Page 483 - Numerical Methods for Chemical Engineering

472 Index

Optimization (cont.) Particle Swarm Optimization (PSO) 367
Example. fitting enzyme kinetics to empirical data Peclet number 270
230 local Peclet number 272
Example. optimal control of 1-D system tubular reactor definition 279
250–251 Permutation
Example. optimal steady-state design of CSTR matrix 41
244–245 parity 33
feasible point 236 Poisson-Boltzmann equation 313
global minimum search 361–364 Poisson distribution 334–336
gradient methods 213–223 MATLAB poisscdf 335
gradient vector 212 MATLAB poissfit 335
inequality constraints 235–240 MATLAB poissinv 335
Karush-Kuhn-Tucker (KKT) conditions 238 MATLAB poisspdf 335
line searches (see also Line searches) 216–217 MATLAB poissrnd 335
local minimum 212 MATLAB poissstat 335
MATLAB fmincon 242–243 Poisson equation 260
MATLAB fminsearch 213 Polymer
MATLAB fminunc 228–230 Brownian dynamics 367
MATLAB optimset 228 ideal chain model 366
Newton line search method 223–225 Polynomial
Newton trust-region method 225–227 approximation by Taylor series expansion 62
optimal control (see also Optimal control) calculating roots by eigenvalue analysis 148
245–251 MATLAB roots 148
penalty method 232 characteristic polynomial of a matrix 106
search direction 214 interpolation (see also Interpolation) 156–161
Sequential Quadratic Programming (SQP) Legendre polynomials 166
240 orthogonal polynomials 165
simplex method 213 Preconditioner matrix 288–291
slack variables 239 definition 289
steepest descent direction 214 incomplete Cholesky factorization 290
steepest descent method 217 incomplete LU factorization 290
stochastic optimization 361–364 Jacobi preconditioner 290
genetic algorithm 362–364 MATLAB cholinc 291
Particle Swarm Optimization (PSO) 367 MATLAB luinc 291
simulated annealing 361–362 Principal Component Analysis (PCA) 412–414
unconstrained problems 212–230 Probability theory 317–338
Orthogonal Bayes’ theorem (see also Bayesian statistics) 321
basis set 27 Bernoulli trials 327–328
Gram-Schmidt method 28 binomial distribution 329–330
collocation 304 Boltzmann distribution 337
functions 164 central limit theorem 333
matrix 105, 119 conditional expectation 323
polynomials 165 conditional probability 321
vectors 6 continuous probability distribution 326
Orthonormal covariance 336
basis set 27 covariance matrix 337
Gram-Schmidt method 28 cumulative probability distribution 327
vectors 6 discrete probability distribution 325
expectation 322
Parabolic PDEs 279 Gaussian distribution (see also Gaussian (normal)
Parameter estimation (see Bayesian statistics) distribution) 331–332
Example. fitting enzyme kinetics to empirical data independent events 321
230 joint probability 320
Partial Differential Equation (PDE) systems (see also normal distribution (see also Gaussian (normal)
Boundary Value Problems) distribution) 331–332
characteristic lines 275–279 Poisson distribution 334–336
elliptic equations 278 probability as statement of belief 382
from conservation principles (see also Balances) probability distributions 325–338
258 probability in frequentist view 319, 381
hyperbolic equations 278 probability of an event 319
parabolic equations 279 random variable 322
Poisson equation 260 random walks 328–329
stochastic PDEs 358–360 Stirling’s approximation 331