stochastic differential equations (SDEs) 338 Markov chains and processes; Monte Carlo methods 353 Genetic programming 362 MATLAB summary 364 Problems 365 8 Bayesian statistics and parameter estimation 372 General problem formulation 372 Example. Fitting kinetic parameters of a chemical reaction 373 Single-response linear regression 377 Linear least-squares regression 378 The Bayesian view of statistical inference 381 The least-squares method reconsidered 388 Selecting a prior for single-response data 389 Confidence intervals from the approximate posterior density 395 MCMC techniques in Bayesian analysis 403 MCMC computation of posterior predictions 404 Applying eigenvalue analysis to experimental design 412 Bayesian multi response regression 414 Analysis of composite data sets 421 Bayesian testing and model criticism 426 Further reading 431 MATLAB summary 431 Problems 432 9 Fourier analysis 436 Fourier series and transforms in one dimension 436 1 -D Fourier transforms in MATLAB 445 Convolution and correlation 447 Fourier transforms in multiple dimensions 450 Scattering theory 452 MATLAB summary 459 Problems 459 References 461 Index 464
adam_txt	Contents Preface page ix 1 Linear algebra 1 Linear systems of algebraic equations 1 Review of scalar, vector, and matrix operations 3 Elimination methods for solving linear systems 10 Existence and uniqueness of solutions 23 The determinant 32 Matrix inversion 36 Matrix factorization 38 Matrix norm and rank 44 Submatrices and matrix partitions 44 Example. Modeling a separation system 45 Sparse and banded matrices 46 MATLAB summary 56 Problems 57 2 Nonlinear algebraic systems 61 Existence and uniqueness of solutions to a nonlinear algebraic equation 61 Iterative methods and the use of Taylor series 62 Newton's method for a single equation 63 The secant method 69 Bracketing and bisection methods 70 Finding complex solutions 70 Systems of multiple nonlinear algebraic equations 71 Newton's method for multiple nonlinear equations 72 Estimating the Jacobian and quasi-Newton methods 77 Robust reduced-step Newton method 79 The trust-region Newton method 81 Solving nonlinear algebraic systems in MATLAB 83 Example. 1 -D laminar flow of a shear-thinning polymer melt 85 Homotopy 88 Example. Steady-state modeling of a condensation polymerization reactor 89 v Bifurcation analysis 94 MATLAB summary 98 Problems 99 3 Matrix eigenvalue analysis 104 Orthogonal matrices 104 A specific example of an orthogonal matrix 105 Eigenvalues and eigenvectors defined 106 Eigenvalues/eigenvectors of a 2 x 2 real matrix 107 Multiplicity and formulas for the trace and determinant 109 Eigenvalues and the existence/uniqueness properties of linear systems 110 Estimating eigenvalues; Gershgorin's theorem 111 Applying Gershgorin's theorem to study the convergence of iterative linear solvers 114 Eigenvector matrix decomposition and basis sets 117 Numerical calculation of eigenvalues and eigenvectors in MATLAB 123 Computing extremal eigenvalues 126 The QR method for computing all eigenvalues 129 Normal mode analysis 134 Relaxing the assumption of equal masses 136 Eigenvalue problems in quantum mechanics 137 Single value decomposition SVD 141 Computing the roots of a polynomial 148 MATLAB summary 149 Problems 149 4 Initial value problems 154 Initial value problems of ordinary differential equations (ODE-IVPs) 155 Polynomial interpolation 156 Newton-Cotes integration 162 Gaussian quadrature 163 Multidimensional integrals 167 Linear ODE systems and dynamic stability 169 Overview of ODE-IVP solvers in MATLAB 176 Accuracy and stability of single-step methods 185 Stiff stability of BDF methods 192 Symplectic methods for classical mechanics 194 Differential-algebraic equation (DAE) systems 195 Parametric continuation 203 MATLAB summary 207 Problems 208 5 Numerical optimization 212 Local methods for unconstrained optimization problems 212 The simplex method 213 Gradient methods 213 Newton line search methods 223 Trust-region Newton method 225 Newton methods for large problems 227 Unconstrained minimizer fminunc in MATLAB 228 Example. Fitting a kinetic rate law to time-dependent data 230 Lagrangian methods for constrained optimization 231 Constrained minimizer fmincon in MATLAB 242 Optimal control 246 MATLAB summary 252 Problems 252 6 Boundary value problems 258 BVPs from conservation principles 258 Real-space vs. function-space BVP methods 260 The finite difference method applied to a 2-D BVP 260 Extending the finite difference method 264 Chemical reaction and diffusion in a spherical catalyst pellet 265 Finite differences for a convection/diffusion equation 270 Modeling a tubular chemical reactor with dispersion; treating multiple fields 279 Numerical issues for discretized PDEs with more than two spatial dimensions 282 The MATLAB 1-D parabolic and elliptic solver pdepe 294 Finite differences in complex geometries 294 The finite volume method 297 The finite element method (FEM) 299 FEM in MATLAB 309 Further study in the numerical solution of BVPs 311 MATLAB summary 311 Problems 312 7 Probability theory and stochastic simulation 317 The theory of probability 317 Important probability distributions 325 Random vectors and multivariate distributions 336 Brownian dynamics and stochastic differential equations (SDEs) 338 Markov chains and processes; Monte Carlo methods 353 Genetic programming 362 MATLAB summary 364 Problems 365 8 Bayesian statistics and parameter estimation 372 General problem formulation 372 Example. Fitting kinetic parameters of a chemical reaction 373 Single-response linear regression 377 Linear least-squares regression 378 The Bayesian view of statistical inference 381 The least-squares method reconsidered 388 Selecting a prior for single-response data 389 Confidence intervals from the approximate posterior density 395 MCMC techniques in Bayesian analysis 403 MCMC computation of posterior predictions 404 Applying eigenvalue analysis to experimental design 412 Bayesian multi response regression 414 Analysis of composite data sets 421 Bayesian testing and model criticism 426 Further reading 431 MATLAB summary 431 Problems 432 9 Fourier analysis 436 Fourier series and transforms in one dimension 436 1 -D Fourier transforms in MATLAB 445 Convolution and correlation 447 Fourier transforms in multiple dimensions 450 Scattering theory 452 MATLAB summary 459 Problems 459 References 461 Index 464
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spelling	Beers, Kenneth J. Verfasser (DE-588)140903984 aut Numerical methods for chemical engineering applications in MATLAB Kenneth J. Beers 1. publ. Cambridge [u.a.] Cambridge Univ. Press 2007 XI, 474 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier MATLAB Ingeniería química - Matemáticas Mathematik Chemical engineering Mathematics Chemische Verfahrenstechnik (DE-588)4069941-9 gnd rswk-swf MATLAB (DE-588)4329066-8 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf Chemische Verfahrenstechnik (DE-588)4069941-9 s Numerisches Verfahren (DE-588)4128130-5 s MATLAB (DE-588)4329066-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015041325&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis
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title	Numerical methods for chemical engineering applications in MATLAB
title_auth	Numerical methods for chemical engineering applications in MATLAB
title_exact_search	Numerical methods for chemical engineering applications in MATLAB
title_exact_search_txtP	Numerical methods for chemical engineering applications in MATLAB
title_full	Numerical methods for chemical engineering applications in MATLAB Kenneth J. Beers
title_fullStr	Numerical methods for chemical engineering applications in MATLAB Kenneth J. Beers
title_full_unstemmed	Numerical methods for chemical engineering applications in MATLAB Kenneth J. Beers
title_short	Numerical methods for chemical engineering
title_sort	numerical methods for chemical engineering applications in matlab
title_sub	applications in MATLAB
topic	MATLAB Ingeniería química - Matemáticas Mathematik Chemical engineering Mathematics Chemische Verfahrenstechnik (DE-588)4069941-9 gnd MATLAB (DE-588)4329066-8 gnd Numerisches Verfahren (DE-588)4128130-5 gnd
topic_facet	MATLAB Ingeniería química - Matemáticas Mathematik Chemical engineering Mathematics Chemische Verfahrenstechnik Numerisches Verfahren
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