1st Edition

# Using R for Numerical Analysis in Science and Engineering

By Victor A. Bloomfield Copyright 2014
360 Pages 133 B/W Illustrations
by Chapman & Hall

359 Pages 133 B/W Illustrations
by Chapman & Hall

Also available as eBook on:

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
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
Placing Several Plots in a Figure
Two- and Three-Dimensional Plots
The Plotrix Package
Animation
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
Mixed-Integer Linear Programming
Case Study
Ordinary Differential Equations
Euler Method
Improved Euler Method
deSolve Package
Matrix Exponential Solution for Sets of Linear ODEs
Events and Roots
Difference Equations
Delay Differential Equations
Differential Algebraic Equations
rootSolve for Steady State Solutions of Systems of ODEs
bvpSolve 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

### Biography

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.

"… the book is well organized, clearly written, and has a large amount of useful R code. It does a good job of answering the question of how to use R to perform numerical analyses of interest to scientists and engineers and, as such, can be recommended to the intended audience."
Journal of the Royal Statistical Society, Series A, 2015

"I would recommend it to those seeking to improve their programming efficiency. … the extensive coverage of optimization, ordinary differential equations, and partial differential equations combined with its exemplary demonstration of R coding through effective examples make this book a valuable resource for a wide audience. … a good reference for scientific and engineering researchers."
The American Statistician, February 2015

"... the book is well organized, clearly written, and has a large amount of useful R code. It does a good job answering the question of how to use R to perform numerical analyses of interest to scientists and engineers, and as such, can be recommended to the intended audience."
—Andrey Kostenko, Teaching Statistics