Python Programming and Numerical Methods. A Guide for Engineers and Scientists

Contents
List of Figures
Preface
	Purpose
	Prerequisites
	Organization
	How to Read This Book?
	Why Python?
	Python and Package Versions
Acknowledgements
1 Python Basics
	1.1 Getting Started With Python
		1.1.1 Setting Up Your Working Environment
		1.1.2 Three Ways to Run Python Code
	1.2 Python as a Calculator
	1.3 Managing Packages
		1.3.1 Managing Packages Using Package Managers
			Install a Package
			Upgrade a Package
			Uninstall a Package
			Other Useful Commands
		1.3.2 Install Packages From Source
	1.4 Introduction to Jupyter Notebook
		1.4.1 Starting the Jupyter Notebook
		1.4.2 Within the Notebook
		1.4.3 How Do I Close a Notebook?
		1.4.4 Shutting Down the Jupyter Notebook Server
	1.5 Logical Expressions and Operators
	1.6 Summary and Problems
		1.6.1 Summary
		1.6.2 Problems
2 Variables and Basic Data Structures
	2.1 Variables and Assignment
	2.2 Data Structure - String
	2.3 Data Structure - List
	2.4 Data Structure - Tuple
	2.5 Data Structure - Set
	2.6 Data Structure - Dictionary
	2.7 Introducing NumPy Arrays
	2.8 Summary and Problems
		2.8.1 Summary
		2.8.2 Problems
3 Functions
	3.1 Function Basics
		3.1.1 Built-In Functions in Python
		3.1.2 Define Your Own Function
	3.2 Local Variables and Global Variables
	3.3 Nested Functions
	3.4 Lambda Functions
	3.5 Functions as Arguments to Functions
	3.6 Summary and Problems
		3.6.1 Summary
		3.6.2 Problems
4 Branching Statements
	4.1 If-Else Statements
	4.2 Ternary Operators
	4.3 Summary and Problems
		4.3.1 Summary
		4.3.2 Problems
5 Iteration
	5.1 For-Loops
	5.2 While Loops
	5.3 Comprehensions
		5.3.1 List Comprehension
		5.3.2 Dictionary Comprehension
	5.4 Summary and Problems
		5.4.1 Summary
		5.4.2 Problems
6 Recursion
	6.1 Recursive Functions
	6.2 Divide-and-Conquer
		6.2.1 Tower of Hanoi
		6.2.2 Quicksort
	6.3 Summary and Problems
		6.3.1 Summary
		6.3.2 Problems
7 Object-Oriented Programming
	7.1 Introduction to OOP
	7.2 Class and Object
		7.2.1 Class
		7.2.2 Object
		7.2.3 Class vs Instance Attributes
	7.3 Inheritance, Encapsulation, and Polymorphism
		7.3.1 Inheritance
			7.3.1.1 Inheriting and Extending New Method
			7.3.1.2 Inheriting and Method Overriding
			7.3.1.3 Inheriting and Updating Attributes With Super
		7.3.2 Encapsulation
		7.3.3 Polymorphism
	7.4 Summary and Problems
		7.4.1 Summary
		7.4.2 Problems
8 Complexity
	8.1 Complexity and Big-O Notation
	8.2 Complexity Matters
	8.3 The Profiler
		8.3.1 Using the Magic Command
		8.3.2 Use Python Profiler
		8.3.3 Use Line Profiler
	8.4 Summary and Problems
		8.4.1 Summary
		8.4.2 Problems
9 Representation of Numbers
	9.1 Base-N and Binary
	9.2 Floating Point Numbers
	9.3 Round-Off Errors
		9.3.1 Representation Error
		9.3.2 Round-Off Error by Floating-Point Arithmetic
		9.3.3 Accumulation of Round-Off Errors
	9.4 Summary and Problems
		9.4.1 Summary
		9.4.2 Problems
10 Errors, Good Programming Practices, and Debugging
	10.1 Error Types
	10.2 Avoiding Errors
		10.2.1 Plan Your Program
		10.2.2 Test Everything Often
		10.2.3 Keep Your Code Clean
	10.3 Try/Except
	10.4 Type Checking
	10.5 Debugging
		10.5.1 Activating Debugger After Running Into an Exception
		10.5.2 Activating Debugger Before Running the Code
		10.5.3 Add a Breakpoint
	10.6 Summary and Problems
		10.6.1 Summary
		10.6.2 Problems
11 Reading and Writing Data
	11.1 TXT Files
		11.1.1 Writing to a File
		11.1.2 Appending a File
		11.1.3 Reading a File
		11.1.4 Dealing With Numbers and Arrays
	11.2 CSV Files
		11.2.1 Writing and Opening a CSV File
		11.2.2 Reading a CSV File
		11.2.3 Beyond NumPy
	11.3 Pickle Files
		11.3.1 Writing to a Pickle File
		11.3.2 Reading a Pickle File
		11.3.3 Reading in Python 2 Pickle File
	11.4 JSON Files
		11.4.1 JSON Format
		11.4.2 Writing a JSON File
		11.4.3 Reading a JSON File
	11.5 HDF5 Files
		11.5.1 Reading an HDF5 File
	11.6 Summary and Problems
		11.6.1 Summary
		11.6.2 Problems
12 Visualization and Plotting
	12.1 2D Plotting
	12.2 3D Plotting
	12.3 Working With Maps
	12.4 Animations and Movies
	12.5 Summary and Problems
		12.5.1 Summary
		12.5.2 Problems
13 Parallelize Your Python
	13.1 Parallel Computing Basics
		13.1.1 Process and Thread
		13.1.2 Python\'s GIL Problem
		13.1.3 Disadvantages of Using Parallel Computing
	13.2 Multiprocessing
		13.2.1 Visualize the Execution Time
	13.3 Using Joblib
	13.4 Summary and Problems
		13.4.1 Summary
		13.4.2 Problems
14 Linear Algebra and Systems of Linear Equations
	14.1 Basics of Linear Algebra
		14.1.1 Sets
		14.1.2 Vectors
		14.1.3 Matrices
	14.2 Linear Transformations
	14.3 Systems of Linear Equations
	14.4 Solutions to Systems of Linear Equations
		14.4.1 Gauss Elimination Method
		14.4.2 Gauss-Jordan Elimination Method
		14.4.3 LU Decomposition Method
		14.4.4 Iterative Methods - Gauss-Seidel Method
			14.4.4.1 Gauss-Seidel Method
	14.5 Solving Systems of Linear Equations in Python
	14.6 Matrix Inversion
	14.7 Summary and Problems
		14.7.1 Summary
		14.7.2 Problems
15 Eigenvalues and Eigenvectors
	15.1 Eigenvalues and Eigenvectors Problem Statement
		15.1.1 Eigenvalues and Eigenvectors
		15.1.2 The Motivation Behind Eigenvalues and Eigenvectors
		15.1.3 The Characteristic Equation
	15.2 The Power Method
		15.2.1 Finding the Largest Eigenvalue
		15.2.2 The Inverse Power Method
		15.2.3 The Shifted Power Method
	15.3 The QR Method
	15.4 Eigenvalues and Eigenvectors in Python
	15.5 Summary and Problems
		15.5.1 Summary
		15.5.2 Problems
16 Least Squares Regression
	16.1 Least Squares Regression Problem Statement
	16.2 Least Squares Regression Derivation (Linear Algebra)
	16.3 Least Squares Regression Derivation (Multivariate Calculus)
	16.4 Least Squares Regression in Python
		16.4.1 Using the Direct Inverse Method
		16.4.2 Using the Pseudo-Inverse
		16.4.3 Using numpy.linalg.lstsq
		16.4.4 Using optimize.curve_fit From SciPy
	16.5 Least Squares Regression for Nonlinear Functions
		16.5.1 Log Tricks for Exponential Functions
		16.5.2 Log Tricks for Power Functions
		16.5.3 Polynomial Regression
		16.5.4 Using optimize.curve_fit From SciPy
	16.6 Summary and Problems
		16.6.1 Summary
		16.6.2 Problems
17 Interpolation
	17.1 Interpolation Problem Statement
	17.2 Linear Interpolation
	17.3 Cubic Spline Interpolation
	17.4 Lagrange Polynomial Interpolation
		17.4.1 Using the Lagrange Function From SciPy
	17.5 Newton\'s Polynomial Interpolation
	17.6 Summary and Problems
		17.6.1 Summary
		17.6.2 Problems
18 Taylor Series
	18.1 Expressing Functions Using a Taylor Series
	18.2 Approximations Using Taylor Series
	18.3 Discussion About Errors
		18.3.1 Truncation Errors for Taylor Series
		18.3.2 Estimating Truncation Errors
		18.3.3 Round-Off Errors for Taylor Series
	18.4 Summary and Problems
		18.4.1 Summary
		18.4.2 Problems
19 Root Finding
	19.1 Root Finding Problem Statement
	19.2 Tolerance
	19.3 Bisection Method
	19.4 Newton-Raphson Method
	19.5 Root Finding in Python
	19.6 Summary and Problems
		19.6.1 Summary
		19.6.2 Problems
20 Numerical Differentiation
	20.1 Numerical Differentiation Problem Statement
	20.2 Using Finite Difference to Approximate Derivatives
		20.2.1 Using Finite Difference to Approximate Derivatives With Taylor Series
	20.3 Approximating of Higher Order Derivatives
	20.4 Numerical Differentiation With Noise
	20.5 Summary and Problems
		20.5.1 Summary
		20.5.2 Problems
21 Numerical Integration
	21.1 Numerical Integration Problem Statement
	21.2 Riemann Integral
	21.3 Trapezoid Rule
	21.4 Simpson\'s Rule
	21.5 Computing Integrals in Python
	21.6 Summary and Problems
		21.6.1 Summary
		21.6.2 Problems
22 Ordinary Differential Equations (ODEs) Initial-Value Problems
	22.1 ODE Initial Value Problem Statement
	22.2 Reduction of Order
	22.3 The Euler Method
	22.4 Numerical Error and Instability
	22.5 Predictor-Corrector and Runge-Kutta Methods
		22.5.1 Predictor-Corrector Methods
		22.5.2 Runge-Kutta Methods
			22.5.2.1 Second-Order Runge-Kutta Method
			22.5.2.2 Fourth-Order Runge-Kutta Method
	22.6 Python ODE Solvers
	22.7 Advanced Topics
		22.7.1 Multistep Methods
		22.7.2 Stiffness ODE
	22.8 Summary and Problems
		22.8.1 Summary
		22.8.2 Problems
23 Boundary-Value Problems for Ordinary Differential Equations (ODEs)
	23.1 ODE Boundary Value Problem Statement
	23.2 The Shooting Method
	23.3 The Finite Difference Method
	23.4 Numerical Error and Instability
	23.5 Summary and Problems
		23.5.1 Summary
		23.5.2 Problems
24 Fourier Transform
	24.1 The Basics of Waves
		24.1.1 Modeling a Wave Using Mathematical Tools
		24.1.2 Characteristics of a Wave
	24.2 Discrete Fourier Transform (DFT)
		24.2.1 DFT
		24.2.2 The Inverse DFT
		24.2.3 The Limit of DFT
	24.3 Fast Fourier Transform (FFT)
		24.3.1 Symmetries in the DFT
		24.3.2 Tricks in FFT
	24.4 FFT in Python
		24.4.1 FFT in NumPy
		24.4.2 FFT in SciPy
		24.4.3 More Examples
			24.4.3.1 Electricity Demand in California
			24.4.3.2 Filtering a Signal in Frequency Domain
	24.5 Summary and Problems
		24.5.1 Summary
		24.5.2 Problems
A Getting Started With Python in Windows
	A.1 Getting Started With Python in Windows
		A.1.1 Setting Up Your Working Environment in Windows
		A.1.2 Three Ways to Run Python Code
Index