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Numerical Methods for Chemical Engineering Applications in MATLAB

ISBN-10: 0521859719

ISBN-13: 9780521859714

Edition: 2006

Authors: Kenneth J. Beers

List price: $102.00
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Description:

Suitable for a first year graduate course, this textbook unites the applications of numerical mathematics and scientific computing to the practice of chemical engineering. Written in a pedagogic style, the book describes basic linear and nonlinear algebric systems all the way through to stochastic methods, Bayesian statistics and parameter estimation. These subjects are developed at a level of mathematics suitable for graduate engineering study without the exhaustive level of the theoretical mathematical detail. The implementation of numerical methods in MATLAB is integrated within each chapter and numerous examples in chemical engineering are provided, with a library of corresponding MATLAB programs. This book will provide the graduate student with essential tools required by industry and research alike. Supplementary material includes solutions to homework problems set in the text, MATLAB programs and tutorial, lecture slides, and complicated derivations for the more advanced reader. These are available online at www.cambridge.org/9780521859714.
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Book details

List price: $102.00
Copyright year: 2006
Publisher: Cambridge University Press
Publication date: 10/30/2006
Binding: Hardcover
Pages: 488
Size: 7.00" wide x 9.75" long x 1.25" tall
Weight: 2.442
Language: English

Kenneth J Beers has been Assistant Professor at MIT since the year 2000. He has taught extensively across the engineering discipline at both the undergraduate and graduate level. This book is a result of the sucessful course the author devised at MIT for numerical methods applied to chemical engineering.

Preface
Linear algebra
Linear systems of algebraic equations
Review of scalar, vector, and matrix operations
Elimination methods for solving linear systems
Existence and uniqueness of solutions
The determinant
Matrix inversion
Matrix factorization
Matrix norm and rank
Submatrices and matrix partitions
Example. Modeling a separation system
Sparse and banded matrices
MATLAB summary
Problems
Nonlinear algebraic systems
Existence and uniqueness of solutions to a nonlinear algebraic equation
Iterative methods and the use of Taylor series
Newton's method for a single equation
The secant method
Bracketing and bisection methods
Finding complex solutions
Systems of multiple nonlinear algebraic equations
Newton's method for multiple nonlinear equations
Estimating the Jacobian and quasi-Newton methods
Robust reduced-step Newton method
The trust-region Newton method
Solving nonlinear algebraic systems in MATLAB
Example. 1-D laminar flow of a shear-thinning polymer melt
Homotopy
Example. Steady-state modeling of a condensation polymerization reactor
Bifurcation analysis
MATLAB summary
Problems
Matrix eigenvalue analysis
Orthogonal matrices
A specific example of an orthogonal matrix
Eigenvalues and eigenvectors defined
Eigenvalues/eigenvectors of a 2 x 2 real matrix
Multiplicity and formulas for the trace and determinant
Eigenvalues and the existence/uniqueness properties of linear systems
Estimating eigenvalues; Gershgorin's theorem
Applying Gershgorin's theorem to study the convergence of iterative linear solvers
Eigenvector matrix decomposition and basis sets
Numerical calculation of eigenvalues and eigenvectors in MATLAB
Computing extremal eigenvalues
The QR method for computing all eigenvalues
Normal mode analysis
Relaxing the assumption of equal masses
Eigenvalue problems in quantum mechanics
Single value decomposition SVD
Computing the roots of a polynomial
MATLAB summary
Problems
Initial value problems
Initial value problems of ordinary differential equations (ODE-IVPs)
Polynomial interpolation
Newton-Cotes integration
Gaussian quadrature
Multidimensional integrals
Linear ODE systems and dynamic stability
Overview of ODE-IVP solvers in MATLAB
Accuracy and stability of single-step methods
Stiff stability of BDF methods
Symplectic methods for classical mechanics
Differential-algebraic equation (DAE) systems
Parametric continuation
MATLAB summary
Problems
Numerical optimization
Local methods for unconstrained optimization problems
The simplex method
Gradient methods
Newton line search methods
Trust-region Newton method
Newton methods for large problems
Unconstrained minimizer fminunc in MATLAB
Example. Fitting a kinetic rate law to time-dependent data
Lagrangian methods for constrained optimization
Constrained minimizer fmincon in MATLAB
Optimal control
MATLAB summary
Problems
Boundary value problems
BVPs from conservation principles
Real-space vs. function-space BVP methods
The finite difference method applied to a 2-D BVP
Extending the finite difference method
Chemical reaction and diffusion in a spherical catalyst pellet
Finite differences for a convection/diffusion equation
Modeling a tubular chemical reactor with dispersion; treating multiple fields
Numerical issues for discretized PDEs with more than two spatial dimensions
The MATLAB 1-D parabolic and elliptic solver pdepe
Finite differences in complex geometries
The finite volume method
The finite element method (FEM)
FEM in MATLAB
Further study in the numerical solution of BVPs
MATLAB summary
Problems
Probability theory and stochastic simulation
The theory of probability
Important probability distributions
Random vectors and multivariate distributions
Brownian dynamics and stochastic differential equations (SDEs)
Markov chains and processes; Monte Carlo methods
Genetic programming
MATLAB summary
Problems
Bayesian statistics and parameter estimation
General problem formulation
Example. Fitting kinetic parameters of a chemical reaction
Single-response linear regression
Linear least-squares regression
The Bayesian view of statistical inference
The least-squares method reconsidered
Selecting a prior for single-response data
Confidence intervals from the approximate posterior density
MCMC techniques in Bayesian analysis
MCMC computation of posterior predictions
Applying eigenvalue analysis to experimental design
Bayesian multi response regression
Analysis of composite data sets
Bayesian testing and model criticism
Further reading
MATLAB summary
Problems
Fourier analysis
Fourier series and transforms in one dimension
1-D Fourier transforms in MATLAB
Convolution and correlation
Fourier transforms in multiple dimensions
Scattering theory
MATLAB summary
Problems
References
Index