Introduction To Calculus And Analysis PDF Download
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| Author | : Richard Courant |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 585 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642571492 |
Download Introduction to Calculus and Analysis II/1 Book in PDF, ePub and Kindle
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 |
Download Introduction to Calculus and Analysis Book in PDF, ePub and Kindle
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 | : Horst R. Beyer |
| Publisher | : John Wiley & Sons |
| Total Pages | : 695 |
| Release | : 2010-04-26 |
| Genre | : Mathematics |
| ISBN | : 0470617950 |
Download Calculus and Analysis Book in PDF, ePub and Kindle
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 | : Omar Hijab |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 370 |
| Release | : 2011-03-19 |
| Genre | : Mathematics |
| ISBN | : 1441994882 |
Download Introduction to Calculus and Classical Analysis Book in PDF, ePub and Kindle
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 | : Steen Pedersen |
| Publisher | : Springer |
| Total Pages | : 345 |
| Release | : 2015-03-21 |
| Genre | : Mathematics |
| ISBN | : 3319136410 |
Download From Calculus to Analysis Book in PDF, ePub and Kindle
This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers. In addition to the standard results of advanced calculus, the book contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section.
| Author | : Kenneth A. Ross |
| Publisher | : CUP Archive |
| Total Pages | : 192 |
| Release | : 2014-01-15 |
| Genre | : Mathematics |
| ISBN | : |
Download Elementary Analysis Book in PDF, ePub and Kindle
| Author | : Louis Brand |
| Publisher | : |
| Total Pages | : 606 |
| Release | : 1955 |
| Genre | : Calculus |
| ISBN | : |
Download Advanced Calculus Book in PDF, ePub and Kindle
| Author | : Pavel Grinfeld |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 303 |
| Release | : 2013-09-24 |
| Genre | : Mathematics |
| ISBN | : 1461478677 |
Download Introduction to Tensor Analysis and the Calculus of Moving Surfaces Book in PDF, ePub and Kindle
This textbook is distinguished from other texts on the subject by the depth of the presentation and the discussion of the calculus of moving surfaces, which is an extension of tensor calculus to deforming manifolds. Designed for advanced undergraduate and graduate students, this text invites its audience to take a fresh look at previously learned material through the prism of tensor calculus. Once the framework is mastered, the student is introduced to new material which includes differential geometry on manifolds, shape optimization, boundary perturbation and dynamic fluid film equations. The language of tensors, originally championed by Einstein, is as fundamental as the languages of calculus and linear algebra and is one that every technical scientist ought to speak. The tensor technique, invented at the turn of the 20th century, is now considered classical. Yet, as the author shows, it remains remarkably vital and relevant. The author’s skilled lecturing capabilities are evident by the inclusion of insightful examples and a plethora of exercises. A great deal of material is devoted to the geometric fundamentals, the mechanics of change of variables, the proper use of the tensor notation and the discussion of the interplay between algebra and geometry. The early chapters have many words and few equations. The definition of a tensor comes only in Chapter 6 – when the reader is ready for it. While this text maintains a consistent level of rigor, it takes great care to avoid formalizing the subject. The last part of the textbook is devoted to the Calculus of Moving Surfaces. It is the first textbook exposition of this important technique and is one of the gems of this text. A number of exciting applications of the calculus are presented including shape optimization, boundary perturbation of boundary value problems and dynamic fluid film equations developed by the author in recent years. Furthermore, the moving surfaces framework is used to offer new derivations of classical results such as the geodesic equation and the celebrated Gauss-Bonnet theorem.
| Author | : Jerry Shurman |
| Publisher | : Springer |
| Total Pages | : 505 |
| Release | : 2016-11-26 |
| Genre | : Mathematics |
| ISBN | : 3319493140 |
Download Calculus and Analysis in Euclidean Space Book in PDF, ePub and Kindle
The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs.
| Author | : Arthur Mattuck |
| Publisher | : Pearson |
| Total Pages | : 0 |
| Release | : 1999 |
| Genre | : Mathematical analysis |
| ISBN | : 9780130811325 |
Download Introduction to Analysis Book in PDF, ePub and Kindle
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.
