Advanced Calculus
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Advanced Calculus Revised Edition
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Author : Lynn Harold Loomis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-26
Advanced Calculus Revised Edition written by Lynn Harold Loomis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-26 with Mathematics categories.
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.
Advanced Calculus
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Author : David V. Widder
language : en
Publisher: Courier Corporation
Release Date : 2012-05-23
Advanced Calculus written by David V. Widder and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-23 with Mathematics categories.
Classic text offers exceptionally precise coverage of partial differentiation, vectors, differential geometry, Stieltjes integral, infinite series, gamma function, Fourier series, Laplace transform, much more. Includes exercises and selected answers.
100 1 Problems In Advanced Calculus
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Author : Paolo Toni
language : en
Publisher: Springer Nature
Release Date : 2022-03-08
100 1 Problems In Advanced Calculus written by Paolo Toni and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-08 with Mathematics categories.
This book convenes a collection of carefully selected problems in mathematical analysis, crafted to achieve maximum synergy between analytic geometry and algebra and favoring mathematical creativity in contrast to mere repetitive techniques. With eight chapters, this work guides the student through the basic principles of the subject, with a level of complexity that requires good use of imagination. In this work, all the fundamental concepts seen in a first-year Calculus course are covered. Problems touch on topics like inequalities, elementary point-set topology, limits of real-valued functions, differentiation, classical theorems of differential calculus (Rolle, Lagrange, Cauchy, and l’Hospital), graphs of functions, and Riemann integrals and antiderivatives. Every chapter starts with a theoretical background, in which relevant definitions and theorems are provided; then, related problems are presented. Formalism is kept at a minimum, and solutions can be found at the end of each chapter. Instructors and students of Mathematical Analysis, Calculus and Advanced Calculus aimed at first-year undergraduates in Mathematics, Physics and Engineering courses can greatly benefit from this book, which can also serve as a rich supplement to any traditional textbook on these subjects as well.
Advanced Calculus Of Several Variables
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Author : Charles Henry Edwards
language : en
Publisher: Courier Corporation
Release Date : 1994-01-01
Advanced Calculus Of Several Variables written by Charles Henry Edwards and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-01-01 with Mathematics categories.
Modern conceptual treatment of multivariable calculus, emphasizing the interplay of geometry and analysis via linear algebra and the approximation of nonlinear mappings by linear ones. At the same time, ample attention is paid to the classical applications and computational methods. Hundreds of examples, problems and figures. 1973 edition.
Advanced Calculus Of A Single Variable
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Author : Tunc Geveci
language : en
Publisher: Springer
Release Date : 2016-03-30
Advanced Calculus Of A Single Variable written by Tunc Geveci and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-30 with Mathematics categories.
This advanced undergraduate textbook is based on a one-semester course on single variable calculus that the author has been teaching at San Diego State University for many years. The aim of this classroom-tested book is to deliver a rigorous discussion of the concepts and theorems that are dealt with informally in the first two semesters of a beginning calculus course. As such, students are expected to gain a deeper understanding of the fundamental concepts of calculus, such as limits (with an emphasis on ε-δ definitions), continuity (including an appreciation of the difference between mere pointwise and uniform continuity), the derivative (with rigorous proofs of various versions of L’Hôpital’s rule) and the Riemann integral (discussing improper integrals in-depth, including the comparison and Dirichlet tests). Success in this course is expected to prepare students for more advanced courses in real and complex analysis and this book will help to accomplish this. The first semester of advanced calculus can be followed by a rigorous course in multivariable calculus and an introductory real analysis course that treats the Lebesgue integral and metric spaces, with special emphasis on Banach and Hilbert spaces.
Advanced Calculus
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Author : Harold M. Edwards
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-10
Advanced Calculus written by Harold M. Edwards and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-10 with Mathematics categories.
In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is genuine mathematics, both in spirit and content, and an exciting choice for an honors or graduate course or indeed for any mathematician in need of a refreshingly informal and flexible reintroduction to the subject. For all these potential readers, the author has made the approach work in the best tradition of creative mathematics. This affordable softcover reprint of the 1994 edition presents the diverse set of topics from which advanced calculus courses are created in beautiful unifying generalization. The author emphasizes the use of differential forms in linear algebra, implicit differentiation in higher dimensions using the calculus of differential forms, and the method of Lagrange multipliers in a general but easy-to-use formulation. There are copious exercises to help guide the reader in testing understanding. The chapters can be read in almost any order, including beginning with the final chapter that contains some of the more traditional topics of advanced calculus courses. In addition, it is ideal for a course on vector analysis from the differential forms point of view. The professional mathematician will find here a delightful example of mathematical literature; the student fortunate enough to have gone through this book will have a firm grasp of the nature of modern mathematics and a solid framework to continue to more advanced studies. The most important feature...is that it is fun—it is fun to read the exercises, it is fun to read the comments printed in the margins, it is fun simply to pick a random spot in the book and begin reading. This is the way mathematics should be presented, with an excitement and liveliness that show why we are interested in the subject. —The American Mathematical Monthly (First Review) An inviting, unusual, high-level introduction to vector calculus, based solidly on differential forms. Superb exposition: informal but sophisticated, down-to-earth but general, geometrically rigorous, entertaining but serious. Remarkable diverse applications, physical and mathematical. —The American Mathematical Monthly (1994) Based on the Second Edition
Advanced Calculus
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Author : H. K. Nickerson
language : en
Publisher: Courier Corporation
Release Date : 2011-08-18
Advanced Calculus written by H. K. Nickerson and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-18 with Mathematics categories.
"Classroom-tested in a Princeton University honors course, this text offers a unified introduction to advanced calculus. Starting with an abstract treatment of vector spaces and linear transforms, the authors present a corresponding theory of integration, concluding with a series of applications to analytic functions of complex variables. 1959 edition"--
Advanced Calculus Partial Differential Equations
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Author : B.R. THAKUR
language : en
Publisher: Ram Prasad Publications(R.P.H.)
Release Date :
Advanced Calculus Partial Differential Equations written by B.R. THAKUR and has been published by Ram Prasad Publications(R.P.H.) this book supported file pdf, txt, epub, kindle and other format this book has been release on with Juvenile Fiction categories.
–Unit-I– 1.1 Historical background : 1.1.1 A brief historical background of Calculus and partial differential equations in the context of India and Indian heritage and culture 1.1.2 Abrief biography of Bodhayana 1.2 Field structure and ordered structure of R, Intervals, Bounded and Unbounded sets, Supremum and Infimum, Completeness in R, Absolute value of a real number. 1.3 Sequence of real numbers 1.4 Limit of a sequence 1.5 Bounded and Monotonic sequences 1.6 Cauchy’s general principle of convergence 1.7 Algebra of sequence and some important theorems –Unit-II– 2.1 Series of non-negative terms 2.2 Convergence of positive term series 2.3 Alternating series and Leibnitz’s test 2.4 Absolute and Conditional Convergence of Series of real terms 2.5 Uniform continuity 2.6 Chain rule of differentiability 2.7 Mean value theorems and their geometrical interpretations –Unit-III– 3.1 Limit and Continuity of functions of two variables 3.2 Change of variables 3.3 Euler’s theorem on homogeneous functions 3.4 Taylor’s theorem for function of two variables 3.5 Jacobians 3.6 Maxima and Minima of functions of two variables 3.7 Lagrange’s multiplier method 3.8 Beta and Gamma Functions –Unit-IV– 4.1 Partial differential equations of the first order 4.2 Lagrange’s solution 4.3 Some special types of equations which can be solved easily by methods other than the general method 4.4 Charpit’s general method 4.5 Partial differential equations of second and higher orders –Unit-V– 5.1 Classification of partial differential equations of second order 5.2 Homogeneous and non-homogeneous partial differential equations of constant coefficients 5.3 Partial differential equations reducible to equations with constant coefficients
Advanced Calculus
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Author : Wilfred Kaplan
language : en
Publisher: Addison Wesley Publishing Company
Release Date : 1984
Advanced Calculus written by Wilfred Kaplan and has been published by Addison Wesley Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
The Fifth Edition of this leading text offers substantial training in vectors and matrices, vector analysis, and partial differential equations. Vectors are introduced at the outset and serve at many points to indicate geometrical and physical significance of mathematical relations. Numerical methods are touched upon at various points, because of their practical value and the insights they give about theory. Vectors and Matrices; Differential Calculus of Functions of Several Variables; Vector Differential Calculus; Integral Calculus of Functions of Several Variables; Vector Integral Calculus; Two-Dimensional Theory; Three-Dimensional Theory and Applications; Infinite Series; Fourier Series and Orthogonal Functions; Functions of a Complex Variable; Ordinary Differential Equations; Partial Differential Equations For all readers interested in advanced calculus.
Advanced Calculus
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Author : James J. Callahan
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-09
Advanced Calculus written by James J. Callahan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-09 with Mathematics categories.
With a fresh geometric approach that incorporates more than 250 illustrations, this textbook sets itself apart from all others in advanced calculus. Besides the classical capstones--the change of variables formula, implicit and inverse function theorems, the integral theorems of Gauss and Stokes--the text treats other important topics in differential analysis, such as Morse's lemma and the Poincaré lemma. The ideas behind most topics can be understood with just two or three variables. The book incorporates modern computational tools to give visualization real power. Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books. This is a textbook for undergraduates and graduate students in mathematics, the physical sciences, and economics. Prerequisites are an introduction to linear algebra and multivariable calculus. There is enough material for a year-long course on advanced calculus and for a variety of semester courses--including topics in geometry. The measured pace of the book, with its extensive examples and illustrations, make it especially suitable for independent study.