Using R for Numerical Analysis in Science and Engineering

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