Unless otherwise noted, the readings are from the required text:

Buy at Amazon Beers, Kenneth J. Numerical Methods for Chemical Engineering: Applications in MATLAB®. New York, NY: Cambridge University Press, November 2006. ISBN: 9780521859714.

In general, the readings were assigned ahead of the corresponding lecture topic.

The calendar below provides information on the course's lecture (L) and quiz (Q) sessions.

L1 Using MATLAB® to evaluate and plot expressions

pp. 1-25.

MATLAB® Tutorial

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

L2 Solving systems of linear equations pp. 25-32 and 36-56.

Linear Algebra

Existence and Uniqueness of Solutions

Matrix Inversion

Matrix Factorization

Matrix Norm and Rank

Submatricies and Matrix Partitions

Example. Modeling a Separation System

Sparse and Banded Matricies


Matrix factorization


Condition Number

Buy at Amazon Heath, Michael T. Scientific Computing: An Introductory Survey. 2nd ed. New York, NY: McGraw-Hill Companies, Inc., 2002, pp. 5-6 and 52-65. ISBN: 9780072399103.

Buy at Amazon Recktenwald, Gerald W. Introduction to Numerical Methods with MATLAB®: Implementations and Applications. Upper Saddle River, NJ: Prentice-Hall, 2000, pp. 402-410. ISBN: 9780201308600.

L4 When algorithms run into problems: Numerical error, ill-conditioning, and tolerances pp. 61-77.

Nonlinear Algebraic Systems

Existence and Uniqueness of Solutions to a Nonlinear Algebraic Equation

Iterative Methods and 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

L5 Introduction to systems of nonlinear equations pp. 77-85 and 88-99.

Nonlinear Algebraic Equations

Estimating the Jacobian and Quasi-Newton Methods

Robust Reduced-step Newton's Method

The Trust - Region Newton Method

Solving Nonlinear Algebraic Systems in MATLAB®


Example. Steady-state Modeling of a Condensation Polymerization Reactor

Bifurcation Analysis

L6 Modern methods for solving nonlinear equations pp. 104-113.

Matrix Eigenvalue Analysis

Orthogonal Matrices

Eigenvalues and Eigenvectors Defined

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

L7 Introduction to eigenvalues and eigenvectors pp. 117-123 and 148-149.

Matrix Eigenvalue Analysis

Eigenvector Matrix Decomposition and Basis Sets

Computing Roots of a Polynomial

L8 Constructing and using the eigenvector basis pp. 123-126 and 137-141.

Matrix Eigenvalue Analysis

Numerical Calculation of Eigenvalues and Eigenvectors in MATLAB®

Eigenvalue Problems in Quantum Mechanics

L9 Function space vs. real space methods for partial differential equations (PDEs) pp. 141-149.

Matrix Eigenvalue Analysis

Singular Value Decomposition

Computing the Roots of a Polynomial

L10 Function space pp. 126-134.

Matrix Eigenvalue Analysis

Computing Extremal Eigenvalues

The QR Method for Computing all Eigenvalues


Numerical calculation of eigenvalues and eigenvectors

Singular value decomposition (SVD)


Initial Value Problems

Initial Value Problems of Ordinary Differential Equations (ODE-IVPs)

Polynomial Interpolation

Newton-cotes Integration

Linear ODE Systems and Dynamic Stability

Q1 Quiz 1 pp. 154-163 and 169-176.

Initial Value Problems

Initial Value Problems of Ordinary Differential Equations (ODE-IVPs)

Polynomial Interpolation

Newton-cotes Integration

Linear ODE Systems and Dynamic Stability

L12 Ordinary differential equation - initial value problems (ODE-IVP) and numerical integration pp. 176-194.

Initial Value Problems

Overview of ODE-IVP Solvers in MATLAB®

Accuracy and Stability of Single-step Methods

Stiff Stability of BDF Methods

L13 Stiffness. MATLAB® ordinary differential equation (ODE) solvers pp. 195-203.

Initial Value Problems

Differential-Algebraic Equation (DAE) Systems


Implicit ordinary differential equation (ODE) solvers


pp. 212-231.

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


Differential algebraic equations (DAEs)

Introduction: Optimization

pp. 231-246.

Numerical Optimization

Lagrangian Methods for Constrained Optimization

Constrained Minimizer fmincon in MATLAB®

L16 Unconstrained optimization pp. 258-270.

Boundary Value Problems (BVPs)

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

L17 Constrained optimization pp. 270-279.

Boundary Value Problems

Finite Differences for a Convection/diffusion Equation



Sensitivity analysis

Introduction: Boundary value problems (BVPs)

pp. 282-299.

Boundary Value Problems

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

L19 Boundary value problems (BVPs) lecture 2 pp. 299-311.

Boundary Value Problems

The Finite Element Method (FEM)


Further Study in the Numerical Solution of BVPs

L20 Boundary value problems (BVPs) lecture 3: Finite differences, method of lines, and finite elements    
L21 TA tutorial on BVPs, FEMLAB®    
L22 Introduction: Models vs. Data pp. 372-389 and 325-338.

Bayesian Statistics and Parameter Estimation

General Problem Formulation

Example. Fitting Kinetic Parameters of a Chemical Reaction

Single-response Linear Regression

The Bayesian View of Statistical Inference

The Least Squares Method Reconsidered

Probability Theory and Stochastic Simulation

Important Probability Distributions

  • Bernoulli Trials
  • The Random Walk Problem
  • The Binomial Distribution
  • The Gaussian (Normal) Distribution
  • The Central Limit Theorem of Statistics
  • The Gaussian Distribution With Non-zero Mean
  • The Poisson Distribution

Random Vectors and Multivariate Distributions

  • The Boltzmann Distribution
  • The Maxwell Distribution
L23 Models vs. Data lecture 2: Bayesian view pp. 389-403.

Bayesian Statistics and Parameter Estimation

Selecting a Prior for Single-response Data

Confidence Intervals From the Approximate Posterior Density

L24 Uncertainties in model predictions pp. 403-431.

Bayesian Statistics and Parameter Estimation

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

L25 Conclude models vs. data    
L26 TA led review    
Q2 Quiz 2 (lectures 1 - 21)  

Probability Theory and Stochastic Simulation

Markov Chains and Processes; Monte Carlo Methods

Markov Chains

Monte Carlo Simulation in Statistical Mechanics

Monte Carlo Integration

Simulated Annealing


Models vs. Data recapitulation

Monte carlo and molecular dynamics

L28 Guest lecture on Monte Carlo / molecular dynamics: Frederick Bernardin pp. 363-364.

Probability Theory and Stochastic Simulation

Genetic Programming


Global optimization

Multiple minima


Modeling intrinsically stochastic processes

multiscale modeling

pp. 338-353.

Probability Theory and Stochastic Simulation

Brownian Dynamics and Stochastic Differential Equations (SDEs)

L31 Fluctuation-dissipation theorem    
L32 Kinetic Monte Carlo and turbulence modeling    

Operator splitting

Strang splitting

Strang Splitting

Schwer, Douglas A., Pisi Lu, William H. Green, Jr., and Viriato Semião. "A Consistent-splitting Approach to Computing Stiff Steady-state Reacting Flows With Adaptive Chemistry." Combust Theory Modelling 7 (2003): 383-399.


Fourier transforms

Fast fourier transform (FFT)

pp. 436-452.

Fourier Analysis

Fourier Series and Transforms in One Dimension

1-D Fourier Transforms in MATLAB®

Convolution and Correlation

Fourier Transforms in Multiple Dimensions

L35 Summary: Problem solving    
L36 TA led final review