Using R for Numerical Analysis in Science and Engineering (The R Series)

Description

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.

Contents

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