NUMERICAL METHODS. lor CHEMICAL ENGINEERS. Using Excel', VBA, and MATLAB* VICTOR J. LAW. CRC Press. Taylor & Francis Group

Transcription

1 NUMERICAL METHODS lor CHEMICAL ENGINEERS Using Excel', VBA, and MATLAB* VICTOR J. LAW CRC Press Taylor & Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business

2 Contents Preface Author Notes to the Instructor xiii xv xvii Chapter 1 Roots of a Single Nonlinear Equation Introduction Algorithms for Solving/(jc) 0 = Plotting the Equation Fixed-Point Iteration (Direct Substitution) Bisection Newton's Method Secant Method Using Excel to Solve Nonlinear Equations (Goal Seek) A Note on In-Ceil Iteration 16 Exercises 16 References 20 Chapter 2 Visual Basic for Applications Programming Introduction Algorithm Design VBA Coding Example VBA Project Getting Help and Documentation on VBA VBA Statements and Features Assignment Statement Expressions Numerical Expressions Logical (Boolean) Expressions Objects and OOP Built-in Functions of VBA Program Control Branching If-Then-Else Looping For...Next While...Wend Statement VBA Data Types Subs and Functions 37

3 vjjj Contents 2.12 Input and Output Getting Data from the Worksheet Putting Data onto the Worksheet Array Data Structures Array Arguments Dynamic Arrays in VBA Alternative I/O Methods Using Range.Select Using Message Box Using Input Box Using Debugger 44 Exercises 50 References 54 Chapter 3 Linear Algebra and Systems of Linear Equations Introduction Notation Vectors Vector Operations Vector Addition and Subtraction Multiplication by a Scalar Vector Transpose Linear Combinations of Vectors Vector Inner Product Vector Norm Orthogonal Vectors Orthonormal Vectors Matrices Matrix Operations Matrix Addition and Subtraction Multiplication by a Scalar Transposition of Matrices Special Matrices Matrix Multiplication Matrix Determinant Matrix Inverse More Special Matrices Solving Systems of Linear Algebraic Equations Gaussian Elimination Determinant Revisited Gauss-Jordan Elimination Rank of Matrix Existence and Uniqueness of Solutions for Ax = b Linear Equations and Vector/Matrix Operations in Excel More about Matrix.xla 71

4 Contents ix 3.10 SVD and Pseudo-Inverse of a Matrix 73 Exercises 76 Reference 80 Chapter 4 Numerical Differentiation and Integration Numerical Differentiation Approximation of a Derivative in One Variable Approximation of Partial Derivatives Numerical Integration Trapezoidal Rule Simpson's Rule Gauss Quadrature Curve Fitting for Integration 91 Exercises 93 Chapter 5 Ordinary Differential Equations (Initial Value Problems) Introduction General Statement of the Problem Euler-Type Methods Euler's Method for Single ODE Stability of Numerical Solutions of ODEs Euler Backward Method Trapezoidal Method (Modified Euler) Accuracy of Euler-Type Methods RK Methods Second-Order RK Method Fourth-Order RK Method Stiff ODEs Solving Systems of ODE-IVPs Higher-Order ODEs Ill Exercises 116 Chapter 6 Ordinary Differential Equations (Boundary Value Problems) Introduction Shooting Method Split BVPs Using Finite Differences More Complex Boundary Conditions with ODE-BVPs 127 Exercises 129 Reference 135 Chapter 7 Regression Analysis and Parameter Estimation Introduction and the General Method of Least Squares 137

5 X Contents 7.2 Linear Regression Analysis Straight Line Regression Curvilinear Regression How Good Is the Fit from a Statistical Perspective? Residual Plots Correlation Coefficient Parameter Standard Deviations Parameter Confidence Intervals Using f-ratios (f-statistics) for Individual Parameter Significance Regression Using Excel's Regression Add-In Numerical Differentiation and Integration Revisited 155 Exercises 156 Chapter 8 Partial Differential Equations Introduction Parabolic PDEs Explicit Method (Centered Difference in x, Forward Difference in 0) Centered Difference in x, Backward Difference in Crank-Nicholson Method (Centered Difference in x, Centered Difference in 6) Thomas Algorithm for Tridiagonal Systems Method of Lines Successive Overrelaxation for Elliptic PDEs 173 Exercises 177 Chapter 9 Linear Programming, Nonlinear Programming, Nonlinear Equations, and Nonlinear Regression Using Solver Introduction Linear Programming Nonlinear Programming Nonlinear Equations Nonlinear Regression Analysis 189 Exercises 191 Chapter 10 Introduction to MATLAB Introduction MATLAB Basics MATLAB Colon Operator MATLAB, M-Files, and Input from Command Window 202

6 Contents xi 10.3 MATLAB Programming Language Statements If-Then-Else Statements Looping Statements (For, While) MATLAB Function Arguments Plotting in MATLAB Plotting Two Functions on the Same Graph Example MATLAB Programs Closing Comment Regarding MATLAB 216 Exercises 217 Appendix: Additional Features of VBA 219 A.l Introduction 219 A.2 Calling Excel Built-in Functions in VBA Macros 219 A.3 Calling Excel Add-In Functions in VBA Macros 220 A.4 Variant Data Type 221 A.5 VBA Function That Returns an Array 223 A.6 Creating Excel Add-Ins 225 Index 227