A Student's Guide to the Navier-Stokes Equations

A Student's Guide to the Navier-Stokes Equations
Author: Justin W. Garvin
Publisher:
Total Pages: 238
Release: 2023-03-13
Genre: Mathematics
ISBN: 1009236121

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The Navier-Stokes equations describe the motion of fluids and are an invaluable addition to the toolbox of every physicist, applied mathematician, and engineer. The equations arise from applying Newton's laws of motion to a moving fluid and are considered, when used in combination with mass and energy conservation rules, to be the fundamental governing equations of fluid motion. They are relevant across many disciplines, from astrophysics and oceanic sciences to aerospace engineering and materials science. This Student's Guide provides a clear and focused presentation of the derivation, significance and applications of the Navier-Stokes equations, along with the associated continuity and energy equations. Designed as a useful supplementary resource for undergraduate and graduate students, each chapter concludes with a selection of exercises intended to reinforce and extend important concepts. Video podcasts demonstrating the solutions in full are provided online, along with written solutions and other additional resources.

A Student's Guide to the Navier-Stokes Equations

A Student's Guide to the Navier-Stokes Equations
Author: Justin W. Garvin
Publisher: Cambridge University Press
Total Pages: 237
Release: 2023-01-31
Genre: Science
ISBN: 1009236156

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A clear and focused guide to the Navier-Stokes equations that govern fluid motion, including exercises and fully worked solutions.

A Student's Guide to the Schrödinger Equation

A Student's Guide to the Schrödinger Equation
Author: Daniel A. Fleisch
Publisher: Cambridge University Press
Total Pages: 237
Release: 2020-02-20
Genre: Mathematics
ISBN: 1108834736

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A clear guide to the key concepts and mathematical techniques underlying the Schrödinger equation, including homework problems and fully worked solutions.

A Student's Guide to Fourier Transforms

A Student's Guide to Fourier Transforms
Author: John Francis James
Publisher: Cambridge University Press
Total Pages: 156
Release: 2002-09-19
Genre: Mathematics
ISBN: 9780521004282

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Fourier transform theory is of central importance in a vast range of applications in physical science, engineering, and applied mathematics. This new edition of a successful student text provides a concise introduction to the theory and practice of Fourier transforms, using qualitative arguments wherever possible and avoiding unnecessary mathematics. After a brief description of the basic ideas and theorems, the power of the technique is then illustrated by referring to particular applications in optics, spectroscopy, electronics and telecommunications. The rarely discussed but important field of multi-dimensional Fourier theory is covered, including a description of computer-aided tomography (CAT-scanning). The final chapter discusses digital methods, with particular attention to the fast Fourier transform. Throughout, discussion of these applications is reinforced by the inclusion of worked examples. The book assumes no previous knowledge of the subject, and will be invaluable to students of physics, electrical and electronic engineering, and computer science.

A Student's Guide to Entropy

A Student's Guide to Entropy
Author: Don S. Lemons
Publisher: Cambridge University Press
Total Pages: 195
Release: 2013-08-29
Genre: Science
ISBN: 1107470048

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Striving to explore the subject in as simple a manner as possible, this book helps readers understand the elusive concept of entropy. Innovative aspects of the book include the construction of statistical entropy from desired properties, the derivation of the entropy of classical systems from purely classical assumptions, and a statistical thermodynamics approach to the ideal Fermi and ideal Bose gases. Derivations are worked through step-by-step and important applications are highlighted in over 20 worked examples. Around 50 end-of-chapter exercises test readers' understanding. The book also features a glossary giving definitions for all essential terms, a time line showing important developments, and list of books for further study. It is an ideal supplement to undergraduate courses in physics, engineering, chemistry and mathematics.

A Student's Guide to Maxwell's Equations

A Student's Guide to Maxwell's Equations
Author: Daniel Fleisch
Publisher: Cambridge University Press
Total Pages: 129
Release: 2008-01-10
Genre: Science
ISBN: 1139468472

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Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law, and the Ampere–Maxwell law are four of the most influential equations in science. In this guide for students, each equation is the subject of an entire chapter, with detailed, plain-language explanations of the physical meaning of each symbol in the equation, for both the integral and differential forms. The final chapter shows how Maxwell's equations may be combined to produce the wave equation, the basis for the electromagnetic theory of light. This book is a wonderful resource for undergraduate and graduate courses in electromagnetism and electromagnetics. A website hosted by the author at www.cambridge.org/9780521701471 contains interactive solutions to every problem in the text as well as audio podcasts to walk students through each chapter.

Navier-Stokes Equations

Navier-Stokes Equations
Author: Peter Constantin
Publisher: University of Chicago Press
Total Pages: 200
Release: 1988
Genre: Mathematics
ISBN: 0226115496

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Lecture notes of graduate courses given by the authors at Indiana University (1985-86) and the University of Chicago (1986-87). Paper edition, $14.95. Annotation copyright Book News, Inc. Portland, Or.

A Student's Guide to Laplace Transforms

A Student's Guide to Laplace Transforms
Author: Daniel Fleisch
Publisher: Cambridge University Press
Total Pages: 221
Release: 2022-01-13
Genre: Mathematics
ISBN: 1009098497

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Clear explanations and supportive online material develop an intuitive understanding of the meaning and use of Laplace.

A Student's Guide to Python for Physical Modeling

A Student's Guide to Python for Physical Modeling
Author: Jesse M. Kinder
Publisher: Princeton University Press
Total Pages: 241
Release: 2021-08-03
Genre: Science
ISBN: 0691223661

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A fully updated tutorial on the basics of the Python programming language for science students Python is a computer programming language that has gained popularity throughout the sciences. This fully updated second edition of A Student's Guide to Python for Physical Modeling aims to help you, the student, teach yourself enough of the Python programming language to get started with physical modeling. You will learn how to install an open-source Python programming environment and use it to accomplish many common scientific computing tasks: importing, exporting, and visualizing data; numerical analysis; and simulation. No prior programming experience is assumed. This guide introduces a wide range of useful tools, including: Basic Python programming and scripting Numerical arrays Two- and three-dimensional graphics Animation Monte Carlo simulations Numerical methods, including solving ordinary differential equations Image processing Numerous code samples and exercises—with solutions—illustrate new ideas as they are introduced. This guide also includes supplemental online resources: code samples, data sets, tutorials, and more. This edition includes new material on symbolic calculations with SymPy, an introduction to Python libraries for data science and machine learning (pandas and sklearn), and a primer on Python classes and object-oriented programming. A new appendix also introduces command line tools and version control with Git.

A Student's Guide to Rotational Motion

A Student's Guide to Rotational Motion
Author: Effrosyni Seitaridou
Publisher: Cambridge University Press
Total Pages: 184
Release: 2023-07-31
Genre: Science
ISBN: 1009213318

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Rotational motion is of fundamental importance in physics and engineering, and an essential topic for undergraduates to master. This accessible yet rigorous Student's Guide focuses on the underlying principles of rotational dynamics, providing the reader with an intuitive understanding of the physical concepts, and a firm grasp of the mathematics. Key concepts covered include torque, moment of inertia, angular momentum, work and energy, and the combination of translational and rotational motion. Each chapter presents one important aspect of the topic, with derivations and analysis of the fundamental equations supported by step-by-step examples and exercises demonstrating important applications. Much of the book is focused on scenarios in which point masses and rigid bodies rotate around fixed axes, while more advanced examples of rotational motion, including gyroscopic motion, are introduced in a final chapter.