Numerical Methods for Chemical Engineers Using Excel, VBA, and MATLAB

Roots of a Single Nonlinear Equation
Introduction
Algorithms for Solving f(x) = 0
Using Excel to Solve Nonlinear Equations (Goal Seek)
A Note on In-Cell Iteration References

Visual Basic^® for Applications Programming
Introduction
Algorithm Design
VBA Coding
Example VBA Project
Getting Help and Documentation on VBA
VBA Statements and Features
Objects and OOP
Built-In Functions of VBA
Program Control
VBA Data Types
Subs and Functions
Input and Output
Array Data Structures
Alternative I/O Methods
Using Debugger
References

Linear Algebra and Systems of Linear Equations
Introduction
Notation
Vectors
Vector Operations
Matrices
Matrix Operations
Solving Systems of Linear Algebraic Equations
Linear Equations and Vector/Matrix Operations in Excel^®
More About Matrix.xla
SVD and Pseudo-Inverse of a Matrix

Numerical Differentiation and Integration
Numerical Differentiation
Numerical Integration
Curve Fitting for Integration

Ordinary Differential Equations (Initial Value Problems)
Introduction
Euler-Type Methods
RK Methods
Stiff ODEs
Solving Systems of ODE-IVPs
Higher-Order ODEs

Ordinary Differential Equations (Boundary Value Problems)
Introduction
Shooting Method
Split BVPs Using Finite Differences
More Complex Boundary Conditions with ODE-BVPs
Reference

Regression Analysis and Parameter Estimation
General Method of Least Squares
Linear Regression Analysis
How Good Is the Fit from a Statistical Perspective?
Regression Using Excel’s Regression Add-In
Numerical Differentiation and Integration Revisited

Partial Differential Equations
Introduction
Parabolic PDEs
Thomas Algorithm for Tridiagonal Systems
Method of Lines
Successive Overrelaxation for Elliptic PDEs

Linear Programming, Nonlinear Programming, Nonlinear Equations, and Nonlinear Regression Using Solver
Introduction
Linear Programming
Nonlinear Programming
Nonlinear Equations
Nonlinear Regression Analysis

Introduction to MATLAB^®
Introduction
MATLAB^® Basics
MATLAB^® Programming Language Statements
MATLAB^® Function Arguments
Plotting in MATLAB^®
Example MATLAB^® Programs
Closing Comment Regarding MATLAB^®

Appendix A: Additional Features of VBA

Index

Biography

Victor J. Law, Ph.D., FAIChE, FIChemE, CE, initiated a program that was to become the Department of Computer Science at Tulane. During his tenure in computer science, he wrote two textbooks on introductory computer programming. In 1988, Dr. Law returned to the Chemical Engineering Department in order to resume his research career. He has taught classes in process control, transport phenomena, process design, engineering statistics, and numerical methods for chemical engineers. His research has included projects in coastal erosion, methane emissions from rice paddies, thermochemical processes for hydrogen production from water, and butanol production from biomass. Dr. Law is a Fellow of the American Institute of Chemical Engineers; a Fellow of the Institution of Chemical Engineers; a Chartered Engineer in the United Kingdom and Europe; and a Registered Professional Engineer, State of Louisiana.