Modern Multidimensional Calculus
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| Author | : Marshall Evans Munroe |
| Publisher | : Courier Dover Publications |
| Total Pages | : 401 |
| Release | : 2019-05-15 |
| Genre | : Mathematics |
| ISBN | : 0486840069 |
A second-year calculus text, this volume is devoted primarily to topics in multidimensional analysis. Concepts and methods are emphasized, and rigorous proofs are sometimes replaced by relevant discussion and explanation. Because of the author's conviction that the differential provides a most elegant and useful tool, especially in a multidimensional setting, the notion of the differential is used extensively and matrix methods are stressed in the study of linear transformations. The first three chapters offer introductory material on functions and variables, differentials, and vectors in the plane. Succeeding chapters examine topics in linear algebra, partial derivatives, and applications as well as topics in vector differential calculus. The final chapters explore multiple integrals in addition to line and surface integrals. Exercises appear throughout the text, and answers are provided, making the book ideal for self-study.
| Author | : Kevin R. Coombes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 282 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461216982 |
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 | : Lynn Harold Loomis |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 595 |
| Release | : 2014-02-26 |
| Genre | : Mathematics |
| ISBN | : 9814583952 |
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 | : C. H. Edwards |
| Publisher | : Academic Press |
| Total Pages | : 470 |
| Release | : 2014-05-10 |
| Genre | : Mathematics |
| ISBN | : 1483268055 |
Advanced Calculus of Several Variables provides a conceptual treatment of multivariable calculus. This book emphasizes the interplay of geometry, analysis through linear algebra, and approximation of nonlinear mappings by linear ones. The classical applications and computational methods that are responsible for much of the interest and importance of calculus are also considered. This text is organized into six chapters. Chapter I deals with linear algebra and geometry of Euclidean n-space Rn. The multivariable differential calculus is treated in Chapters II and III, while multivariable integral calculus is covered in Chapters IV and V. The last chapter is devoted to venerable problems of the calculus of variations. This publication is intended for students who have completed a standard introductory calculus sequence.
| Author | : Alan J. Izenman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 757 |
| Release | : 2009-03-02 |
| Genre | : Mathematics |
| ISBN | : 0387781897 |
This is the first book on multivariate analysis to look at large data sets which describes the state of the art in analyzing such data. Material such as database management systems is included that has never appeared in statistics books before.
| Author | : Don Shimamoto |
| Publisher | : |
| Total Pages | : 322 |
| Release | : 2019-11-17 |
| Genre | : Calculus |
| ISBN | : 9781708246990 |
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 | : Peter D. Lax |
| Publisher | : Springer |
| Total Pages | : 488 |
| Release | : 2018-03-12 |
| Genre | : Mathematics |
| ISBN | : 3319740733 |
This text in multivariable calculus fosters comprehension through meaningful explanations. Written with students in mathematics, the physical sciences, and engineering in mind, it extends concepts from single variable calculus such as derivative, integral, and important theorems to partial derivatives, multiple integrals, Stokes’ and divergence theorems. Students with a background in single variable calculus are guided through a variety of problem solving techniques and practice problems. Examples from the physical sciences are utilized to highlight the essential relationship between calculus and modern science. The symbiotic relationship between science and mathematics is shown by deriving and discussing several conservation laws, and vector calculus is utilized to describe a number of physical theories via partial differential equations. Students will learn that mathematics is the language that enables scientific ideas to be precisely formulated and that science is a source for the development of mathematics.
| Author | : Ronald L. Lipsman |
| Publisher | : Springer |
| Total Pages | : 280 |
| Release | : 2017-12-06 |
| Genre | : Mathematics |
| ISBN | : 331965070X |
This comprehensive treatment of multivariable calculus focuses on the numerous tools that MATLAB® brings to the subject, as it presents introductions to geometry, mathematical physics, and kinematics. Covering simple calculations with MATLAB®, relevant plots, integration, and optimization, the numerous problem sets encourage practice with newly learned skills that cultivate the reader’s understanding of the material. Significant examples illustrate each topic, and fundamental physical applications such as Kepler’s Law, electromagnetism, fluid flow, and energy estimation are brought to prominent position. Perfect for use as a supplement to any standard multivariable calculus text, a “mathematical methods in physics or engineering” class, for independent study, or even as the class text in an “honors” multivariable calculus course, this textbook will appeal to mathematics, engineering, and physical science students. MATLAB® is tightly integrated into every portion of this book, and its graphical capabilities are used to present vibrant pictures of curves and surfaces. Readers benefit from the deep connections made between mathematics and science while learning more about the intrinsic geometry of curves and surfaces. With serious yet elementary explanation of various numerical algorithms, this textbook enlivens the teaching of multivariable calculus and mathematical methods courses for scientists and engineers.
| Author | : Сергей Петрович Новиков |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 658 |
| Release | : 2006 |
| Genre | : Mathematics |
| ISBN | : 0821839292 |
Presents the basics of Riemannian geometry in its modern form as geometry of differentiable manifolds and the important structures on them. This book shows that Riemannian geometry has a great influence to several fundamental areas of modern mathematics and its applications.
| Author | : Michael Spivak |
| Publisher | : Westview Press |
| Total Pages | : 164 |
| Release | : 1965 |
| Genre | : Science |
| ISBN | : 9780805390216 |
This book uses elementary versions of modern methods found in sophisticated mathematics to discuss portions of "advanced calculus" in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level.
