# Practical Numerical Methods for Chemical Engineers: Using Excel with VBA

## Davis, Richard A.

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From the Publisher:

This NEW 3rd edition builds on the popular success of earlier versions to expand the breadth of Practical Numerical Methods with more VBA macros that extend Excel's power for modeling and analysis. Engineers and scientists will find the 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 and scientists. Use this book to become proficient with VBA programming and boost your worksheets with time saving enhancements and powerful numerical techniques.

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

A companion web site has digital files for downloading 200 illustrations, examples, and the refined PNM3Suite workbook with 100 VBA user-defined functions, macros, and user forms for advanced numerical techniques. Practice problems are available for each chapter at the web site (www.d.umn.edu/~rdavis/PNM/PNMExcelVBA3). Example files and 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 and energy balances with reactions. The next two chapters cover frequently overlooked features of Excel and VBA for engineering programming 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 Uncertainty, Weighted Regression
10. Interpolation: Linear, Newton Divided Difference & Lagrange Polynomials, Rational, Stineman, Cubic & Constrained Splines, Linear & Spline Bivariate
11. Integration: Graphical, Trapezoidal, Midpoint for Improper Integrals, Romberg, Adaptive Simpson & Gauss-Kronrod, Multiple Integrals by Guass-Kronrod & Monte Carlo
12. Initial-value Problems: Single Step Euler & Backward Euler, Implicit Trapezoidal, 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

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