Numerical methods for chemical engineering : applications in Matlab
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Livre papier |
| Lenguaje: | Anglais |
| Publicado: |
Cambridge ; New York :
Cambridge University Press
cop. 2007.
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| Materias: | |
| Nota: |
Informations supplémentaires (solutions aux problèmes, programmes Matlab, tutoriels...) disponible en ligne. Table des matières. http://www.loc.gov/catdir/enhancements/fy0619/2006303066-t.html |
| Autres localisations: | Voir dans le Sudoc |
Tabla de Contenidos:
- 1 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
- 2 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
- 3 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
- 4 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
- 5 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
- 6 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
- 7 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
- 8 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
- 9 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