Science

A Student's Guide to Vectors and Tensors

Author: Daniel A. Fleisch

Publisher: Cambridge University Press

ISBN:

Category: Science

Page:

View: 283

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.
Science

A Student's Guide to the Mathematics of Astronomy

Author: Daniel Fleisch

Publisher: Cambridge University Press

ISBN:

Category: Science

Page: 205

View: 886

Plain-language explanations and a rich set of supporting material help students understand the mathematical concepts and techniques of astronomy.
Mathematics

A Student's Guide to Infinite Series and Sequences

Author: Bernhard W. Bach, Jr.

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 160

View: 524

An informal and practically focused introduction for undergraduate students exploring infinite series and sequences in engineering and the physical sciences. With a focus on practical applications in real world situations, it helps students to conceptualize the theory with real-world examples and to build their skill set.
Science

A Student's Guide to the Schrödinger Equation

Author: Daniel A. Fleisch

Publisher: Cambridge University Press

ISBN:

Category: Science

Page: 250

View: 818

Quantum mechanics is a hugely important topic in science and engineering, but many students struggle to understand the abstract mathematical techniques used to solve the Schrödinger equation and to analyse the resulting wave functions. Retaining the popular approach used in Fleisch's other student's guides, this friendly resource uses plain language to provide detailed explanations of the fundamental concepts and mathematical techniques underlying the Schrödinger equation in quantum mechanics. It addresses the problems students find most troublesome in a clear and intuitive way, and each chapter includes several homework problems with fully worked solutions. A companion app from Edukado hosts additional resources, including an extensive glossary, quick quizzes, interactive graphs and a series of videos in which the author explains the most important concepts from each section of the book. The supporting app enables students to test their learning and develop a deeper understanding of the topic.
Science

A Student's Guide to General Relativity

Author: Norman Gray

Publisher: Cambridge University Press

ISBN:

Category: Science

Page: 162

View: 212

Vectors, tensors and functions -- Manifolds, vectors and differentiation -- Energy, momentum and Einstein's equations
Mathematics

Large Strain Finite Element Method

Author: Antonio Munjiza

Publisher: John Wiley & Sons

ISBN:

Category: Mathematics

Page: 488

View: 962

An introductory approach to the subject of large strains andlarge displacements in finite elements. Large Strain Finite Element Method: A Practical Course,takes an introductory approach to the subject of large strains andlarge displacements in finite elements and starts from the basicconcepts of finite strain deformability, including finite rotationsand finite displacements. The necessary elements of vector analysisand tensorial calculus on the lines of modern understanding of theconcept of tensor will also be introduced. This book explains how tensors and vectors can be describedusing matrices and also introduces different stress and straintensors. Building on these, step by step finite element techniquesfor both hyper and hypo-elastic approach will be considered. Material models including isotropic, unisotropic, plastic andviscoplastic materials will be independently discussed tofacilitate clarity and ease of learning. Elements of transientdynamics will also be covered and key explicit and iterativesolvers including the direct numerical integration, relaxationtechniques and conjugate gradient method will also be explored. This book contains a large number of easy to followillustrations, examples and source code details that facilitateboth reading and understanding. Takes an introductory approach to the subject of large strainsand large displacements in finite elements. No prior knowledge ofthe subject is required. Discusses computational methods and algorithms to tackle largestrains and teaches the basic knowledge required to be able tocritically gauge the results of computational models. Contains a large number of easy to follow illustrations,examples and source code details. Accompanied by a website hosting code examples.
Mathematics

Vector Analysis

Author: N. Kemmer

Publisher: CUP Archive

ISBN:

Category: Mathematics

Page: 254

View: 133

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.
Science

A Student's Guide to Geophysical Equations

Author: William Lowrie

Publisher: Cambridge University Press

ISBN:

Category: Science

Page:

View: 359

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.
Mathematics

Tensor Calculus for Physics

Author: Dwight E. Neuenschwander

Publisher: JHU Press

ISBN:

Category: Mathematics

Page: 248

View: 339

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.