A Student's Guide to Vectors and Tensors

Author: Daniel A. Fleisch

Publisher: Cambridge University Press

ISBN: 1139503944

Category: Science

Page: N.A

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Vectors and tensors are among the most powerful problem-solving tools available, with applications ranging from mechanics and electromagnetics to general relativity. Understanding the nature and application of vectors and tensors is critically important to students of physics and engineering. Adopting the same approach used in his highly popular A Student's Guide to Maxwell's Equations, Fleisch explains vectors and tensors in plain language. Written for undergraduate and beginning graduate students, the book provides a thorough grounding in vectors and vector calculus before transitioning through contra and covariant components to tensors and their applications. Matrices and their algebra are reviewed on the book's supporting website, which also features interactive solutions to every problem in the text where students can work through a series of hints or choose to see the entire solution at once. Audio podcasts give students the opportunity to hear important concepts in the book explained by the author.
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A Student's Guide to the Schrödinger Equation

Author: Daniel A. Fleisch

Publisher: Cambridge University Press

ISBN: 1108834736

Category: Mathematics

Page: 234

View: 6025

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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.
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A Student's Guide to the Mathematics of Astronomy

Author: Daniel Fleisch,Julia Kregenow

Publisher: Cambridge University Press

ISBN: 1107292557

Category: Science

Page: N.A

View: 8523

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The study of astronomy offers an unlimited opportunity for us to gain a deeper understanding of our planet, the Solar System, the Milky Way Galaxy and the known Universe. Using the plain-language approach that has proven highly popular in Fleisch's other Student's Guides, this book is ideal for non-science majors taking introductory astronomy courses. The authors address topics that students find most troublesome, on subjects ranging from stars and light to gravity and black holes. Dozens of fully worked examples and over 150 exercises and homework problems help readers get to grips with the concepts in each chapter. An accompanying website features a host of supporting materials, including interactive solutions for every exercise and problem in the text and a series of video podcasts in which the authors explain the important concepts of every section of the book.
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A Student's Guide to Geophysical Equations

Author: William Lowrie

Publisher: Cambridge University Press

ISBN: 1139499246

Category: Science

Page: N.A

View: 5753

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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.
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A Student's Guide to Einstein's Major Papers

Author: Robert E Kennedy

Publisher: Oxford University Press

ISBN: 0199694036

Category: Science

Page: 303

View: 8263

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In 1905 Albert Einstein produced breakthrough work in three major areas of physics (atoms and Brownian motion, quanta, and the special theory of relativity), followed, in 1916, by the general theory of relativity. This book develops the detail of the papers, including the mathematics, to guide the reader in working through them.
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Tensor Calculus for Physics

A Concise Guide

Author: Dwight E. Neuenschwander

Publisher: JHU Press

ISBN: 142141564X

Category: Mathematics

Page: 248

View: 4590

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Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism, they encounter the "polarization tensor." However, this piecemeal approach can set students up for misconceptions when they have to learn about tensors in more advanced physics and mathematics studies (e.g., while enrolled in a graduate-level general relativity course or when studying non-Euclidean geometries in a higher mathematics class). Dwight E. Neuenschwander's Tensor Calculus for Physics is a bottom-up approach that emphasizes motivations before providing definitions. Using a clear, step-by-step approach, the book strives to embed the logic of tensors in contexts that demonstrate why that logic is worth pursuing. It is an ideal companion for courses such as mathematical methods of physics, classical mechanics, electricity and magnetism, and relativity.
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Vector Analysis

A Physicist's Guide to the Mathematics of Fields in Three Dimensions

Author: N. Kemmer

Publisher: CUP Archive

ISBN: 9780521211581

Category: Mathematics

Page: 254

View: 6241

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Vector analysis provides the language that is needed for a precise quantitative statement of the general laws and relationships governing such branches of physics as electromagnetism and fluid dynamics. The account of the subject is aimed principally at physicists but the presentation is equally appropriate for engineers. The justification for adding to the available textbooks on vector analysis stems from Professor Kemmer's novel presentation of the subject developed through many years of teaching, and in relating the mathematics to physical models. While maintaining mathematical precision, the methodology of presentation relies greatly on the visual, geometric aspects of the subject and is supported throughout the text by many beautiful illustrations that are more than just schematic. A unification of the whole body of results developed in the book - from the simple ideas of differentiation and integration of vector fields to the theory of orthogonal curvilinear coordinates and to the treatment of time-dependent integrals over fields - is achieved by the introduction from the outset of a method of general parametrisation of curves and surfaces.
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Maxwell's Equations

Author: Paul G. Huray

Publisher: John Wiley & Sons

ISBN: 0470549904

Category: Science

Page: 312

View: 4698

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An authoritative view of Maxwell's Equations that takes theory to practice Maxwell's Equations is a practical guide to one of the most remarkable sets of equations ever devised. Professor Paul Huray presents techniques that show the reader how to obtain analytic solutions for Maxwell's equations for ideal materials and boundary conditions. These solutions are then used as a benchmark for solving real-world problems. Coverage includes: An historical overview of electromagnetic concepts before Maxwell and how we define fundamental units and universal constants today A review of vector analysis and vector operations of scalar, vector, and tensor products Electrostatic fields and the interaction of those fields with dielectric materials and good conductors A method for solving electrostatic problems through the use of Poisson's and Laplace's equations and Green's function Electrical resistance and power dissipation; superconductivity from an experimental perspective; and the equation of continuity An introduction to magnetism from the experimental inverse square of the Biot-Savart law so that Maxwell's magnetic flux equations can be deduced Maxwell's Equations serves as an ideal textbook for undergraduate students in junior/senior electromagnetics courses and graduate students, as well as a resource for electrical engineers.
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Schaum's Outline of Vector Analysis, 2ed

Author: Murray Spiegel,Seymour Lipschutz

Publisher: McGraw Hill Professional

ISBN: 0071815228

Category: Study Aids

Page: 272

View: 2464

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The guide to vector analysis that helps students study faster, learn better, and get top grades More than 40 million students have trusted Schaum's to help them study faster, learn better, and get top grades. Now Schaum's is better than ever-with a new look, a new format with hundreds of practice problems, and completely updated information to conform to the latest developments in every field of study. Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores! Schaum's Outlines-Problem Solved.
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