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• Cover
• 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 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 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-LATEXusers
• 5.8.2 LATEXusers
• 5.8.3 Alternatives for LATEXusers
• 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
• 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
• B Fortran77 Subroutines for Pseudospectral Methods
• References
• Hints for Using the Index
• Index