Lessons in Scientific Computing: Numerical Mathematics, Computer Technology, and Scientific Discover

Taking an interdisciplinary approach, this new book provides a modern introduction to scientific computing, exploring numerical methods, computer technology, and their interconnections, which are treated with the goal of facilitating scientific research across all disciplines. Each chapter provides an insightful lesson and viewpoints from several subject areas are often compounded within a single chapter. Written with an eye on usefulness, longevity, and breadth, Lessons in Scientific Computing will serve as a "one stop shop" for students taking a unified course in scientific computing, or seeking a single cohesive text spanning multiple courses. Features: Provides a unique combination of numerical analysis, computer programming, and computer hardware in a single text Includes essential topics such as numerical methods, approximation theory, parallel computing, algorithms, and examples of computational discoveries in science Not wedded to a specific programming language

Review: "The book is a modernized, compact introduction into scientific computing. It combines the various components of the field (numerical analysis, discrete numerical mathematics, computer science, and computational hardware), subjects that are most often taught separately, into one book. The book takes a broad and interdisciplinary approach." -Hans Benker, Merseburg, in Zentralblatt MATH 1397 "The short, but insightful and deep book fills a gap in between scientific computing, computer science, numerics, and programming in various languages. I like very much that it does not build on one or the other language, but conveys concepts. I will definitely recommend it to bachelor and master students of any science or engineering major and will use it for teaching myself. " -Detlef Lohse, Physics of Fluids, University of Twente, The Netherlands "In an age when technical information is readily available on the Internet, what should a textbook on scientific computing look like? Norbert Schorghofer has a clear vision: his book provides a basic introduction to an extremely broad set of topics, enough to get a student started, and enough to pique the student's interest in delving deeper, either on the web or with more advanced books. Topics covered range across traditional numerical analysis, programming languages, modeling, computer architectures and parallel computing, and handling big data." - William H. Press, University of Texas at Austin

Author Biography: Norbert Schoerghofer is a Senior Scientist at the Planetary Science Institute and lives in Honolulu, Hawaii. After earning degrees in physics from the University of Vienna and the University of Chicago, he held visiting positions at MIT and Caltech, before moving to the University of Hawaii. His research areas are scientific modelling, planetary science, and astrogeophysics. He has published over 60 peer reviewed publications and has been a reviewer for 30 journals. His research has been featured in New Scientist, National Geographic Magazine, Astronomy Magazine, Huffington Post, and other mass media.

Chapter 1. Analytical and Numerical Solutions Chapter 2. A Few Concepts from Numerical Analysis Chapter 3. Roundoff and Number Representation Chapter 4. Programming Languages and Tools Chapter 5. Sample Problems; Building Conclusions Chapter 6. Approximation Theory Chapter 7. Other Common Computational Methods Chapter 8. Performance Basics and Computer Architectures Chapter 9. High-Performance and Parallel Computing Chapter 10. The Operation Count; Numerical Linear Algebra Chapter 11. Random Numbers and Stochastic Methods Chapter 12. Algorithms, Data Structures, and Complexity Chapter 13. Data Chapter 14. Building Programs for Computation and Data Analysis Chapter 15. Crash Course on Partial Differential Equiations Chapter 16. Reformulated Problems