Book Description

This latest 3rd edition expands the breadth of Practical Numerical Methods with over 100 VBA macros for extending Excel's power for engineering and scientific analysis. Engineers and scientists will find the enhanced coverage of computational tools applicable to a 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 & 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, documentation, Excel & VBA, root-finding for linear & nonlinear systems of equations, multivariate optimization, experimental uncertainty propagation & analysis, least-squares regression & model validation, interpolation, integration, and ordinary & partial differential equations. ** A companion web site has links to digital files for downloading up to 200 illustrations & examples & the refined PNM3Suite workbook with VBA user-defined functions, macros, & user forms for advanced numerical techniques. Practice problems are also available from the web site (https: //www.d.umn.edu/ rdavis/PNM/PNMExcelVBA3/). Example files & 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 & 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 & VBA, including: ** General Methods: Sub & User-defined Function Procedures, Pseudo-random Number Generation, Sorting, Formula Graphing & Evaluation, Random Sampling, User forms ** Linear Equations: Gaussian Elimination with Maximum Column Pivoting, Error Correction, Crout Reduction, Thomas algorithm for tri-diagonal & Cholesky's method for symmetric matrices, Matrix functions, Jacobi & Gauss-Seidel Iteration, Wegstein & Steffenson's version of Aitkin's Delta Square methods, Power method for Eigenproblems ** Nonlinear Equations: Ordinary Fixed-Point Iteration, Bisection, Secant, Regula Falsi, Newton & Quasi-Newton, Continuation (homotopy), Goal Seek, Solver, Bairstow's method for polynomial roots ** Derivative Approximation: Finite Difference, Richardson's extrapolation, Jacobian, 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: multivariate linear models, Gauss-Newton, Levenberg-Marquardt, and Monte Carlo for nonlinear regression with parameter uncertainty, Rational Least Squares, Weighting ** Interpolation: Linear, Newton Divided Difference, Lagrange, Rational, Stineman, Cubic Spline, Constrained Splines, Bivariate 2-D, Data Smoothing ** Integration: Trapezoid, Improper, Midpoint, Romberg, Adaptive Gauss-Kronrod & Simpson, Splines, multiple integrals with Simpson, Kronrod, & Monte Carlo methods ** Initial-Value ODEs: Taylor Series, improved & modified Euler, implicit Trapezoidal for stiff problems, fixed & variable single step 4-5 order Runge-Kutta, Cash-Karp & 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 m