Mathematical Methods Using Python
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| Author | : Vasilis Pagonis |
| Publisher | : CRC Press |
| Total Pages | : 505 |
| Release | : 2024-05-14 |
| Genre | : Computers |
| ISBN | : 1040023029 |
This advanced undergraduate textbook presents a new approach to teaching mathematical methods for scientists and engineers. It provides a practical, pedagogical introduction to utilizing Python in Mathematical and Computational Methods courses. Both analytical and computational examples are integrated from its start. Each chapter concludes with a set of problems designed to help students hone their skills in mathematical techniques, computer programming, and numerical analysis. The book places less emphasis on mathematical proofs, and more emphasis on how to use computers for both symbolic and numerical calculations. It contains 182 extensively documented coding examples, based on topics that students will encounter in their advanced courses in Mechanics, Electronics, Optics, Electromagnetism, Quantum Mechanics etc. An introductory chapter gives students a crash course in Python programming and the most often used libraries (SymPy, NumPy, SciPy, Matplotlib). This is followed by chapters dedicated to differentiation, integration, vectors and multiple integration techniques. The next group of chapters covers complex numbers, matrices, vector analysis and vector spaces. Extensive chapters cover ordinary and partial differential equations, followed by chapters on nonlinear systems and on the analysis of experimental data using linear and nonlinear regression techniques, Fourier transforms, binomial and Gaussian distributions. The book is accompanied by a dedicated GitHub website, which contains all codes from the book in the form of ready to run Jupyter notebooks. A detailed solutions manual is also available for instructors using the textbook in their courses. Key Features: A unique teaching approach which merges mathematical methods and the Python programming skills which physicists and engineering students need in their courses Uses examples and models from physical and engineering systems, to motivate the mathematics being taught Students learn to solve scientific problems in three different ways: traditional pen-and-paper methods, using scientific numerical techniques with NumPy and SciPy, and using Symbolic Python (SymPy).
| Author | : Amit Saha |
| Publisher | : No Starch Press |
| Total Pages | : 265 |
| Release | : 2015-08-01 |
| Genre | : Computers |
| ISBN | : 1593277199 |
Doing Math with Python shows you how to use Python to delve into high school–level math topics like statistics, geometry, probability, and calculus. You’ll start with simple projects, like a factoring program and a quadratic-equation solver, and then create more complex projects once you’ve gotten the hang of things. Along the way, you’ll discover new ways to explore math and gain valuable programming skills that you’ll use throughout your study of math and computer science. Learn how to: –Describe your data with statistics, and visualize it with line graphs, bar charts, and scatter plots –Explore set theory and probability with programs for coin flips, dicing, and other games of chance –Solve algebra problems using Python’s symbolic math functions –Draw geometric shapes and explore fractals like the Barnsley fern, the Sierpinski triangle, and the Mandelbrot set –Write programs to find derivatives and integrate functions Creative coding challenges and applied examples help you see how you can put your new math and coding skills into practice. You’ll write an inequality solver, plot gravity’s effect on how far a bullet will travel, shuffle a deck of cards, estimate the area of a circle by throwing 100,000 "darts" at a board, explore the relationship between the Fibonacci sequence and the golden ratio, and more. Whether you’re interested in math but have yet to dip into programming or you’re a teacher looking to bring programming into the classroom, you’ll find that Python makes programming easy and practical. Let Python handle the grunt work while you focus on the math. Uses Python 3
| Author | : Qingkai Kong |
| Publisher | : Academic Press |
| Total Pages | : 482 |
| Release | : 2020-11-27 |
| Genre | : Technology & Engineering |
| ISBN | : 0128195509 |
Python 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
| Author | : Sam Morley |
| Publisher | : Packt Publishing Ltd |
| Total Pages | : 353 |
| Release | : 2020-07-31 |
| Genre | : Computers |
| ISBN | : 1838986561 |
Discover easy-to-follow solutions and techniques to help you to implement applied mathematical concepts such as probability, calculus, and equations using Python's numeric and scientific libraries Key FeaturesCompute complex mathematical problems using programming logic with the help of step-by-step recipesLearn how to utilize Python's libraries for computation, mathematical modeling, and statisticsDiscover simple yet effective techniques for solving mathematical equations and apply them in real-world statisticsBook Description Python, one of the world's most popular programming languages, has a number of powerful packages to help you tackle complex mathematical problems in a simple and efficient way. These core capabilities help programmers pave the way for building exciting applications in various domains, such as machine learning and data science, using knowledge in the computational mathematics domain. The book teaches you how to solve problems faced in a wide variety of mathematical fields, including calculus, probability, statistics and data science, graph theory, optimization, and geometry. You'll start by developing core skills and learning about packages covered in Python's scientific stack, including NumPy, SciPy, and Matplotlib. As you advance, you'll get to grips with more advanced topics of calculus, probability, and networks (graph theory). After you gain a solid understanding of these topics, you'll discover Python's applications in data science and statistics, forecasting, geometry, and optimization. The final chapters will take you through a collection of miscellaneous problems, including working with specific data formats and accelerating code. By the end of this book, you'll have an arsenal of practical coding solutions that can be used and modified to solve a wide range of practical problems in computational mathematics and data science. What you will learnGet familiar with basic packages, tools, and libraries in Python for solving mathematical problemsExplore various techniques that will help you to solve computational mathematical problemsUnderstand the core concepts of applied mathematics and how you can apply them in computer scienceDiscover how to choose the most suitable package, tool, or technique to solve a certain problemImplement basic mathematical plotting, change plot styles, and add labels to the plots using MatplotlibGet to grips with probability theory with the Bayesian inference and Markov Chain Monte Carlo (MCMC) methodsWho this book is for This book is for professional programmers and students looking to solve mathematical problems computationally using Python. Advanced mathematics knowledge is not a requirement, but a basic knowledge of mathematics will help you to get the most out of this book. The book assumes familiarity with Python concepts of data structures.
| Author | : Hans Petter Langtangen |
| Publisher | : Springer |
| Total Pages | : 942 |
| Release | : 2016-07-28 |
| Genre | : Computers |
| ISBN | : 3662498871 |
The book serves as a first introduction to computer programming of scientific applications, using the high-level Python language. The exposition is example and problem-oriented, where the applications are taken from mathematics, numerical calculus, statistics, physics, biology and finance. The book teaches "Matlab-style" and procedural programming as well as object-oriented programming. High school mathematics is a required background and it is advantageous to study classical and numerical one-variable calculus in parallel with reading this book. Besides learning how to program computers, the reader will also learn how to solve mathematical problems, arising in various branches of science and engineering, with the aid of numerical methods and programming. By blending programming, mathematics and scientific applications, the book lays a solid foundation for practicing computational science. From the reviews: Langtangen ... does an excellent job of introducing programming as a set of skills in problem solving. He guides the reader into thinking properly about producing program logic and data structures for modeling real-world problems using objects and functions and embracing the object-oriented paradigm. ... Summing Up: Highly recommended. F. H. Wild III, Choice, Vol. 47 (8), April 2010 Those of us who have learned scientific programming in Python ‘on the streets’ could be a little jealous of students who have the opportunity to take a course out of Langtangen’s Primer.” John D. Cook, The Mathematical Association of America, September 2011 This book goes through Python in particular, and programming in general, via tasks that scientists will likely perform. It contains valuable information for students new to scientific computing and would be the perfect bridge between an introduction to programming and an advanced course on numerical methods or computational science. Alex Small, IEEE, CiSE Vol. 14 (2), March /April 2012 “This fourth edition is a wonderful, inclusive textbook that covers pretty much everything one needs to know to go from zero to fairly sophisticated scientific programming in Python...” Joan Horvath, Computing Reviews, March 2015
| Author | : Raymond T. Pierrehumbert |
| Publisher | : Cambridge University Press |
| Total Pages | : 679 |
| Release | : 2010-12-02 |
| Genre | : Science |
| ISBN | : 1139495062 |
This book introduces the reader to all the basic physical building blocks of climate needed to understand the present and past climate of Earth, the climates of Solar System planets, and the climates of extrasolar planets. These building blocks include thermodynamics, infrared radiative transfer, scattering, surface heat transfer and various processes governing the evolution of atmospheric composition. Nearly four hundred problems are supplied to help consolidate the reader's understanding, and to lead the reader towards original research on planetary climate. This textbook is invaluable for advanced undergraduate or beginning graduate students in atmospheric science, Earth and planetary science, astrobiology, and physics. It also provides a superb reference text for researchers in these subjects, and is very suitable for academic researchers trained in physics or chemistry who wish to rapidly gain enough background to participate in the excitement of the new research opportunities opening in planetary climate.
| Author | : Alex Gezerlis |
| Publisher | : Cambridge University Press |
| Total Pages | : 705 |
| Release | : 2023-07-31 |
| Genre | : Computers |
| ISBN | : 1009303856 |
A standalone text on computational physics combining idiomatic Python, foundational numerical methods, and physics applications.
| Author | : Dirk P. Kroese |
| Publisher | : CRC Press |
| Total Pages | : 538 |
| Release | : 2019-11-20 |
| Genre | : Business & Economics |
| ISBN | : 1000730778 |
Focuses on mathematical understanding Presentation is self-contained, accessible, and comprehensive Full color throughout Extensive list of exercises and worked-out examples Many concrete algorithms with actual code
| Author | : Krishnendu Chaudhury |
| Publisher | : Simon and Schuster |
| Total Pages | : 550 |
| Release | : 2024-03-26 |
| Genre | : Computers |
| ISBN | : 1617296481 |
Math and Architectures of Deep Learning bridges the gap between theory and practice, laying out the math of deep learning side by side with practical implementations in Python and PyTorch. You'll peer inside the "black box" to understand how your code is working, and learn to comprehend cutting-edge research you can turn into practical applications. Math and Architectures of Deep Learning sets out the foundations of DL usefully and accessibly to working practitioners. Each chapter explores a new fundamental DL concept or architectural pattern, explaining the underpinning mathematics and demonstrating how they work in practice with well-annotated Python code. You'll start with a primer of basic algebra, calculus, and statistics, working your way up to state-of-the-art DL paradigms taken from the latest research. Learning mathematical foundations and neural network architecture can be challenging, but the payoff is big. You'll be free from blind reliance on pre-packaged DL models and able to build, customize, and re-architect for your specific needs. And when things go wrong, you'll be glad you can quickly identify and fix problems.
| Author | : Peter Farrell |
| Publisher | : Packt Publishing Ltd |
| Total Pages | : 739 |
| Release | : 2020-08-18 |
| Genre | : Computers |
| ISBN | : 1800208367 |
With examples and activities that help you achieve real results, applying calculus and statistical methods relevant to advanced data science has never been so easy Key FeaturesDiscover how most programmers use the main Python libraries when performing statistics with PythonUse descriptive statistics and visualizations to answer business and scientific questionsSolve complicated calculus problems, such as arc length and solids of revolution using derivatives and integralsBook Description Are you looking to start developing artificial intelligence applications? Do you need a refresher on key mathematical concepts? Full of engaging practical exercises, The Statistics and Calculus with Python Workshop will show you how to apply your understanding of advanced mathematics in the context of Python. The book begins by giving you a high-level overview of the libraries you'll use while performing statistics with Python. As you progress, you'll perform various mathematical tasks using the Python programming language, such as solving algebraic functions with Python starting with basic functions, and then working through transformations and solving equations. Later chapters in the book will cover statistics and calculus concepts and how to use them to solve problems and gain useful insights. Finally, you'll study differential equations with an emphasis on numerical methods and learn about algorithms that directly calculate values of functions. By the end of this book, you'll have learned how to apply essential statistics and calculus concepts to develop robust Python applications that solve business challenges. What you will learnGet to grips with the fundamental mathematical functions in PythonPerform calculations on tabular datasets using pandasUnderstand the differences between polynomials, rational functions, exponential functions, and trigonometric functionsUse algebra techniques for solving systems of equationsSolve real-world problems with probabilitySolve optimization problems with derivatives and integralsWho this book is for If you are a Python programmer who wants to develop intelligent solutions that solve challenging business problems, then this book is for you. To better grasp the concepts explained in this book, you must have a thorough understanding of advanced mathematical concepts, such as Markov chains, Euler's formula, and Runge-Kutta methods as the book only explains how these techniques and concepts can be implemented in Python.
