COMPUTER PROGRAMMING EXAMPLES FOR CHEMICAL ENGINEERS
CONTENTS 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 ?OW OF A SHEAR-THINNING POLYMER MELT HOMOTOPY EXAMPLE STEADY-STATE MODELING OF A CONDENSATION POLYMERIZATION REACTOR BIFURCATION ANALYSIS MATRIX EIGENVALUE ANALYSIS ORTHOGONAL MATRICES A SPECI?C EXAMPLE OF AN ORTHOGONAL MATRIX EIGENVALUES AND EIGENVECTORS DE?NED EIGENVALUES/EIGENVECTORS OF A 2 × 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 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 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 BOUNDARY VALUE PROBLEMS BVPS FROM CONSERVATION PRINCIPLES REAL-SPACE VS FUNCTION-SPACE BVP METHODS THE ?NITE DIFFERENCE METHOD APPLIED TO A 2-D BVP EXTENDING THE ?NITE 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 ?ELDS 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 ?NITE VOLUME METHOD THE ?NITE ELEMENT METHOD (FEM) FEM IN MATLAB FURTHER STUDY IN THE NUMERICAL SOLUTION OF BVPS 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 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 CON?DENCE 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 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 REFERENCES (1 1) AN1X1 + AN2X2 + + AN N XN = BN AI J IS THE CONSTANT COEF?CIENT (ASSUMED REAL) THAT MULTIPLIES THE UNKNOWN XJ IN EQUATION I BI IS THE CONSTANT “RIGHT-HAND-SIDE” COEF?CIENT FOR EQUATION I, ALSO ASSUMED REAL AS A PARTICULAR EXAMPLE, CONSIDER THE SYSTEM X1 + X2 + X3 = 2X1 + X2 + 3X3 = (1 2) 3X1 + X2 + 6X3 = FOR WHICH A11 = A12 = A13 = B1 = A21 = A22 = A23 = B2 = (1 3) A31 = A32 = A33 = B3 = BN ? ???? (1 6) FOR THE EXAMPLE SYSTEM (1 2), A = ? ? ? ? B = ? ?