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| Author | : Richard Courant |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 585 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642571492 |
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991
| Author | : Courant Institute of Mathematical Sciences Richard Courant |
| Publisher | : |
| Total Pages | : 688 |
| Release | : 1998-12-03 |
| Genre | : |
| ISBN | : 9783642586057 |
From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficu
| 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 | : Michael E. Taylor |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 462 |
| Release | : 2020-07-27 |
| Genre | : Education |
| ISBN | : 1470456699 |
This text was produced for the second part of a two-part sequence on advanced calculus, whose aim is to provide a firm logical foundation for analysis. The first part treats analysis in one variable, and the text at hand treats analysis in several variables. After a review of topics from one-variable analysis and linear algebra, the text treats in succession multivariable differential calculus, including systems of differential equations, and multivariable integral calculus. It builds on this to develop calculus on surfaces in Euclidean space and also on manifolds. It introduces differential forms and establishes a general Stokes formula. It describes various applications of Stokes formula, from harmonic functions to degree theory. The text then studies the differential geometry of surfaces, including geodesics and curvature, and makes contact with degree theory, via the Gauss–Bonnet theorem. The text also takes up Fourier analysis, and bridges this with results on surfaces, via Fourier analysis on spheres and on compact matrix groups.
| Author | : Omar Hijab |
| Publisher | : Springer |
| Total Pages | : 364 |
| Release | : 2013-04-19 |
| Genre | : Mathematics |
| ISBN | : 9781461428428 |
This text is intended for an honors calculus course or for an introduction to analysis. Involving rigorous analysis, computational dexterity, and a breadth of applications, it is ideal for undergraduate majors. This third edition includes corrections as well as some additional material. Some features of the text include: The text is completely self-contained and starts with the real number axioms; The integral is defined as the area under the graph, while the area is defined for every subset of the plane; There is a heavy emphasis on computational problems, from the high-school quadratic formula to the formula for the derivative of the zeta function at zero; There are applications from many parts of analysis, e.g., convexity, the Cantor set, continued fractions, the AGM, the theta and zeta functions, transcendental numbers, the Bessel and gamma functions, and many more; Traditionally transcendentally presented material, such as infinite products, the Bernoulli series, and the zeta functional equation, is developed over the reals; and There are 385 problems with all the solutions at the back of the text.
| Author | : Richard Courant |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 594 |
| Release | : 1999-12-14 |
| Genre | : Mathematics |
| ISBN | : 9783540665694 |
From the reviews: "...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991
| Author | : Terence Tao |
| Publisher | : Springer |
| Total Pages | : 366 |
| Release | : 2016-08-29 |
| Genre | : Mathematics |
| ISBN | : 9811017891 |
This is part one of a two-volume book on real analysis and is intended for senior undergraduate students of mathematics who have already been exposed to calculus. The emphasis is on rigour and foundations of analysis. Beginning with the construction of the number systems and set theory, the book discusses the basics of analysis (limits, series, continuity, differentiation, Riemann integration), through to power series, several variable calculus and Fourier analysis, and then finally the Lebesgue integral. These are almost entirely set in the concrete setting of the real line and Euclidean spaces, although there is some material on abstract metric and topological spaces. The book also has appendices on mathematical logic and the decimal system. The entire text (omitting some less central topics) can be taught in two quarters of 25–30 lectures each. The course material is deeply intertwined with the exercises, as it is intended that the student actively learn the material (and practice thinking and writing rigorously) by proving several of the key results in the theory.
| 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.
| Author | : Horst R. Beyer |
| Publisher | : John Wiley & Sons |
| Total Pages | : 695 |
| Release | : 2010-04-26 |
| Genre | : Mathematics |
| ISBN | : 0470617950 |
A NEW APPROACH TO CALCULUS THAT BETTER ENABLES STUDENTS TO PROGRESS TO MORE ADVANCED COURSES AND APPLICATIONS Calculus and Analysis: A Combined Approach bridges the gap between mathematical thinking skills and advanced calculus topics by providing an introduction to the key theory for understanding and working with applications in engineering and the sciences. Through a modern approach that utilizes fully calculated problems, the book addresses the importance of calculus and analysis in the applied sciences, with a focus on differential equations. Differing from the common classical approach to the topic, this book presents a modern perspective on calculus that follows motivations from Otto Toeplitz's famous genetic model. The result is an introduction that leads to great simplifications and provides a focused treatment commonly found in the applied sciences, particularly differential equations. The author begins with a short introduction to elementary mathematical logic. Next, the book explores the concept of sets and maps, providing readers with a strong foundation for understanding and solving modern mathematical problems. Ensuring a complete presentation, topics are uniformly presented in chapters that consist of three parts: Introductory Motivations presents historical mathematical problems or problems arising from applications that led to the development of mathematical solutions Theory provides rigorous development of the essential parts of the machinery of analysis; proofs are intentionally detailed, but simplified as much as possible to aid reader comprehension Examples and Problems promotes problem-solving skills through application-based exercises that emphasize theoretical mechanics, general relativity, and quantum mechanics Calculus and Analysis: A Combined Approach is an excellent book for courses on calculus and mathematical analysis at the upper-undergraduate and graduate levels. It is also a valuable resource for engineers, physicists, mathematicians, and anyone working in the applied sciences who would like to master their understanding of basic tools in modern calculus and analysis.
| Author | : Arthur Mattuck |
| Publisher | : Pearson |
| Total Pages | : 0 |
| Release | : 1999 |
| Genre | : Mathematical analysis |
| ISBN | : 9780130811325 |
KEY BENEFIT:This new book is written in a conversational, accessible style, offering a great deal of examples. It gradually ascends in difficulty to help the student avoid sudden changes in difficulty.Discusses analysis from the start of the book, to avoid unnecessary discussion on real numbers beyond what is immediately needed. Includes simplified and meaningful proofs. Features Exercises and Problemsat the end of each chapter as well as Questionsat the end of each section with answers at the end of each chapter. Presents analysis in a unified way as the mathematics based on inequalities, estimations, and approximations.For mathematicians.
