# Practical Numerical Methods for Chemical Engineers: Using Excel with VBA, 3rd Edition

## Richard A Davis

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This NEW 3rd edition builds on the popular success of prior editions to expand the breadth of Practical Numerical Methods with more VBA macros that boost Excel's power for modeling and analysis. Engineers & scientists will find enhanced coverage of computational tools applicable to a wider variety of problems in their own disciplines.

Excel is the de facto computational tool used by practicing engineers & scientists. Use this book to become proficient with VBA programming & customize your workbooks with time saving enhancements & powerful numerical techniques.

Topics include an introduction to modeling, Excel & VBA programming, root-finding for systems of linear & nonlinear equations, eigenproblems, derivative approximation, optimization, experimental uncertainty analysis, least-squares regression & model validation, interpolation, integration, ordinary & partial differential equations.

A companion web site has digital files for downloading 200 illustrations, examples, & the refined PNM3Suite workbook with 100 VBA user-defined functions, macros, & user forms for advanced numerical techniques. End-of-chapter practice problems for self-study are also available at the site (www.d.umn.edu/~rdavis/PNM/PNMExcelVBA3). Example files & macros are ready to be modified by users for their own needs.

The introduction includes a primer on chemical reaction engineering for problems involving mass & energy balances with reactions. The next two chapters cover frequently overlooked features of Excel & VBA to apply numerical methods in Excel, as well as document results. The remaining chapters present powerful numerical techniques using Excel & VBA.

1. Introduction to Numerical Methods & Mathematical Modeling
2. Introduction to Excel: Documentation, Graphing, Worksheet Functions, Validation & Formatting, What-if Analysis
3. VBA: Editor, Functions & Sub Procedures, Data Types, Structured Programming, Arithmetic & Worksheet Functions, Flow Control, Arrays, Communication, Message & Input Boxes, User Forms, Reading/Writing Files, Debugging
4. Linear Equations: Matrix Algebra, Gaussian Elimination & Crout Reduction with Pivoting, Thomas, Cholesky, Power, Jacobi, & Interpolation Method for Eigenvalues & Eigenvectors, Jacobi & Gauss-Seidel Iteration, Relaxation
5. Taylor Series Analysis: Finite Difference Derivative Approximations, Richardson's Extrapolation
6. Nonlinear Equations: Root Finding, Bisection, Regula Falsi, Newton & Secant Methods, Wegstein, Quasi-Newton, Aitkin & Steffensen, Homotopy, Goal Seek & Solver, Bairstow's Method for Polynomial Roots
7. Optimization: Solver, Luus-Jaakola, Quadratic Interpolation, Golden Section, Powell, Constraints, Scaling
8. Uncertainty Analysis: Law of Propagation, Monte Carlo Simulations with Latin Hypercube Sampling
9. Least-squares Regression: Linear & Nonlinear, LINEST, Gauss-Newton, Levenberg-Marquardt, Model Validation & Assessment, Parameter & Model Uncertainty Analysis, Weighted Regression
10. Interpolation: Linear, Newton Divided Difference & Lagrange Polynomials, Rational, Stineman, Cubic & Constrained Splines, Linear & Spline Bivariate Interpolation
11. Integration: Graphical, Trapezoidal, Midpoint for Improper Integrals, Romberg, Adaptive Simpson & Gauss-Kronrod, Multiple Integrals by Simpson, Guass-Kronrod & Monte Carlo
12. Initial-value Problems: Single Step Euler & Backward Euler, Implicit Trapezoidal for Stiffness, Variable Step Runge-Kutta Cash Karp, Dormand-Prince, Multi-step Adams-Bashforth-Moulton, Differential-Algebraic Systems
13. Boundary-value Problems & Partial Differential Equations: Shooting, Finite Difference, Orthogonal Collocation, Quasilinearization, Method of Lines, Crank-Nicholson
14. Review: Summary Tables of Excel & VBA Functions, User-defined Functions, Macros, User Forms

Reseña del editor:

The latest 3rd edition expands Practical Numerical Methods with more VBA to boost Excel's power for numerical modeling and analysis. Visit the companion web site to access the book's Excel and VBA files, and learn how to customize your Excel workbooks with the same numerical techniques found in specialized math software:

www.d.umn.edu/~rdavis/PNM/PNMExcelVBA3

1. A refined macro-enabled Excel workbook with a suite of over 170 VBA user-defined functions, macros and user forms for learning VBA and implementing advanced numerical techniques in Excel.
2. More than 200 practical example and animation workbook files from the book that demonstrate the power of numerical methods. Customize the example files and macros to tackle your own problems using VBA in Excel.
3. Hundreds of practice problems for self-guided study to sharpen your Excel and VBA skills.

The first chapter sets the stage for problem solving with numerical methods. The next two chapters cover frequently overlooked features of Excel (2007, 2010, 2013 and later) and VBA for implementing numerical methods in Excel, as well as documenting results. The remaining chapters present powerful numerical techniques using Excel and VBA to find roots to algebraic equations, approximate derivatives, optimize, model data by least-squares regression and interpolation, analyze risk and uncertainty, solve integrals & ordinary & partial differential equations:

1. Numerical Methods & Mathematical Modeling: expert problem solving
2. Excel: Documentation, Graphing, Worksheet Functions, Input Validation and Formatting, What-if Analysis
3. VBA: Editor and objects, Function and Sub Procedures, Data Types, Structured Programming, Arithmetic and Worksheet Functions, Flow Control, Arrays, Communication, Message and Input Boxes, User Forms, Reading/Writing Files, Debugging, Unit Conversions
4. Linear Equations: Matrix Algebra, Gaussian Elimination and Crout Reduction with Pivoting, Thomas, Cholesky, Power, Jacobi, and Interpolation Methods for Eigenvalues and Eigenvectors, Jacobi and Gauss-Seidel Iteration, Relaxation
5. Taylor Series Analysis: Finite Difference Derivative Approximation, Richardson's Extrapolation, Ridder's algorithm, Sensitivity
6. Nonlinear Equations Root Finding: Methods of Bisection, Regula Falsi, Newton, Secant, Pade, Wegstein, Quasi-Newton, Aitkin/Steffensen, Homotopy, Bairstow (for polynomial roots), Goal Seek and Solver
7. Optimization: Solver, Luus-Jaakola, Quadratic, Golden Section, Powell, Downhill Simplex, Firefly, Constraints, Scaling and Sensitivity
8. Uncertainty and Risk Analysis: Bootstrap, Confidence Intervals, Law of Propagation, Monte Carlo Simulations with Latin Hypercube Sampling
9. Least-squares Regression: Linear, Nonlinear, LINEST, Gauss-Newton, Levenberg-Marquardt, Validation and Assessment, Uncertainty Analysis, Weighted Regression
10. Interpolation: Linear, Newton Divided Difference and Lagrange Polynomials, Rational, Bulirsh-Stoer, Pade, Stineman, Cubic, B, Akima and Constrained Hermite Splines, Bivariate Interpolation
11. Integration: Graphical, Trapezoidal, Midpoint and transformation for Improper Integrals, Romberg, Adaptive Simpson and Gauss-Kronrod, Multiple Integrals by Simpson, Kronrod and Monte Carlo
12. Initial-value Problems: Single Step Euler and Backward Euler, Implicit Trapezoidal for Stiffness, Variable Step Runge-Kutta Cash-Karp, Dormand-Prince, Multi-step Adams-Bashforth-Moulton, Differential-Algebraic Systems
13. Boundary-value Problems and Partial Differential Equations: Shooting, Finite Difference, Orthogonal Collocation, Quasilinearization, Method of Lines, Crank-Nicholson
14. Review: Reference Tables of Excel and VBA Functions, User-defined Functions, Macros, User Forms
15. Primer on chemical reaction engineering

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