Practical Numerical Computing Using Python

Review: "This excellent book of Prof. Verma is a single resource which a student can use to learn the fast-developing field of computational science. In addition to the description of Python language, it provides a broad overview of hardware, software, classic numerical methods, and everything in between. I recommend it strongly to all!" -- Prof. Prateek Sharma, IISc Bengaluru Key Features of the Book: Perfect book for introduction to practical numerical algorithms and programs for advanced undergraduate and beginning graduate students. Introduces Python programming language and its modules related to numerical computing Covers Numpy, Matplotlib, and Scipy modules in details. Illustrates how to make a variety of plots and animations. Detailed discussions on important numerical algorithms: Interpolation, Integration, Differentiation, ODE and PDE solvers, and Linear algebra solvers. Practical implementation of the algorithms in Python. Introduces Spectral and Finite-difference methods and applications to fluid mechanics and quantum mechanics. Includes chapters on Monte Carlo methods and applications to statistical physics, as well as on error analysis. A brief introduction to Computer hardware, complexity estimates, and nondimensionalization.

Practical Numerical and Scientific Computing with MATLAB® and Python concentrates on the practical aspects of numerical analysis and linear and non-linear programming. It discusses the methods for solving different types of mathematical problems using MATLAB and Python. Although the book focuses on the approximation problem rather than on error analysis of mathematical problems, it provides practical ways to calculate errors. The book is divided into three parts, covering topics in numerical linear algebra, methods of interpolation, numerical differentiation and integration, solutions of differential equations, linear and non-linear programming problems, and optimal control problems. This book has the following advantages: It adopts the programming languages, MATLAB and Python, which are widely used among academics, scientists, and engineers, for ease of use and contain many libraries covering many scientific and engineering fields. It contains topics that are rarely found in other numerical analysis books, such as ill-conditioned linear systems and methods of regularization to stabilize their solutions, nonstandard finite differences methods for solutions of ordinary differential equations, and the computations of the optimal controls. It provides a practical explanation of how to apply these topics using MATLAB and Python. It discusses software libraries to solve mathematical problems, such as software Gekko, pulp, and pyomo. These libraries use Python for solutions to differential equations and static and dynamic optimization problems. Most programs in the book can be applied in versions prior to MATLAB 2017b and Python 3.7.4 without the need to modify these programs. This book is aimed at newcomers and middle-level students, as well as members of the scientific community who are interested in solving math problems using MATLAB or Python.

Python is an interpreted, object-oriented, high-level programming language with dynamic semantics. The high-level built-in data structures of python combined with dynamic typing and dynamic binding can be efficiently used for rapid application development (RAD). The simple and easy to learn syntax of Python significantly draws attention on readability. This aspect greatly helps in reducing the cost of program maintenance. There are several applications of python such as language development, prototyping, database access, software development, and graphic design. Python supports modules and packages, which encourage modular programming and code reuse. The simple and versatile nature of Python makes it a powerful tool in scientific and engineering computations. The data and numerical analysis as well as the plotting libraries of python such as NumPy, SciPy and matplotlib have become very popular programming tools in industry and academia. This book outlines the importance of Python as an important computer language for solving numerical problems. It will serve as a valuable source of reference for graduate and post graduate students.

Numerical Python by Robert Johansson shows you how to leverage the numerical and mathematical modules in Python and its Standard Library as well as popular open source numerical Python packages like NumPy, FiPy, matplotlib and more to numerically compute solutions and mathematically model applications in a number of areas like big data, cloud computing, financial engineering, business management and more. After reading and using this book, you'll get some takeaway case study examples of applications that can be found in areas like business management, big data/cloud computing, financial engineering (i.e., options trading investment alternatives), and even games. Up until very recently, Python was mostly regarded as just a web scripting language. Well, computational scientists and engineers have recently discovered the flexibility and power of Python to do more. Big data analytics and cloud computing programmers are seeing Python's immense use. Financial engineers are also now employing Python in their work. Python seems to be evolving as a language that can even rival C++, Fortran, and Pascal/Delphi for numerical and mathematical computations.

Understand, explore, and effectively present data using the powerful data visualization techniques of Python Key FeaturesUse the power of Pandas and Matplotlib to easily solve data mining issuesUnderstand the basics of statistics to build powerful predictive data modelsGrasp data mining concepts with helpful use-cases and examplesBook Description Data mining, or parsing the data to extract useful insights, is a niche skill that can transform your career as a data scientist Python is a flexible programming language that is equipped with a strong suite of libraries and toolkits, and gives you the perfect platform to sift through your data and mine the insights you seek. This Learning Path is designed to familiarize you with the Python libraries and the underlying statistics that you need to get comfortable with data mining. You will learn how to use Pandas, Python's popular library to analyze different kinds of data, and leverage the power of Matplotlib to generate appealing and impressive visualizations for the insights you have derived. You will also explore different machine learning techniques and statistics that enable you to build powerful predictive models. By the end of this Learning Path, you will have the perfect foundation to take your data mining skills to the next level and set yourself on the path to become a sought-after data science professional. This Learning Path includes content from the following Packt products: Statistics for Machine Learning by Pratap DangetiMatplotlib 2.x By Example by Allen Yu, Claire Chung, Aldrin YimPandas Cookbook by Theodore PetrouWhat you will learnUnderstand the statistical fundamentals to build data modelsSplit data into independent groups Apply aggregations and transformations to each groupCreate impressive data visualizationsPrepare your data and design models Clean up data to ease data analysis and visualizationCreate insightful visualizations with Matplotlib and SeabornCustomize the model to suit your own predictive goalsWho this book is for If you want to learn how to use the many libraries of Python to extract impactful information from your data and present it as engaging visuals, then this is the ideal Learning Path for you. Some basic knowledge of Python is enough to get started with this Learning Path.

Leverage the numerical and mathematical modules in Python and its standard library as well as popular open source numerical Python packages like NumPy, SciPy, FiPy, matplotlib and more. This fully revised edition, updated with the latest details of each package and changes to Jupyter projects, demonstrates how to numerically compute solutions and mathematically model applications in big data, cloud computing, financial engineering, business management and more. Numerical Python, Second Edition, presents many brand-new case study examples of applications in data science and statistics using Python, along with extensions to many previous examples. Each of these demonstrates the power of Python for rapid development and exploratory computing due to its simple and high-level syntax and multiple options for data analysis. After reading this book, readers will be familiar with many computing techniques including array-based and symbolic computing, visualization and numerical file I/O, equation solving, optimization, interpolation and integration, and domain-specific computational problems, such as differential equation solving, data analysis, statistical modeling and machine learning. What You'll Learn Work with vectors and matrices using NumPy Plot and visualize data with Matplotlib Perform data analysis tasks with Pandas and SciPy Review statistical modeling and machine learning with statsmodels and scikit-learn Optimize Python code using Numba and Cython Who This Book Is For Developers who want to understand how to use Python and its related ecosystem for numerical computing.

Makes Numerical Programming More Accessible to a Wider Audience Bearing in mind the evolution of modern programming, most specifically emergent programming languages that reflect modern practice, Numerical Programming: A Practical Guide for Scientists and Engineers Using Python and C/C++ utilizes the author’s many years of practical research and teaching experience to offer a systematic approach to relevant programming concepts. Adopting a practical, broad appeal, this user-friendly book offers guidance to anyone interested in using numerical programming to solve science and engineering problems. Emphasizing methods generally used in physics and engineering—from elementary methods to complex algorithms—it gradually incorporates algorithmic elements with increasing complexity. Develop a Combination of Theoretical Knowledge, Efficient Analysis Skills, and Code Design Know-How The book encourages algorithmic thinking, which is essential to numerical analysis. Establishing the fundamental numerical methods, application numerical behavior and graphical output needed to foster algorithmic reasoning, coding dexterity, and a scientific programming style, it enables readers to successfully navigate relevant algorithms, understand coding design, and develop efficient programming skills. The book incorporates real code, and includes examples and problem sets to assist in hands-on learning. Begins with an overview on approximate numbers and programming in Python and C/C++, followed by discussion of basic sorting and indexing methods, as well as portable graphic functionality Contains methods for function evaluation, solving algebraic and transcendental equations, systems of linear algebraic equations, ordinary differential equations, and eigenvalue problems Addresses approximation of tabulated functions, regression, integration of one- and multi-dimensional functions by classical and Gaussian quadratures, Monte Carlo integration techniques, generation of random variables, discretization methods for ordinary and partial differential equations, and stability analysis This text introduces platform-independent numerical programming using Python and C/C++, and appeals to advanced undergraduate and graduate students in natural sciences and engineering, researchers involved in scientific computing, and engineers carrying out applicative calculations.

This book targets programmers and scientists who have basic Python knowledge and who are keen to perform scientific and numerical computations with SciPy.