Efnisyfirlit

• Half title
• Title
• Copyright
• Contents
• Preface
• 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 Generalities
• 2.2 Tab completion
• 2.3 Introspection
• 2.4 History
• 2.5 Magic commands
• 2.6 The magic %run command
• 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 loops
• 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 The Python print function
• 3.8.7 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 Cartesian plots
• 5.3.1 The matplotlib plot function
• 5.3.2 Curve styles
• 5.3.3 Marker styles
• 5.3.4 Axes, grid, labels and title
• 5.3.5 A not-so-simple example: partial sums of Fourier series
• 5.4 Polar plots
• 5.5 Error bars
• 5.6 Text and annotations
• 5.7 Displaying mathematical formulae
• 5.7.1 Non-LATEX users
• 5.7.2 LATEX users
• 5.7.3 Alternatives for LATEX users
• 5.8 Contour plots
• 5.9 Compound figures
• 5.9.1 Multiple figures
• 5.9.2 Multiple plots
• 5.10 Animations
• 5.10.1 In situ animations
• 5.10.2 Movies
• 5.11 Mandelbrot sets: a worked example
• 6 Three-dimensional graphics
• 6.1 Introduction
• 6.1.1 Three-dimensional data sets
• 6.1.2 The reduction to two dimensions
• 6.2 Visualization software
• 6.3 A three-dimensional curve
• 6.3.1 Visualizing the curve with mplot3d
• 6.3.2 Visualizing the curve with mlab
• 6.4 A simple surface
• 6.4.1 Visualizing the simple surface with mplot3d
• 6.4.2 Visualizing the simple surface with mlab
• 6.5 A parametrically defined surface
• 6.5.1 Visualizing Enneper?s surface using mplot3d
• 6.5.2 Visualizing Enneper?s surface using mlab
• 6.6 Three-dimensional visualization of a Julia set
• 7 Ordinary differential equations
• 7.1 Initial value problems
• 7.2 Basic concepts
• 7.3 The odeint function
• 7.3.1 Theoretical background
• 7.3.2 Practical usage
• 7.4 Two-point boundary value problems
• 7.4.1 Introduction
• 7.4.2 Formulation of the boundary value problem
• 7.4.3 A simple example
• 7.4.4 A linear eigenvalue problem
• 7.4.5 A non-linear boundary value problem
• 7.5 Delay differential equations
• 7.5.1 A model equation
• 7.5.2 More general equations and their numerical solution
• 7.5.3 The logistic equation
• 7.5.4 The Mackey-Glass equation
• 7.6 Stochastic differential equations
• 7.6.1 The Wiener process
• 7.6.2 The It? calculus
• 7.6.3 It? and Stratanovich stochastic integrals
• 7.6.4 Numerical solution of stochastic differential equations
• 8 Partial differential equations: a pseudospectral approach
• 8.1 Initial-boundary value problems
• 8.2 Method of lines
• 8.3 Spatial derivatives via finite differencing
• 8.4 Spatial derivatives by spectral techniques for periodic problems
• 8.5 The IVP for spatially periodic problems
• 8.6 Spectral techniques for non-periodic problems
• 8.7 An introduction to f2py
• 8.7.1 Simple examples with scalar arguments
• 8.7.2 Vector arguments
• 8.7.3 A simple example with multi-dimensional arguments
• 8.7.4 Undiscussed features of f2py
• 8.8 A real-life f2py example
• 8.9 Worked example: Burgers? equation
• 8.9.1 Boundary conditions: the traditional approach
• 8.9.2 Boundary conditions: the penalty approach
• 9 Case study: multigrid
• 9.1 The one-dimensional case
• 9.1.1 Linear elliptic equations
• 9.1.2 Smooth and rough modes
• 9.2 The tools of multigrid
• 9.2.1 Relaxation methods
• 9.2.2 Residual and error
• 9.2.3 Prolongation and restriction
• 9.3 Multigrid schemes
• 9.3.1 The two-grid algorithm
• 9.3.2 The V-cycle scheme
• 9.3.3 The full multigrid scheme (FMG)
• 9.4 A simple Python multigrid implementation
• 9.4.1 Utility functions
• 9.4.2 Smoothing functions
• 9.4.3 Multigrid functions
• Appendix A Installing a Python environment
• A.1 Installing Python packages
• A.2 Communicating with Python
• A.2.1 Editors for programming
• A.2.2 The IPython-editor interaction
• A.2.3 The two windows approach
• A.2.4 Calling the editor from within IPython
• A.2.5 Calling IPython from within the editor
• A.2.6 The IPython pager
• A.3 The Python Package Index
• Appendix B Fortran77 subroutines for pseudospectral methods
• References
• Index