Using R for Numerical Analysis in Science and Engineering

This book shows how the free and open-source R environment can be used as a powerful and comprehensive platform for the kinds of numerical analysis that are traditionally employed by MATLAB(R). With R code fully integrated, the book offers brief descriptions of basic approaches and emphasizes detailed worked examples. It covers functions in the base installation of R as well as those in contributed packages, which greatly enhance the numerical analysis capabilities of R.

Instead of presenting the standard theoretical treatments that underlie the various numerical methods used by scientists and engineers, Using R for Numerical Analysis in Science and Engineering shows how to use R and its add-on packages to obtain numerical solutions to the complex mathematical problems commonly faced by scientists and engineers. This practical guide to the capabilities of R demonstrates Monte Carlo, stochastic, deterministic, and other numerical methods through an abundance of worked examples and code, covering the solution of systems of linear algebraic equations and nonlinear equations as well as ordinary differential equations and partial differential equations. It not only shows how to use R’s powerful graphic tools to construct the types of plots most useful in scientific and engineering work, but also: Explains how to statistically analyze and fit data to linear and nonlinear models Explores numerical differentiation, integration, and optimization Describes how to find eigenvalues and eigenfunctions Discusses interpolation and curve fitting Considers the analysis of time series Using R for Numerical Analysis in Science and Engineering provides a solid introduction to the most useful numerical methods for scientific and engineering data analysis using R.

Introduction Obtaining and Installing R Learning R Learning Numerical Methods Finding Help Augmenting R with Packages Learning More about R Calculating Basic Operators and Functions Complex Numbers Numerical Display, Round-Off Error, and Rounding Assigning Variables Relational Operators Vectors Matrices Time and Date Calculations Graphing Scatter Plots Function Plots Other Common Plots Customizing Plots Error Bars Superimposing Vectors in a Plot Modifying Axes Adding Text and Math Expressions Placing Several Plots in a Figure Two- and Three-Dimensional Plots The Plotrix Package Animation Additional Plotting Packages Programming and Functions Conditional Execution: If and If Else Loops User-Defined Functions Debugging Built-in Mathematical Functions Special Functions of Mathematical Physics Polynomial Functions in Packages Case Studies Solving Systems Of Algebraic Equations Finding the Zeroes of a Polynomial Finding the Zeroes of a Function Systems of Linear Equations: Matrix Solve Matrix Inverse Singular Matrix Overdetermined Systems and Generalized Inverse Sparse Matrices Matrix Decomposition Systems of Nonlinear Equations Case Studies Numerical Differentiation and Integration Numerical Differentiation Numerical Integration Symbolic Manipulations in R Case Studies Optimization One-Dimensional Optimization Multi-Dimensional Optimization with Optim() Other Optimization Packages Optimization with Constraints Global Optimization with Many Local Minima Linear and Quadratic Programming Mixed-Integer Linear Programming Case Study Ordinary Differential Equations Euler Method Improved Euler Method deSolve Package Matrix Exponential Solution for Sets of Linear ODEsEvents and Roots Difference Equations Delay Differential Equations Differential Algebraic Equations rootSolve for Steady State Solutions of Systems of ODEsbvpSolve Package for Boundary Value ODE Problems Stochastic Differential Equations: Gillespiessa Package Case Studies Partial Differential Equations Diffusion Equation Wave Equation Laplace’s Equation Solving PDEs with the Reactran Package Examples with the Reactran Package Case Studies Analyzing Data Getting Data into R Data Frames Summary Statistics for a Single Data Set Statistical Comparison of Two Samples Chi-Squared Test for Goodness of Fit Correlation Principal Component Analysis Cluster Analysis Case Studies Fitting Models To Data Fitting Data with Linear Models Fitting Data with Nonlinear Models Inverse Modeling of ODEs with the FME Package Improving the Convergence of Series: Padé and Shanks Interpolation Time Series, Spectrum Analysis, and Signal Processing Case Studies

Victor A. Bloomfield is currently emeritus professor at University of Minnesota, Minneapolis, USA. His research has encompassed more than four decades and a variety of topics, including enzyme kinetics, dynamic laser light scattering, bacteriophage assembly, DNA condensation, scanning tunneling microscopy, and single molecule stretching experiments on DNA. His theoretical work on biopolymer hydrodynamics and polyelectrolyte behavior has resulted in over 200 peer-reviewed journal publications. Using R for Numerical Analysis in Science and Engineering is an extension and broadening of his 2009 book, Computer Simulation and Data Analysis in Molecular Biology and Biophysics: An Introduction Using R, for general usage in science and engineering.