Mathematical Principles for Scientific Computing and Visualization

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. 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. Many Areas Of Scientific Research, Such As Biology, Geography, And Psychology, Involve Gathering Data And Computing Results. A Number Of Software Packages, Such As Mathematica And Maple, Have Been Developed To Interpret And Share Those Results With Others In A Meaningful Way. However, Without Understanding The Mathematics Behind These Programs, One Might Produce Meaningless Or Erroneous Results. In This Non-traditional Introduction To The Mathematics Of Scientific Computation, The Authors Use Many Hands-on Examples To Provide The Reader With The Tools And Insight Necessary For The Effective And Intelligent Use Of Such Software Packages.--jacket. 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. Gerald Farin, Dianne Hansford. Includes Bibliographical References (p. 269-270) And Index. Front cover; Contents; Preface; Chapter 1. Introduction; Chapter 2. Computational Basics; Chapter 3. Coordinate Systems; Chapter 4. Background: Numerical Linear Algebra; Chapter 5. Solving Linear Systems; Chapter 6. Eigen-Problems; Chapter 7. Background: Numerical Calculus; Chapter 8. Data Fitting; Chapter 9. Computing Dynamic Processes; Chapter 10. Finding Roots; Chapter 11. Computing with Multivariate Functions; Chapter 12. Visualizing Empirical Data; Chapter 13. Facets; Chapter 14. Visualizing Scalar Values over 2D Data; Chapter 15. Volume Visualization