Essential Python for the Physicist

Preface
Contents
1 Python Basics and the Interactive Mode
	1.1 Using the Command Line
	1.2 Installing Python
		1.2.1 General
		1.2.2 Downloading Python for Windows
		1.2.3 Downloading Python for macOS
	1.3 Using Python in Interactive Mode
	1.4 Variables
		1.4.1 Variable Types
		1.4.2 Variable-Type Conversion
	1.5 Arithmetic Operators
	1.6 Assignment Operators
	1.7 Comparison and Logical Operators
	1.8 Python Packages and the import Statement
	1.9 Conditional Statements
	1.10 Lists and Tuples
	1.11 List Methods
	1.12 Lists and the = Assignment Operator
		1.12.1 Copying Lists
		1.12.2 Copying the Elements of Lists and Tuples
	1.13 Slicing Lists and Strings
	1.14 Dictionaries
	1.15 The print() Function and Formatting
		1.15.1 Old Style
		1.15.2 New Style
		1.15.3 Format Types and Flags
	1.16 Loops
		1.16.1 The for Loop
		1.16.2 The while Loop
		1.16.3 Breaking a Loop
		1.16.4 The continue Statement
	1.17 Operations with Matrices and Vectors
		1.17.1 Lists and Arrays
		1.17.2 Slicing out Rows and Columns from a Matrix
		1.17.3 Arrays and Matrix Arithmetics
		1.17.4 Further Matrix Operations
	1.18 Exiting Interactive Mode
	1.19 Exercises
2 Python Scripts
	2.1 Scripts
		2.1.1 Running Scripts on a Terminal
		2.1.2 Running Scripts on Spyder3
		2.1.3 A First Script
	2.2 Functions
		2.2.1 General
		2.2.2 Local and Global Variables
	2.3 Reading and Writing Files
	2.4 Calling External Commands from Python Scripts
	2.5 Exercises
3 Plotting with Matplotlib
	3.1 Pyplot
	3.2 Plotting Lists of Numbers
	3.3 Plotting Functions
	3.4 Multiple Figures
	3.5 Logarithmic Axis Scales
	3.6 Plotting Field Lines
	3.7 Pyplot Animation
	3.8 Exercises
4 Numerical Solution of Equations
	4.1 Introduction
	4.2 Systems of Linear Equations
	4.3 Nonlinear Equations
		4.3.1 Common Methods for the Numerical Solution
		4.3.2 Bisection Method
		4.3.3 The Secant Method
	4.4 Root Finding with the scipy.optimize Package
	4.5 Algebraic Equations
	4.6 Systems of Nonlinear Equations
		4.6.1 Equations Involving only Unknowns
		4.6.2 Equations Involving Unknowns and Parameters
	4.7 Integration of Functions
		4.7.1 Introduction
		4.7.2 Rectangular and Trapezoidal Rules
		4.7.3 The Simpson Rule
		4.7.4 The scipy.integrate.simps Function
	4.8 Exercises
	Reference
5 Numerical Solution of Ordinary Differential Equations (ODE)
	5.1 Introduction
	5.2 Euler and Runge–Kutta Methods
	5.3 The scipy.integrate.odeint Function
	5.4 Large-Amplitude Pendulum
	5.5 The Shooting Method
		5.5.1 The Finite Square Well
		5.5.2 The Shooting Method
		5.5.3 The Harmonic Oscillator
	5.6 Exercises
	Reference
6 Tkinter Graphics
	6.1 Tkinter
	6.2 The Root Window and Tkinter Color Management
	6.3 Drawing Geometric Shapes on the Canvas
	6.4 Plotting a Function with Tkinter
		6.4.1 Plotting a Hyperbola
		6.4.2 Saving an Image of the Canvas
	6.5 Exercises
7 Tkinter Animation
	7.1 Introduction
	7.2 Adding Uniform Acceleration
	7.3 Adding Interactive Buttons
	7.4 Numerical Parameters, Entries, Labels and Mouse Dragging
	7.5 Creating Video Files Under Tkinter
	7.6 Animation and Ordinary Differential Equations
		7.6.1 Euler's Method
		7.6.2 The Leapfrog Method
		7.6.3 The odeint Integration
	7.7 Length and Time Scaling
	7.8 Exercises
8 Classes
	8.1 The class Statement
	8.2 A First Example: Two Colliding Balls
	8.3 A ``Classical'' Atom
		8.3.1 A ``C-Style'' dfdt() Alternative Function
	8.4 Exercises
9 3D Graphics and Animation with VPython
	9.1 Introduction and Installation
	9.2 The VPython Vector Object
	9.3 VPython Displayable Objects
		9.3.1 Sphere
		9.3.2 Box
		9.3.3 Cylinder
		9.3.4 Cone
		9.3.5 Pyramid
		9.3.6 Ellipsoid
		9.3.7 Helix
		9.3.8 Ring
		9.3.9 Curve
		9.3.10 Arrow
		9.3.11 Compound
		9.3.12 Clone
		9.3.13 Points
		9.3.14 Extrusion
		9.3.15 Triangle/quad
		9.3.16 Label
		9.3.17 Text
	9.4 Controlling the View
	9.5 VPython Animation
		9.5.1 Basics
		9.5.2 Interactive Control
	9.6 2D Graphics
	9.7 Exercises
10 Answers to the Exercises
Appendix A Relevant Mathematical Functions
A.1  The math Module
A.1.1  Number-Theoretic and Representation Functions
A.1.2  Power and Logarithmic Functions
A.1.3  Trigonometric Functions
A.1.4  Angular Conversion
A.1.5  Hyperbolic Functions
A.1.6  Special Functions
A.1.7  Constants
A.2  The cmath Module
A.2.1  Conversions to and from Polar coordinates
A.2.2  Power and Logarithmic Functions
A.2.3  Trigonometric Functions
A.2.4  Hyperbolic Functions
A.2.5  Classification Functions
A.2.6  Constants
Appendix B Building Your Own Library
B.1  Writing a Module
B.2  The PYTHONPATH Environment Variable
Appendix C The integrate Subpackage
C.1  simps()
C.2  odeint()
Appendix D Methods for Drawing and Writing  on the Canvas
Appendix E Unicode Characters
Appendix F Tkinter Events
F.1  Mouse Events
F.2  Keyboard Events
Appendix G VPython
G.1  Colors
G.2  Extrusion: Shapes and Paths Library
G.2.1  Rectangle
G.2.2  Circle
G.2.3  Ellipse
G.2.4  Arc
G.2.5  Line
G.2.6  Triangle
G.2.7  Pentagon, Hexagon, Octagon, Ngon
G.2.8  Star
G.2.9  Trapezoid
Index