This practical guide shows how to use R and its add-on packages to obtain numerical solutions to complex mathematical problems commonly faced by scientists and engineers. Providing worked examples and code, the text not only addresses necessary aspects of the R programming language but also demonstrates how to produce useful graphs and statistically analyze and fit data to linear and nonlinear models. It covers Monte Carlo, stochastic, and deterministic methods and explores topics such as numerical differentiation and integration, interpolation and curve fitting, and optimization.