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Python Programming and Numerical Methods
A Guide for Engineers and Scientists
- 1st Edition - November 27, 2020
- Authors: Qingkai Kong, Timmy Siauw, Alexandre Bayen
- Language: English
- Paperback ISBN:9 7 8 - 0 - 1 2 - 8 1 9 5 4 9 - 9
- eBook ISBN:9 7 8 - 0 - 1 2 - 8 1 9 5 5 0 - 5
Python Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the go… Read more
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Request a sales quotePython Programming and Numerical Methods: A Guide for Engineers and Scientists introduces programming tools and numerical methods to engineering and science students, with the goal of helping the students to develop good computational problem-solving techniques through the use of numerical methods and the Python programming language. Part One introduces fundamental programming concepts, using simple examples to put new concepts quickly into practice. Part Two covers the fundamentals of algorithms and numerical analysis at a level that allows students to quickly apply results in practical settings.
- Includes tips, warnings and "try this" features within each chapter to help the reader develop good programming practice
- Summaries at the end of each chapter allow for quick access to important information
- Includes code in Jupyter notebook format that can be directly run online
Senior undergraduates or graduate students in engineering and science who are taking a numerical methods course using Python
PART 1 INTRODUCTION TO PYTHON PROGRAMMING
CHAPTER 1 Python Basics
1.1 Getting Started With Python
1.2
Python as a Calculator1.3
Managing Packages1.4
Introduction to Jupyter Notebook1.5
Logical Expressions and Operators1.6
Summary and ProblemsCHAPTER 2 Variables and Basic Data Structures
2.1
Variables and Assignment2.2
Data Structure – String2.3
Data Structure – List2.4
Data Structure – Tuple2.5
Data Structure – Set2.6
Data Structure – Dictionary2.7 Introducing Numpy Arrays
2.8
Summary and ProblemsCHAPTER 3 Functions
3.1
Function Basics3.2
Local Variables and Global Variables3.3 Nested Functions
3.4
Lambda Functions3.5 Functions as Arguments to Functions
3.6
Summary and ProblemsCHAPTER 4 Branching Statements
4.1
If-Else Statements4.2 Ternary Operators
4.3 Summary and Problems
CHAPTER 5 Iteration
5.1
For-Loops5.2 While Loops
5.3
Comprehensions5.4
Summary and ProblemsCHAPTER 6 Recursion
6.1
Recursive Functions6.2
Divide-and-Conquer6.3
Summary and ProblemsCHAPTER 7 Object-Oriented Programming
7.1
Introduction to OOP7.2
Class and Object7.3
Inheritance, Encapsulation, and Polymorphism7.4
Summary and ProblemsCHAPTER 8 Complexity
8.1 Complexity and Big-ONotation
8.2
Complexity Matters8.3
The Profiler8.4
Summary and ProblemsCHAPTER 9 Representation of Numbers
9.1
Base-N and Binary9.2
Floating Point Numbers9.3
Round-Off Errors9.4
Summary and ProblemsCHAPTER 10 Errors, Good Programming Practices, and Debugging
10.1
Error Types10.2
Avoiding Errors10.3
Try/Except10.4
Type Checking10.5
Debugging10.6
Summary and ProblemsCHAPTER 11 Reading and Writing Data
11.1
TXT Files11.2
CSVFiles11.3
Pickle Files11.4
JSONFiles11.5
HDF5 Files11.6
Summary and ProblemsCHAPTER 12 Visualization and Plotting
12.1
2D Plotting12.2 3D Plotting
12.3 Working With Maps
12.4
Animations and Movies12.5
Summary and ProblemsCHAPTER 13 Parallelize Your Python
13.1
Parallel Computing Basics13.2
Multiprocessing13.3
Using Joblib13.4
Summary and ProblemsPART 2 INTRODUCTION TO NUMERICAL METHODS
CHAPTER 14 Linear Algebra and Systems of Linear Equations
14.1
Basics of Linear Algebra14.2
Linear Transformations14.3
Systems of Linear Equations14.4 Solutions to Systems of Linear Equations
14.5
Solving Systems of Linear Equations in Python14.6
Matrix Inversion14.7
Summary and ProblemsCHAPTER 15 Eigenvalues and Eigenvectors
15.1
Eigenvalues and Eigenvectors Problem Statement15.2
The Power Method15.3
The QR Method15.4
Eigenvalues and Eigenvectors in Python15.5
Summary and ProblemsCHAPTER 16 Least Squares Regression
16.1
Least Squares Regression Problem Statement16.2
Least Squares Regression Derivation (Linear Algebra)16.3
Least Squares Regression Derivation (Multivariate Calculus)16.4
Least Squares Regression in Python16.5
Least Squares Regression for Nonlinear Functions16.6
Summary and ProblemsCHAPTER 17 Interpolation
17.1
Interpolation Problem Statement17.2 Linear Interpolation
17.3
Cubic Spline Interpolation17.4
Lagrange Polynomial Interpolation17.5
Newton’s Polynomial Interpolation17.6
Summary and ProblemsCHAPTER 18 Taylor Series
18.1
18.2 Approximations Using Taylor Series
18.3
Discussion About Errors18.4
Summary and ProblemsCHAPTER 19 Root Finding
19.1
19.2
Tolerance19.3
Bisection Method19.4
Newton–Raphson Method19.5 Root Finding in Python
19.6 Summary and Problems
CHAPTER 20 Numerical Differentiation
20.1
Numerical Differentiation Problem Statement20.2
Using Finite Difference to Approximate Derivatives20.3
Approximating of Higher Order Derivatives20.4
Numerical Differentiation With Noise20.5
Summary and ProblemsCHAPTER 21 Numerical Integration
21.1
21.2
Riemann Integral21.3 Trapezoid Rule
21.4 Simpson’s Rule
21.5
Computing Integrals in Python21.6 Summary and Problems
CHAPTER 22 Ordinary Differential Equations (ODEs) Initial-Value Problems
22.1
ODE Initial Value Problem Statement22.2
Reduction of Order22.3 The Euler Method
22.4 Numerical Error and Instability
22.5 Predictor–Corrector and Runge–Kutta Methods
22.6
Python ODE Solvers22.7
Advanced Topics22.8
Summary and ProblemsCHAPTER 23 Boundary-Value Problems for Ordinary Differential Equations (ODEs)
23.1
ODE Boundary Value Problem Statement23.2
The Shooting Method23.3
The Finite Difference Method23.4
Numerical Error and Instability23.5
Summary and ProblemsCHAPTER 24 Fourier Transform
24.1
24.2
Discrete Fourier Transform (DFT)24.3
Fast Fourier Transform (FFT)24.4
FFT in Python24.5
Summary and ProblemsAppendix A Getting Started With Python in Windows
Index
- No. of pages: 480
- Language: English
- Edition: 1
- Published: November 27, 2020
- Imprint: Academic Press
- Paperback ISBN: 9780128195499
- eBook ISBN: 9780128195505
QK
Qingkai Kong
Qingkai Kong is an Assistant Data Science Researcher at the Berkeley Division of Data Sciences and Berkeley Seismology Lab. He has a Master’s degree in Structural Engineering and a PhD. in Earth Science. He is actively working on applying data science/machine learning to Earth science and engineering, especially using Python language.
Affiliations and expertise
Assistant Data Science Researcher, University of California, BerkeleyTS
Timmy Siauw
Affiliations and expertise
University of California, Berkeley, USAAB
Alexandre Bayen
Alexandre Bayen is the Liao-Cho Professor of Engineering at UC Berkeley. He is a Professor of Electrical Engineering and Computer Science, and Civil and Environmental Engineering. He is currently the Director of the Institute of Transportation Studies (ITS). He is also a Faculty Scientist in Mechanical Engineering, at the Lawrence Berkeley National Laboratory (LBNL). He received the Engineering Degree in applied mathematics from the Ecole Polytechnique, France, in 1998, the M.S. and Ph.D. in aeronautics and astronautics from Stanford University in 1998 and 1999 respectively. He was a Visiting Researcher at NASA Ames Research Center from 2000 to 2003. Between January 2004 and December 2004, he worked as the Research Director of the Autonomous Navigation Laboratory at the Laboratoire de Recherches Balistiques et Aerodynamiques, (Ministere de la Defense, Vernon, France), where he holds the rank of Major. He has been on the faculty at UC Berkeley since 2005. Bayen has authored two books and over 200 articles in peer reviewed journals and conferences. He is the recipient of the Ballhaus Award from Stanford University, 2004, of the CAREER award from the National Science Foundation, 2009 and he is a NASA Top 10 Innovators on Water Sustainability, 2010. His projects Mobile Century and Mobile Millennium received the 2008 Best of ITS Award for ‘Best Innovative Practice’, at the ITS World Congress and a TRANNY Award from the California Transportation Foundation, 2009. Mobile Millennium has been featured more than 200 times in the media, including TV channels and radio stations (CBS, NBC, ABC, CNET, NPR, KGO, the BBC), and in the popular press (Wall Street Journal, Washington Post, LA Times). Bayen is the recipient of the Presidential Early Career Award for Scientists and Engineers (PECASE) award from the White House, 2010. He is also the recipient of the Okawa Research Grant Award, the Ruberti Prize from the IEEE, and the Huber Prize from the ASCE.
Affiliations and expertise
Associate Professor, Department of Electrical Engineering and Computer Sciences and the Department of Civil and Environmental Engineering, University of California, Berkeley, USARead Python Programming and Numerical Methods on ScienceDirect