Geometry Vector Calculus
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| Author | : Alan Macdonald |
| Publisher | : Createspace Independent Publishing Platform |
| Total Pages | : 0 |
| Release | : 2012 |
| Genre | : Calculus |
| ISBN | : 9781480132450 |
This textbook for the undergraduate vector calculus course presents a unified treatment of vector and geometric calculus. This is the printing of August 2022. The book is a sequel to the text Linear and Geometric Algebra by the same author. That text is a prerequisite for this one. Its web page is at faculty.luther.edu/ macdonal/laga. Linear algebra and vector calculus have provided the basic vocabulary of mathematics in dimensions greater than one for the past one hundred years. Just as geometric algebra generalizes linear algebra in powerful ways, geometric calculus generalizes vector calculus in powerful ways. Traditional vector calculus topics are covered, as they must be, since readers will encounter them in other texts and out in the world. Differential geometry is used today in many disciplines. A final chapter is devoted to it. Download the book's table of contents, preface, and index at the book's web site: faculty.luther.edu/ macdonal/vagc. From a review of Linear and Geometric Algebra: Alan Macdonald's text is an excellent resource if you are just beginning the study of geometric algebra and would like to learn or review traditional linear algebra in the process. The clarity and evenness of the writing, as well as the originality of presentation that is evident throughout this text, suggest that the author has been successful as a mathematics teacher in the undergraduate classroom. This carefully crafted text is ideal for anyone learning geometric algebra in relative isolation, which I suspect will be the case for many readers. -- Jeffrey Dunham, William R. Kenan Jr. Professor of Natural Sciences, Middlebury College
| Author | : D. E. Rutherford |
| Publisher | : Courier Corporation |
| Total Pages | : 148 |
| Release | : 2012-04-27 |
| Genre | : Mathematics |
| ISBN | : 048615453X |
This text offers both a clear view of the abstract theory as well as a concise survey of the theory's applications to various branches of pure and applied mathematics. 1957 edition.
| Author | : A. R. Vasishtha |
| Publisher | : Krishna Prakashan Media |
| Total Pages | : 581 |
| Release | : |
| Genre | : |
| ISBN | : 8182835372 |
| Author | : Paul C. Matthews |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 189 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1447105974 |
Vector calculus is the fundamental language of mathematical physics. It pro vides a way to describe physical quantities in three-dimensional space and the way in which these quantities vary. Many topics in the physical sciences can be analysed mathematically using the techniques of vector calculus. These top ics include fluid dynamics, solid mechanics and electromagnetism, all of which involve a description of vector and scalar quantities in three dimensions. This book assumes no previous knowledge of vectors. However, it is assumed that the reader has a knowledge of basic calculus, including differentiation, integration and partial differentiation. Some knowledge of linear algebra is also required, particularly the concepts of matrices and determinants. The book is designed to be self-contained, so that it is suitable for a pro gramme of individual study. Each of the eight chapters introduces a new topic, and to facilitate understanding of the material, frequent reference is made to physical applications. The physical nature of the subject is clarified with over sixty diagrams, which provide an important aid to the comprehension of the new concepts. Following the introduction of each new topic, worked examples are provided. It is essential that these are studied carefully, so that a full un derstanding is developed before moving ahead. Like much of mathematics, each section of the book is built on the foundations laid in the earlier sections and chapters.
| Author | : John Hamal Hubbard |
| Publisher | : |
| Total Pages | : 284 |
| Release | : 2009 |
| Genre | : Algebras, Linear |
| ISBN | : 9780971576674 |
| Author | : Michael J. Crowe |
| Publisher | : Courier Corporation |
| Total Pages | : 306 |
| Release | : 1994-01-01 |
| Genre | : Mathematics |
| ISBN | : 0486679101 |
Prize-winning study traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers to the final acceptance around 1910 of the modern system of vector analysis.
| Author | : Antonio Galbis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 383 |
| Release | : 2012-03-29 |
| Genre | : Mathematics |
| ISBN | : 1461422000 |
The aim of this book is to facilitate the use of Stokes' Theorem in applications. The text takes a differential geometric point of view and provides for the student a bridge between pure and applied mathematics by carefully building a formal rigorous development of the topic and following this through to concrete applications in two and three variables. Key topics include vectors and vector fields, line integrals, regular k-surfaces, flux of a vector field, orientation of a surface, differential forms, Stokes' theorem, and divergence theorem. This book is intended for upper undergraduate students who have completed a standard introduction to differential and integral calculus for functions of several variables. The book can also be useful to engineering and physics students who know how to handle the theorems of Green, Stokes and Gauss, but would like to explore the topic further.
| Author | : Zbigniew Nitecki |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 417 |
| Release | : 2018-10-16 |
| Genre | : Mathematics |
| ISBN | : 1470443600 |
Calculus in 3D is an accessible, well-written textbook for an honors course in multivariable calculus for mathematically strong first- or second-year university students. The treatment given here carefully balances theoretical rigor, the development of student facility in the procedures and algorithms, and inculcating intuition into underlying geometric principles. The focus throughout is on two or three dimensions. All of the standard multivariable material is thoroughly covered, including vector calculus treated through both vector fields and differential forms. There are rich collections of problems ranging from the routine through the theoretical to deep, challenging problems suitable for in-depth projects. Linear algebra is developed as needed. Unusual features include a rigorous formulation of cross products and determinants as oriented area, an in-depth treatment of conics harking back to the classical Greek ideas, and a more extensive than usual exploration and use of parametrized curves and surfaces. Zbigniew Nitecki is Professor of Mathematics at Tufts University and a leading authority on smooth dynamical systems. He is the author of Differentiable Dynamics, MIT Press; Differential Equations, A First Course (with M. Guterman), Saunders; Differential Equations with Linear Algebra (with M. Guterman), Saunders; and Calculus Deconstructed, AMS.
| Author | : Sarhan M. Musa |
| Publisher | : Mercury Learning and Information |
| Total Pages | : 491 |
| Release | : 2023-02-08 |
| Genre | : Mathematics |
| ISBN | : 1683929179 |
This book is designed primarily for undergraduates in mathematics, engineering, and the physical sciences. Rather than concentrating on technical skills, it focuses on a deeper understanding of the subject by providing many unusual and challenging examples. The basic topics of vector geometry, differentiation and integration in several variables are explored. Furthermore, it can be used to impower the mathematical knowledge for Artificial Intelligence (AI) concepts. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. Partial solutions and instructor ancillaries available for use as a textbook. FEATURES Includes numerous computer illustrations and tutorials using MATLAB®and Maple® Covers the major topics of vector geometry, differentiation, and integration in several variables Instructors’ ancillaries available upon adoption
| Author | : Serge Lang |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 624 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461210682 |
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
