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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: 0
Release: 2023-01-31
Genre: Science
ISBN: 9781009236164

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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 Geophysical Equations

A Student's Guide to Geophysical Equations
Author: William Lowrie
Publisher: Cambridge University Press
Total Pages: 297
Release: 2011-05-26
Genre: Science
ISBN: 1139499246

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The advent of accessible student computing packages has meant that geophysics students can now easily manipulate datasets and gain first-hand modeling experience - essential in developing an intuitive understanding of the physics of the Earth. Yet to gain a more in-depth understanding of physical theory, and to develop new models and solutions, it is necessary to be able to derive the relevant equations from first principles. This compact, handy book fills a gap left by most modern geophysics textbooks, which generally do not have space to derive all of the important formulae, showing the intermediate steps. This guide presents full derivations for the classical equations of gravitation, gravity, tides, earth rotation, heat, geomagnetism and foundational seismology, illustrated with simple schematic diagrams. It supports students through the successive steps and explains the logical sequence of a derivation - facilitating self-study and helping students to tackle homework exercises and prepare for exams.


The Navier-Stokes Problem in the 21st Century

The Navier-Stokes Problem in the 21st Century
Author: Pierre Gilles Lemarie-Rieusset
Publisher: CRC Press
Total Pages: 732
Release: 2016-04-06
Genre: Mathematics
ISBN: 146656623X

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Up-to-Date Coverage of the Navier–Stokes Equation from an Expert in Harmonic Analysis The complete resolution of the Navier–Stokes equation—one of the Clay Millennium Prize Problems—remains an important open challenge in partial differential equations (PDEs) research despite substantial studies on turbulence and three-dimensional fluids. The Navier–Stokes Problem in the 21st Century provides a self-contained guide to the role of harmonic analysis in the PDEs of fluid mechanics. The book focuses on incompressible deterministic Navier–Stokes equations in the case of a fluid filling the whole space. It explores the meaning of the equations, open problems, and recent progress. It includes classical results on local existence and studies criterion for regularity or uniqueness of solutions. The book also incorporates historical references to the (pre)history of the equations as well as recent references that highlight active mathematical research in the field.


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 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.


Introduction to Mathematical Fluid Dynamics

Introduction to Mathematical Fluid Dynamics
Author: Richard E. Meyer
Publisher: Courier Corporation
Total Pages: 194
Release: 2012-03-08
Genre: Science
ISBN: 0486138941

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Geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences, this introductory text covers kinematics, momentum principle, Newtonian fluid, compressibility, and other subjects. 1971 edition.


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 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.


A Student's Guide to Numerical Methods

A Student's Guide to Numerical Methods
Author: Ian H. Hutchinson
Publisher: Cambridge University Press
Total Pages: 223
Release: 2015-04-30
Genre: Computers
ISBN: 1107095670

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The plain language style, worked examples and exercises in this book help students to understand the foundations of computational physics and engineering.