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

    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 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