.

0 (hodnocen0 x )

BK

Secon edition

Cambridge (UK) : Cambridge University Press, 2023

xvi, 688 stran : ilustrace ; 26 cm

ISBN 978-1-00-930386-6 (brožováno)

Obsahuje bibliografické odkazy a rejstřík

001941530

Preface xi // 1 idiomatic Python 1 // 1.1 Why Python? 2 // 1.2 Code Quality 3 // 1.3 Summary of Python Features 4 // 1.4 Core-Python Idioms 10 // 1.5 Basic Plotting with matplotlib 13 // 1.6 NumPy Idioms 15 // 1.7 Project: Visualizing Electric Fields 21 // Problems 25 // 2 Numbers 31 // 2.1 Motivation 31 // 2.2 Errors 32 // 2.3 Representing Real Numbers 41 // 2.4 Rounding Errors in the Wild 48 // 2.5 Project: the Multipole Expansion in Electromagnetism 63 // Problems 78 // 3 Derivatives 89 // 3.1 Motivation 89 // 3.2 Analytical Differentiation 90 // 3.3 Finite Differences 91 // 3.4 Automatic Differentiation 109 // 3.5 Project: Local Kinetic Energy in Quantum Mechanics 113 // Problems 121 // 4 Matrices 126 // 4.1 Motivation 126 // 4.2 Error Analysis 130 // 4.3 Solving Systems of Linear Equations 138 // 4.4 Eigenproblems 167 // 4.5 The Singular-Value Decomposition 197 // 4.6 Project: the Schrodinger Eigenvalue Problem 205 // Problems 213 // 5 Zeros and Minima 232 // 5.1 Motivation 232 // 5.2 Non-linear Equation in One Variable 235 // 5.3 Zeros of Polynomials 261 // 5.4 Systems of Non-Linear Equations 268 // 5.5 One-Dimensional Minimization 276 // 5.6 Multidimensional Minimization 282 // 5.7 Project: Extremizing the Action in Classical Mechanics 297 // Problems 305 // 6 Approximation 317 // 6.1 Motivation 317 // 6.2 Polynomial Interpolation 323 // 6.3 Cubic-Spline Interpolation 339 // 6.4 Trigonometric Interpolation 347 // 6.5 Linear Least-Squares Fitting 367 // 6.6 Linear Statistical Inference 383 //

6.7 Non-Linear Least-Squares Fitting 408 // 6.8 Project: Testing the Stefan-Boltzmann Law 422 // Problems 429 // 7 Integrals 453 // 7.1 Motivation 453 // 7.2 Newton-Cotes Methods 456 // 7.3 Adaptive Integration 474 // 7.4 Romberg Integration 479 // 7.5 Gaussian Quadrature 487 // 7.6 Complicating the Narrative 501 // 7.7 Monte Carlo 508 // 7.8 Project: Variational Quantum Monte Carlo 534 // Problems 546 // 8 Differential Equations 566 // 8.1 Motivation 566 // 8.2 Initial-Value Problems 570 // 8.3 Boundary-Value Problems 601 // 8.4 Eigenvalue Problems 608 // 8.5 Partial Differential Equations 617 // 8.6 Project: Poisson’s Equation in Two Dimensions 625 // Problems 632 // Appendix A Installation and Setup 657 // Appendix B Number Representations // B.1 Integers 658 // B.2 Real Numbers 658 // Problems 659 // 663 // AppendixC Math Background // C.1 Taylor Series 664 // C.2 Matrix Terminology 664 // C.3 Probability 66$ // 668 // Bibliography // Index 671