This non-traditional introduction to the mathematics of scientific computation describes the principles behind the major methods, from statistics, applied mathematics, scientific visualization, and elsewhere, in a way that is accessible to a large part of the scientific community. The authors use many hands-on examples to provide the reader with the tools and insight necessary for the effective and intelligent use of Mathematica or other software packages for this purpose.
Introductory material includes computational basics, a review of coordinate systems, an introduction to facets (planes and triangle meshes), and an introduction to computer graphics. The scientific computing part of the book covers topics in numerical linear algebra (basics, solving linear system, eigen-problems, SVD, and PCA) and numerical calculus (basics, data fitting, dynamic processes, root finding, and multivariate functions). The visualization component of the book is separated into three parts: empirical data, scalar values over 2D data, and volumes.
The book contains many figures that were created using Mathematica. Those figure notebooks as well as several tutorial-like notebooks can be found on the book's companion website.
Introduction | Computational Basics | Coordinate Systems | Background: Numerical Linear Algebra | Solving Linear Systems | Eigen-Problems | Background: Numerical Calculus | Data Fitting | Computing Dynamic Processes | Finding Roots | Computing with Multivariate Functions | Visualizing Empirical Data | Facets | Visualizing Scalar Values over 2D Data | Volume Visualization | Background: Computer Graphics
, Modeling and Simulation