Practical Numerical Methods for Chemical Engineers: Using Excel with VBA

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9781495409653: Practical Numerical Methods for Chemical Engineers: Using Excel with VBA
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

From the Publisher:

This latest third edition expands the breadth of Practical Numerical Methods with more VBA macros to 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. ** The selection of software reflects Excel's status as the de facto computational tool used by practicing engineers. Engineers and scientists should become proficient at extending Excel’s capabilities with VBA programming to boost their worksheets with time saving enhancements and powerful numerical techniques. ** Topics include an introduction to modeling, Excel and VBA programming, root-finding for systems of equations, optimization, experimental uncertainty propagation, least-squares regression and model validation, interpolation, integration, and ordinary and partial differential equations. ** A companion web site has links to 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 with the examples from 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. ** Chapter 1 includes a brief introduction to chemical reaction engineering that provides some background needed for problems involving mass and energy balances with reactions. ** The next two chapters introduce 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 and VBA, including: ** General Methods: Sub and User-defined Function Procedures, User Forms, Pseudo-random Number Generation, Sorting, Formula Graphing and Evaluation, Random Sampling ** Linear Equations: Gaussian Elimination with Maximum Column Pivoting, Error Correction, Crout Reduction, Thomas algorithm for tri-diagonal and Cholesky's method for symmetric matrices, Matrix functions, Jacobi and Gauss-Seidel Iteration, Wegstein and Steffenson's version of Aitkin's Delta Square methods, Power method for Eigenproblems ** Nonlinear Equations: Ordinary Fixed-Point Iteration, Bisection, Secant, Regula Falsi, Newton and Quasi-Newton, Continuation (Homotopy), Goal Seek, Solver, Bairstow's method for polynomial roots ** Derivative Approximation: Finite Difference, Richardson's extrapolation, Sensitivity Analysis, Lagrange polynomials, splines ** Uncertainty Analysis: Jitter method for the Law of Propagation of Uncertainty, Monte Carlo with Latin-Hypercube sampling, Jack knife for regression parameter uncertainty ** Optimization: Graphical, Quadratic with acceleration, Powell, Golden Section, Luus-Jaakola, Solver (for linear and nonlinear programming), Parameter Scaling ** Least-squares Regression: multivariable linear and nonlinear models, Gauss-Newton, Levenberg-Marquardt, and Monte Carlo methods with parameter uncertainty, Rational Least Squares, Weighting ** Interpolation: Linear, Newton Divided Difference, Lagrange, Rational, Stineman, Cubic Spline, Constrained Splines, Bivariate 2-D, comments on Data Smoothing ** Integration: Trapezoid, Improper, Midpoint, Romberg, Adaptive Gauss-Kronrod and Simpson, Splines, multiple integrals with Simpson, Kronrod, and Monte Carlo methods ** Initial-Value ODEs: Taylor Series, improved and modified Euler, implicit Trapezoidal for stiff problems, fixed and variable single step 4-5 order Runge-Kutta, Cash-Karp and Dormand-Prince, Adams-Bashforth-Moulton multi-step methods ** Boundary Value ODEs and PDEs: Shooting, Finite Difference, Collocation on Finite Elements, Quasilinearization, Method of Lines, semi-implicit Crank-Nicholson methods ** Tables for quick reference of Excel, VBA, and custom functions & macros for numerical methods.

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