Calculus In 3d Geometry Vectors And Multivariate Calculus

Author : Zbigniew Nitecki
Publisher : American Mathematical Soc.
Page : 405 pages
File Size : 55,6 Mb
Release : 2018-10-16
Category : Calculus
ISBN : 9781470443603

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Calculus in 3D: Geometry, Vectors, and Multivariate Calculus by Zbigniew Nitecki Pdf

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 : Joseph D. Fehribach
Publisher : Walter de Gruyter GmbH & Co KG
Page : 257 pages
File Size : 51,8 Mb
Release : 2024-07-22
Category : Mathematics
ISBN : 9783111394282

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Multivariable and Vector Calculus by Joseph D. Fehribach Pdf

This book covers multivariable and vector calculus. It can be used as a textbook for a one-semester course or self-study. It includes worked-through exercises, with answers provided for many of the basic computational ones and hints for the more complex ones.. This second edition features new exercises, new sections on twist and binormal vectors for curves in space, linear approximations, and the Laplace and Poisson equations.

Author : Kevin R. Coombes,Ronald L. Lipsman,Jonathan M. Rosenberg
Publisher : Springer Science & Business Media
Page : 282 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461216988

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Multivariable Calculus and Mathematica® by Kevin R. Coombes,Ronald L. Lipsman,Jonathan M. Rosenberg Pdf

Aiming to "modernise" the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook. The accompanying diskette contains both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students, which can be used with any standard multivariable calculus textbook. It is assumed that students will also have access to an introductory primer for Mathematica.

Author : Seán Dineen
Publisher : Unknown
Page : 254 pages
File Size : 55,6 Mb
Release : 2001
Category : Calculus
ISBN : 3540761764

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Multivariate Calculus and Geometry by Seán Dineen Pdf

Author : David A. Santos,Sarhan M. Musa
Publisher : Mercury Learning and Information
Page : 450 pages
File Size : 44,5 Mb
Release : 2015-07-30
Category : Mathematics
ISBN : 9781942270256

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Multivariable and Vector Calculus by David A. Santos,Sarhan M. Musa Pdf

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. It also provides numerous computer illustrations and tutorials using MATLAB® and Maple®, that bridge the gap between analysis and computation. 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 : Terrance J Quinn,Zine Boudhraa,Sanjay Rai
Publisher : World Scientific
Page : 250 pages
File Size : 40,8 Mb
Release : 2020-07-24
Category : Mathematics
ISBN : 9789811222580

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Basic Insights In Vector Calculus: With A Supplement On Mathematical Understanding by Terrance J Quinn,Zine Boudhraa,Sanjay Rai Pdf

Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.

Author : Gerald L. Bradley,Karl J. Smith
Publisher : Unknown
Page : 510 pages
File Size : 49,5 Mb
Release : 1999
Category : Mathematics
ISBN : 0138639450

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Multivariable Calculus by Gerald L. Bradley,Karl J. Smith Pdf

This book blends much of the best aspects of calculus reform with the reasonable goals and methodology of traditional calculus. Readers benefit from an innovative pedagogy and a superb range of problems. Modeling is a major theme -- qualitative and quantitative problems demonstrate an extremely wide variety of mathematical, engineering, scientific, and social models. This book emphasizes writing in addition to algebra. This book thoroughly addresses topics such as Infinite Series, Polar Coordinates and Parametric Forms, Vectors in the Plane and in Space, Vector-Valued Functions, Partial Differentiation, Multiple Integration, Introduction to Vector Analysis, and Introduction to Differential Equations. Suitable for professionals in engineering, science, and math.

Author : Lynn Harold Loomis,Shlomo Sternberg
Publisher : World Scientific Publishing Company
Page : 596 pages
File Size : 52,7 Mb
Release : 2014-02-26
Category : Mathematics
ISBN : 9789814583954

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Advanced Calculus by Lynn Harold Loomis,Shlomo Sternberg Pdf

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 : F. Beatrous,Caspar R. Curjel
Publisher : Unknown
Page : 484 pages
File Size : 45,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0130304379

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Multivariable Calculus by F. Beatrous,Caspar R. Curjel Pdf

For a one-semester sophomore-level course in multivariable calculus, for Engineering, Mathematics, or Science students. Reform ideas, traditional ideas, and original ideas are combined in this text that is designed to teach concepts and computations, especially intuitive ones about the geometry of 3 space. The core concepts of multivariable calculus are presented in a straightforward, but never simplistic language that will familiarize students with the thinking and speaking habits of mathematicians and ease their access to the mathematics of applications and higher mathematics courses. *Students are engaged through formulas and geometric reasoning-In addition to calculating accurately, students are asked to draw accurately in both two and three dimensions, reason geometrically from figures, make estimates based on ruler-and pencil-constructions, and present their results verbally. *Helps students learn conceptual reasoning and reinforces learning by asking students to work the material in two different modes. *This is a spiral bound text. *Lays flat so students can draw in blank diagrams while reading the text. *A multitude of exercises are interwoven within the flow of the text-T

Author : William F. Trench,Bernard Kolman
Publisher : Unknown
Page : 784 pages
File Size : 42,9 Mb
Release : 1972
Category : Mathematics
ISBN : STANFORD:36105031205839

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Multivariable Calculus with Linear Algebra and Series by William F. Trench,Bernard Kolman Pdf

Author : Alice Gorguis
Publisher : Xlibris Corporation
Page : 121 pages
File Size : 49,9 Mb
Release : 2013-07-31
Category : Mathematics
ISBN : 9781483672588

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Vector Calculus by Alice Gorguis Pdf

This text is intended for a one-semester course in the Calculus of functions of several variables and vector analysis taught at college level. This course is, normally known as , vector calculus, or multi variable calculus, or simply calculus-III. The course usually is preceded by a beginning course in linear algebra. The prerequisite for this course is the knowledge of the fundamen- tal of one-variable calculus, differentiation and integration of the standard functions. The text includes most of the basic theories as well as many related examples and problems. There are many exercises throughout the text, which in my experience are more than enough for a semester course in this subject. I include enough examples for each topics in each section to illustrate and help the student to practice his/her skills. Also, added problems that ask the student to reflect on and explore in his/her own words some of the important ideas of Vector Calculus. I have included material enough to be covered during a simple semester with- out a hassle, and it should be possible to work through the entire book with reasonable care. Most of the exercises are relatively routine computations to moderate and productive problems, to help the students understand the concept of each topic. Each section in a chapter is concluded with a set of exercises that review and extend the ideas that was introduced in the chapter, or section. Computer softwares were not included in this book. Most of the exercises can be solved easily by hand, but I advise the students to use Mathematica, or Maple to graph the functions in each problem to visualize the problem, and understand it better. Some of the homework might require the use of Mathematica.

Author : Sean Dineen
Publisher : Springer
Page : 0 pages
File Size : 48,7 Mb
Release : 2001
Category : Mathematics
ISBN : 1447103033

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Multivariate Calculus and Geometry by Sean Dineen Pdf

This book provides the higher-level reader with a comprehensive review of all important aspects of Differential Calculus, Integral Calculus and Geometric Calculus of several variables The revised edition, which includes additional exercises and expanded solutions, and gives a solid description of the basic concepts via simple familiar examples which are then tested in technically demanding situations. Readers will gain a deep understanding of the uses and limitations of multivariate calculus.

Author : Dineen Sean
Publisher : Unknown
Page : 254 pages
File Size : 55,7 Mb
Release : 2004-01-01
Category : Electronic
ISBN : 8181282388

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Multivariate Calculus And Geometry, 2E by Dineen Sean Pdf

Author : Jerrold Marsden,Alan Weinstein
Publisher : Springer Science & Business Media
Page : 359 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461250289

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Calculus III by Jerrold Marsden,Alan Weinstein Pdf

The third of a three-volume work, this book is the outgrowth of the authors' experience teaching calculus at Berkeley. It covers multivariable calculus and begins with the necessary material from analytical geometry. It goes on to cover partial differention, the gradient and its applications, multiple integration, and the theorems of Green, Gauss and Stokes. The authors motivate the study of calculus using its applications. Features many solved problems and extensive exercises.

Author : Antonio Galbis,Manuel Maestre
Publisher : Springer Science & Business Media
Page : 375 pages
File Size : 44,5 Mb
Release : 2012-03-29
Category : Mathematics
ISBN : 9781461422006

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Vector Analysis Versus Vector Calculus by Antonio Galbis,Manuel Maestre Pdf

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.