| Description |
1 online resource (711 p.) |
| Series |
New York Academy of Sciences Ser |
|
New York Academy of Sciences Ser
|
| Contents |
Intro -- Table of Contents -- Related Titles -- Title -- Authors -- Copyright -- Dedication -- Preface -- Acknowledgments -- 1: Introduction -- 1.1 Computational Physics and Computational Science -- 1.2 This Book's Subjects -- 1.3 This Book's Problems -- 1.4 This Book's Language: The Python Ecosystem -- 1.5 Python's Visualization Tools -- 1.6 Plotting Exercises -- 1.7 Python's Algebraic Tools -- 2: Computing Software Basics -- 2.1 Making Computers Obey -- 2.2 Programming Warmup -- 2.3 Python I/O -- 2.4 Computer Number Representations (Theory) -- 2.5 Problem: Summing Series |
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3: Errors and Uncertainties in Computations -- 3.1 Types of Errors (Theory) -- 3.2 Error in Bessel Functions (Problem) -- 3.3 Experimental Error Investigation -- 4: Monte Carlo: Randomness, Walks, and Decays -- 4.1 Deterministic Randomness -- 4.2 Random Sequences (Theory) -- 4.3 Random Walks (Problem) -- 4.4 Extension: Protein Folding and Self-Avoiding Random Walks -- 4.5 Spontaneous Decay (Problem) -- 4.6 Decay Implementation and Visualization -- 5: Differentiation and Integration -- 5.1 Differentiation -- 5.2 Forward Difference (Algorithm) -- 5.3 Central Difference (Algorithm) |
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5.4 Extrapolated Difference (Algorithm) -- 5.5 Error Assessment -- 5.6 Second Derivatives (Problem) -- 5.7 Integration -- 5.8 Quadrature as Box Counting (Math) -- 5.9 Algorithm: Trapezoid Rule -- 5.10 Algorithm: Simpson's Rule -- 5.11 Integration Error (Assessment) -- 5.12 Algorithm: Gaussian Quadrature -- 5.13 Higher Order Rules (Algorithm) -- 5.14 Monte Carlo Integration by Stone Throwing (Problem) -- 5.15 Mean Value Integration (Theory and Math) -- 5.16 Integration Exercises -- 5.17 Multidimensional Monte Carlo Integration (Problem) -- 5.18 Integrating Rapidly Varying Functions (Problem) |
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5.19 Variance Reduction (Method) -- 5.20 Importance Sampling (Method) -- 5.21 von Neumann Rejection (Method) -- 5.22 Nonuniform Assessment -- 6: Matrix Computing -- 6.1 Problem 3: N-D Newton-Raphson -- Two Masses on a String -- 6.2 Why Matrix Computing? -- 6.3 Classes of Matrix Problems (Math) -- 6.4 Python Lists as Arrays -- 6.5 Numerical Python (NumPy) Arrays -- 6.6 Exercise: Testing Matrix Programs -- 7: Trial-and-Error Searching and Data Fitting -- 7.1 Problem 1: A Search for Quantum States in a Box -- 7.2 Algorithm: Trial-and-Error Roots via Bisection |
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7.3 Improved Algorithm: Newton-Raphson Searching -- 7.4 Problem 2: Temperature Dependence of Magnetization -- 7.5 Problem 3: Fitting An Experimental Spectrum -- 7.6 Problem 4: Fitting Exponential Decay -- 7.7 Least-Squares Fitting (Theory) -- 7.8 Exercises: Fitting Exponential Decay, Heat Flow and Hubble's Law -- 8: Solving Differential Equations: Nonlinear Oscillations -- 8.1 Free Nonlinear Oscillations -- 8.2 Nonlinear Oscillators (Models) -- 8.3 Types of Differential Equations (Math) -- 8.4 Dynamic Form for ODEs (Theory) -- 8.5 ODE Algorithms -- 8.6 Runge-Kutta Rule |
| Notes |
Description based upon print version of record |
|
8.7 Adams-Bashforth-Moulton Predictor-Corrector Rule |
| Genre/Form |
Electronic books
|
| Form |
Electronic book
|
| ISBN |
9783527684694 |
|
3527684697 |
|
