tailieunhanh - THE THIRD BRANCH OF PHYSICS Essays on Scientic Computing

Fundamental scienti¯c discoveries have been made with the help of computational methods. For instance, commonalities in the behavior of chaotic systems, most prominently Feigenbaum universality, had not been discovered or understood without computers. And only with numerical computations is it possible to predict the mass of the proton so accurately that fundamental theories of matter can be put to test. Such examples highlight the enormous role of numerical calculations for basic science | THE THIRD BRANCH OF PHYSICS Essays on Scientific Computing Norbert Schorghofer December 30 2006 Copyright 2005 by Norbert Schorghofer Contents About This Book iii 1 Analytic and Numeric Solutions Chaos 1 2 Themes of Numerical Analysis 5 3 Roundoff and Number Representation 11 4 Programming Tools 17 5 Physics Sampler 22 6 Discrete Approximations of the Continuum 27 7 From Programs to Data Analysis 34 8 Performance Basics 39 9 Deep inside Computers 45 10 Counting Operations 50 11 Random Numbers and Stochastic Methods 56 12 Algorithms Data Structures and Complexity 64 13 Symbolic Computation 70 14 A Crash Course on Partial Differential Equations 74 15 Reformulated Boundary-Value Problems 82 Answers to Problems 88

• Tin học văn phòng
• Number Representation
• Physics Sampler
• Performance Basics
• Counting Operations
• Data Analysis
• Random Numbers
• Computer Architecture
• Data Representation
• Positional Number Systems
• Binary and Hexadecimal Numbers
• Base Conversions
• Binary and Hexadecimal Addition
• Number Sense
• Numeration
• Quantity
• Operational Sense
• Instructional Strategies
• Representation