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 --Laplaces 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: Pad and Shanks --Interpolation --Time Series, Spectrum Analysis, and Signal Processing --Case Studies