Efnisyfirlit

• Half-title page
• Title page
• Copyright page
• Contents
• Preface to the Second Edition
• Preface to the First Edition
• 1 Introduction
  • 1.1 Scientific Software
  • 1.2 The Plan of This Book
  • 1.3 Can Python Compete with Compiled Languages?
  • 1.4 Limitations of This Book
  • 1.5 Installing Python and Add-ons
• 2 Getting Started with IPython
  • 2.1 Tab Completion
  • 2.2 Introspection
  • 2.3 History
  • 2.4 Magic Commands
  • 2.5 IPython in Action: An Extended Example
    • 2.5.1 An IPython terminal workflow
    • 2.5.2 An IPython notebook workflow
• 3 A Short Python Tutorial
  • 3.1 Typing Python
  • 3.2 Objects and Identifiers
  • 3.3 Numbers
    • 3.3.1 Integers
    • 3.3.2 Real numbers
    • 3.3.3 Boolean numbers
    • 3.3.4 Complex numbers
  • 3.4 Namespaces and Modules
  • 3.5 Container Objects
    • 3.5.1 Lists
    • 3.5.2 List indexing
    • 3.5.3 List slicing
    • 3.5.4 List mutability
    • 3.5.5 Tuples
    • 3.5.6 Strings
    • 3.5.7 Dictionaries
  • 3.6 Python if Statements
  • 3.7 Loop Constructs
    • 3.7.1 The Python for loop
    • 3.7.2 The Python continue statement
    • 3.7.3 The Python break statement
    • 3.7.4 List comprehensions
    • 3.7.5 Python while loop
  • 3.8 Functions
    • 3.8.1 Syntax and scope
    • 3.8.2 Positional arguments
    • 3.8.3 Keyword arguments
    • 3.8.4 Variable number of positional arguments
    • 3.8.5 Variable number of keyword arguments
    • 3.8.6 Python input/output functions
    • 3.8.7 The Python print function
    • 3.8.8 Anonymous functions
  • 3.9 Introduction to Python Classes
  • 3.10 The Structure of Python
  • 3.11 Prime Numbers: A Worked Example
• 4 NumPy
  • 4.1 One-Dimensional Arrays
    • 4.1.1 Ab initio constructors
    • 4.1.2 Look-alike constructors
    • 4.1.3 Arithmetical operations on vectors
    • 4.1.4 Ufuncs
    • 4.1.5 Logical operations on vectors
  • 4.2 Two-Dimensional Arrays
    • 4.2.1 Broadcasting
    • 4.2.2 Ab initio constructors
    • 4.2.3 Look-alike constructors
    • 4.2.4 Operations on arrays and ufuncs
  • 4.3 Higher-Dimensional Arrays
  • 4.4 Domestic Input and Output
    • 4.4.1 Discursive output and input
    • 4.4.2 NumPy text output and input
    • 4.4.3 NumPy binary output and input
  • 4.5 Foreign Input and Output
    • 4.5.1 Small amounts of data
    • 4.5.2 Large amounts of data
  • 4.6 Miscellaneous Ufuncs
    • 4.6.1 Maxima and minima
    • 4.6.2 Sums and products
    • 4.6.3 Simple statistics
  • 4.7 Polynomials
    • 4.7.1 Converting data to coefficients
    • 4.7.2 Converting coefficients to data
    • 4.7.3 Manipulating polynomials in coefficient form
  • 4.8 Linear Algebra
    • 4.8.1 Basic operations on matrices
    • 4.8.2 More specialized operations on matrices
    • 4.8.3 Solving linear systems of equations
  • 4.9 More NumPy and Beyond
    • 4.9.1 SciPy
    • 4.9.2 SciKits
• 5 Two-Dimensional Graphics
  • 5.1 Introduction
  • 5.2 Getting Started: Simple Figures
    • 5.2.1 Front-ends
    • 5.2.2 Back-ends
    • 5.2.3 A simple figure
    • 5.2.4 Interactive controls
  • 5.3 Object-Oriented Matplotlib
  • 5.4 Cartesian Plots
    • 5.4.1 The Matplotlib plot function
    • 5.4.2 Curve styles
    • 5.4.3 Marker styles
    • 5.4.4 Axes, grid, labels and title
    • 5.4.5 A not-so-simple example: partial sums of Fourier series
  • 5.5 Polar Plots
  • 5.6 Error Bars
  • 5.7 Text and Annotations
  • 5.8 Displaying Mathematical Formulae
    • 5.8.1 Non-LATEX users
    • 5.8.2 LATEX users
    • 5.8.3 Alternatives for LATEX users
  • 5.9 Contour Plots
  • 5.10 Compound Figures
    • 5.10.1 Multiple figures
    • 5.10.2 Multiple plots
  • 5.11 Mandelbrot Sets: A Worked Example
• 6 Multi-Dimensional Graphics
  • 6.1 Introduction
    • 6.1.1 Multi-dimensional data sets
  • 6.2 The Reduction to Two Dimensions
  • 6.3 Visualization Software
  • 6.4 Example Visualization Tasks
  • 6.5 Visualization of Solitary Waves
    • 6.5.1 The interactivity task
    • 6.5.2 The animation task
    • 6.5.3 The movie task
  • 6.6 Visualization of Three-Dimensional Objects
  • 6.7 A Three-Dimensional Curve
    • 6.7.1 Visualizing the curve with mplot3d
    • 6.7.2 Visualizing the curve with mlab
  • 6.8 A Simple Surface
    • 6.8.1 Visualizing the simple surface with mplot3d
    • 6.8.2 Visualizing the simple surface with mlab
  • 6.9 A Parametrically Defined Surface
    • 6.9.1 Visualizing Enneper’s surface using mplot3d
    • 6.9.2 Visualizing Enneper’s surface using mlab
  • 6.10 Three-Dimensional Visualization of a Julia Set
• 7 SymPy: A Computer Algebra System
  • 7.1 Computer Algebra Systems
  • 7.2 Symbols and Functions
  • 7.3 Conversions from Python to SymPy and Vice Versa
  • 7.4 Matrices and Vectors
  • 7.5 Some Elementary Calculus
    • 7.5.1 Differentiation
    • 7.5.2 Integration
    • 7.5.3 Series and limits
  • 7.6 Equality, Symbolic Equality and Simplification
  • 7.7 Solving Equations
    • 7.7.1 Equations with one independent variable
    • 7.7.2 Linear equations with more than one independent variable
    • 7.7.3 More general equations
  • 7.8 Solving Ordinary Differential Equations
  • 7.9 Plotting from within SymPy
• 8 Ordinary Differential Equations
  • 8.1 Initial Value Problems
  • 8.2 Basic Concepts
  • 8.3 The odeint Function
    • 8.3.1 Theoretical background
    • 8.3.2 The harmonic oscillator
    • 8.3.3 The van der Pol oscillator
    • 8.3.4 The Lorenz equations
  • 8.4 Two-Point Boundary Value Problems
    • 8.4.1 Introduction
    • 8.4.2 Formulation of the boundary value problem
    • 8.4.3 A simple example
    • 8.4.4 A linear eigenvalue problem
    • 8.4.5 A non-linear boundary value problem
  • 8.5 Delay Differential Equations
    • 8.5.1 A model equation
    • 8.5.2 More general equations and their numerical solution
    • 8.5.3 The logistic equation
    • 8.5.4 The Mackey–Glass equation
  • 8.6 Stochastic Differential Equations
    • 8.6.1 The Wiener process
    • 8.6.2 The Itô calculus
    • 8.6.3 Itô and Stratonovich stochastic integrals
    • 8.6.4 Numerical solution of stochastic differential equations
• 9 Partial Differential Equations: A Pseudospectral Approach
  • 9.1 Initial Boundary Value Problems
  • 9.2 Method of Lines
  • 9.3 Spatial Derivatives via Finite Differencing
  • 9.4 Spatial Derivatives by Spectral Techniques for Periodic Problems
  • 9.5 The IVP for Spatially Periodic Problems
  • 9.6 Spectral Techniques for Non-Periodic Problems
  • 9.7 An Introduction to f2py
    • 9.7.1 Simple examples with scalar arguments
    • 9.7.2 Vector arguments
    • 9.7.3 A simple example with multi-dimensional arguments
    • 9.7.4 Undiscussed features of f2py
  • 9.8 A Real-Life f2py Example
  • 9.9 Worked Example: Burgers’ Equation
    • 9.9.1 Boundary conditions: the traditional approach
    • 9.9.2 Boundary conditions: the penalty approach
• 10 Case Study: Multigrid
  • 10.1 The One-Dimensional Case
    • 10.1.1 Linear elliptic equations
    • 10.1.2 Smooth and rough modes
  • 10.2 The Tools of Multigrid
    • 10.2.1 Relaxation methods
    • 10.2.2 Residual and error
    • 10.2.3 Prolongation and restriction
  • 10.3 Multigrid Schemes
    • 10.3.1 The two-grid algorithm
    • 10.3.2 The V-cycle scheme
    • 10.3.3 The full multigrid (FMG) scheme
  • 10.4 A Simple Python Multigrid Implementation
    • 10.4.1 Utility functions
    • 10.4.2 Smoothing functions
    • 10.4.3 Multigrid functions
• Appendix A Installing a Python Environment
  • A.1 Installing Python Packages
  • A.2 Communication with IPython Using the Jupyter Notebook
    • A.2.1 Starting and stopping the notebook
    • A.2.2 Working in the notebook
      • A.2.2.1 Entering headers
      • A.2.2.2 Entering Markdown text
      • A.2.2.3 Converting notebooks to other formats
  • A.3 Communication with IPython Using Terminal Mode
    • A.3.1 Editors for programming
    • A.3.2 The two-windows approach
    • A.3.3 Calling the editor from within IPython
    • A.3.4 Calling IPython from within the editor
  • A.4 Communication with IPython via an IDE
  • A.5 Installing Additional Packages
• Appendix B Fortran77 Subroutines for Pseudospectral Methods
• References
• Hints for Using the Index
• Index

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