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Author : Anil Kumar Sharma
Publisher : Discovery Publishing House
Page : 312 pages
File Size : 42,7 Mb
Release : 2010
Category : Vector analysis
ISBN : 8183560946
Contents: Differentiation and Integration of Vectors, Multiple Vectors, Gradient, Divergence and Curl, Green s Gauss s and Stoke s Theorem.
Author : SHANTI NARAYAN
Publisher : S. Chand Publishing
Page : 368 pages
File Size : 47,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9788121901611
A TEXTBOOK OF VECTOR CALCULUS
Author : David M. Bressoud
Publisher : Springer Science & Business Media
Page : 399 pages
File Size : 46,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461209591
Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.
Author : Paul C. Matthews
Publisher : Springer Science & Business Media
Page : 189 pages
File Size : 46,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447105978
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,Barbara Burke Hubbard
Publisher : Unknown
Page : 284 pages
File Size : 47,7 Mb
Release : 2009
Category : Algebras, Linear
ISBN : 097157667X
Author : Stanley J. Miklavcic
Publisher : Springer Nature
Page : 319 pages
File Size : 41,8 Mb
Release : 2020-02-17
Category : Mathematics
ISBN : 9783030334598
This textbook focuses on one of the most valuable skills in multivariable and vector calculus: visualization. With over one hundred carefully drawn color images, students who have long struggled picturing, for example, level sets or vector fields will find these abstract concepts rendered with clarity and ingenuity. This illustrative approach to the material covered in standard multivariable and vector calculus textbooks will serve as a much-needed and highly useful companion. Emphasizing portability, this book is an ideal complement to other references in the area. It begins by exploring preliminary ideas such as vector algebra, sets, and coordinate systems, before moving into the core areas of multivariable differentiation and integration, and vector calculus. Sections on the chain rule for second derivatives, implicit functions, PDEs, and the method of least squares offer additional depth; ample illustrations are woven throughout. Mastery Checks engage students in material on the spot, while longer exercise sets at the end of each chapter reinforce techniques. An Illustrative Guide to Multivariable and Vector Calculus will appeal to multivariable and vector calculus students and instructors around the world who seek an accessible, visual approach to this subject. Higher-level students, called upon to apply these concepts across science and engineering, will also find this a valuable and concise resource.
Author : Shanti Narayan | PK Mittal
Publisher : S. Chand Publishing
Page : 422 pages
File Size : 45,6 Mb
Release : 2010
Category : Mathematics
ISBN : 8121922437
A Textbook of Vector Analysis
Author : Harry Moritz Schey
Publisher : W W Norton & Company Incorporated
Page : 163 pages
File Size : 52,6 Mb
Release : 2005
Category : Mathematics
ISBN : 0393925161
This new fourth edition of the acclaimed and bestselling Div, Grad, Curl, and All That has been carefully revised and now includes updated notations and seven new example exercises.
Author : Bernard Kolman,William F. Trench
Publisher : Unknown
Page : 518 pages
File Size : 55,8 Mb
Release : 1971
Category : Mathematics
ISBN : MINN:31951P008383801
Author : Theodore Shifrin
Publisher : John Wiley & Sons
Page : 514 pages
File Size : 46,7 Mb
Release : 2004-01-26
Category : Mathematics
ISBN : 9780471526384
Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. * Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. * Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. * Exercises are arranged in order of increasing difficulty.
Author : P. R. Baxandall,Hans Liebeck
Publisher : Unknown
Page : 0 pages
File Size : 54,6 Mb
Release : 2008
Category : Calculus
ISBN : 0486466205
This introductory text offers a rigorous, comprehensive treatment. Classical theorems of vector calculus are amply illustrated with figures, worked examples, physical applications, and exercises with hints and answers. 1986 edition.
Author : Don Shimamoto
Publisher : Unknown
Page : 322 pages
File Size : 49,8 Mb
Release : 2019-11-17
Category : Calculus
ISBN : 1708246991
This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking, the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and, finally, the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise, the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required. Latest corrected printing: January 8, 2020. Updated information available online at the Open Textbook Library.
Author : Antonio Galbis,Manuel Maestre
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 43,8 Mb
Release : 2012-03-29
Category : Mathematics
ISBN : 9781461422006
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 : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 47,5 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
Author : Jay S. Treiman
Publisher : Springer
Page : 399 pages
File Size : 53,7 Mb
Release : 2014-10-30
Category : Mathematics
ISBN : 9783319094380
Calculus with Vectors grew out of a strong need for a beginning calculus textbook for undergraduates who intend to pursue careers in STEM fields. The approach introduces vector-valued functions from the start, emphasizing the connections between one-variable and multi-variable calculus. The text includes early vectors and early transcendentals and includes a rigorous but informal approach to vectors. Examples and focused applications are well presented along with an abundance of motivating exercises. The approaches taken to topics such as the derivation of the derivatives of sine and cosine, the approach to limits and the use of "tables" of integration have been modified from the standards seen in other textbooks in order to maximize the ease with which students may comprehend the material. Additionally, the material presented is intentionally non-specific to any software or hardware platform in order to accommodate the wide variety and rapid evolution of tools used. Technology is referenced in the text and is required for a good number of problems.