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Lessons in Scientific Computing: Numerical Mathematics, Computer Technology, and Scientific Discovery [Pehme köide]

(University of Hawaii, USA)
  • Formaat: Paperback / softback, 190 pages, kõrgus x laius: 234x156 mm, kaal: 385 g, 20 Tables, black and white; 31 Line drawings, black and white; 31 Illustrations, black and white
  • Ilmumisaeg: 10-Oct-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138070580
  • ISBN-13: 9781138070585
Teised raamatud teemal:
Lessons in Scientific Computing: Numerical Mathematics, Computer Technology, and Scientific DiscoverySuurem pilt
  • Formaat: Paperback / softback, 190 pages, kõrgus x laius: 234x156 mm, kaal: 385 g, 20 Tables, black and white; 31 Line drawings, black and white; 31 Illustrations, black and white
  • Ilmumisaeg: 10-Oct-2018
  • Kirjastus: CRC Press
  • ISBN-10: 1138070580
  • ISBN-13: 9781138070585
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781138070585.html
Märksõnad:

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
  • Written in a clear and engaging style
  • Not wedded to a specific programming language

Arvustused

"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

Preface ix
To the Instructor xi
Behind the Scenes: Design of a Modern and Integrated Course xiii
Chapter 1 Analytical & Numerical Solutions
1(8)
1.1 Numerical Exploration
1(3)
1.2 A Computational Discovery: Universality of Period Doubling
4(5)
Chapter 2 A Few Concepts from Numerical Analysis
9(10)
2.1 Root Finding: Fast And Unreliable
9(4)
2.2 Error Propagation
13(2)
2.3 Numerical Instabilities
15(4)
Chapter 3 Roundoff & Number Representation
19(10)
3.1 Number Representation
19(3)
3.2 Ieee Standardization
22(3)
3.3 Roundoff Sensitivity
25(4)
Chapter 4 Programming Languages & Tools
29(12)
4.1 High-Level Programming Languages
29(3)
4.2 Interactive Computational Environments
32(2)
4.3 Relevant Language And Implementation Features
34(4)
4.4 Data Visualization
38(3)
Chapter 5 Sample Problems; Building Conclusions
41(10)
5.1 Chaotic Standard Map
41(4)
5.2 Gravitational 3-Body Problem
45(6)
Chapter 6 Approximation Theory
51(12)
6.1 Differentiation: Finite Differences
51(2)
6.2 Verifying The Convergence of a Method
53(2)
6.3 Numerical Integration: Illusions About What Lies Between
55(2)
6.4 Notions of Error and Convergence*
57(1)
6.5 Polynomial Interpolation
58(5)
Chapter 7 Other Common Computational Methods
63(14)
7.1 Fitting Graphs to Data in the age of Computation
63(2)
7.2 Fourier Transforms
65(3)
7.3 Ordinary Differential Equations
68(2)
7.4 Symbolic Computation
70(7)
Chapter 8 Performance Basics & Computer Architectures
77(12)
8.1 Execution Speed and Limiting Factors of Computations
77(2)
8.2 Memory And Data Transfer
79(3)
8.3 A Programmer's View of Computer Hardware
82(3)
8.4 Computer Architectures And Technological Change
85(4)
Chapter 9 High-Performance & Parallel Computing
89(14)
9.1 Code Optimization
89(4)
9.2 Parallel Computing
93(2)
9.3 Programming And Utilizing Parallel Hardware
95(4)
9.4 Hardware Acceleration
99(4)
Chapter 10 "The Operation Count; Numerical Linear Algebra
103(10)
10.1 Introduction
103(1)
10.2 Operation Counts in Linear Algebra
104(3)
10.3 Operation Counts for a Few Common Methods
107(2)
10.4 Data Movement and Data Locality
109(4)
Chapter 11 Random Numbers & Stochastic Methods
113(10)
11.1 Generation of Probabilistic Distributions
113(1)
11.2 Monte Carlo Integration: Accuracy Through Randomness
114(2)
11.3 Sample Problem: Ising Model*
116(7)
Chapter 12 Algorithms, Data Structures, and Complexity
123(12)
12.1 An Example Algorithm: Heapsort
123(2)
12.2 Data Structures
125(2)
12.3 Computational Complexity & Intractable Problems
127(2)
12.4 Approximations can Reduce Complexity
129(6)
Chapter 13 Data
135(14)
13.1 Data Files And Formats
136(4)
13.2 Text Processing Utilities
140(3)
13.3 Network And Storage Technologies
143(2)
13.4 Web Scraping And Data Archiving
145(4)
Chapter 14 Building Programs for Computation and Data Analysis
149(8)
14.1 Programming
149(3)
14.2 Scripting Languages
152(1)
14.3 Data-Intensive Problems
153(4)
Chapter 15 A Crash Course on Partial Differential Equations
157(12)
15.1 Initial Value Problems by Finite Differences
157(5)
15.2 Numerical Stability Revisited
162(1)
15.3 Boundary Value Problems by Finite Differences
163(2)
15.4 Other Methods for PDEs
165(4)
Chapter 16 Reformulated Problems
169(8)
16.1 Three And a Half Formulations Of Electrostatics
169(2)
16.2 Schrodinger Equation*
171(2)
16.3 Outline of Density Functional Method*
173(4)
Appendix A The Unix Environment 177(4)
Appendix B Numerical Libraries 181(2)
Appendix C Answers to Brainteasers 183(2)
Bibliography 185(2)
Index 187
Norbert Schörghofer 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.