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Author: Steven G. Krantz Publisher: MAA ISBN: 9780883853443 Category : Mathematics Languages : en Pages : 176
Book Description
A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland's A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis. Together these books provide a concise guide to the subject at all levels, ideal for student preparation for exams.
Author: Steven G. Krantz Publisher: MAA ISBN: 9780883853443 Category : Mathematics Languages : en Pages : 176
Book Description
A Guide to Real Variables is an aid and conceptual support for students taking an undergraduate course on real analysis. It focuses on concepts, results, examples and illustrative figures, rather than the details of proofs, in order to remain a concise guide which students can dip into. The core topics of a first real analysis course are covered, including sequences, series, modes of convergence, the derivative, the integral and metric spaces. The next book in this series, Folland's A Guide to Advanced Real Analysis is designed to naturally follow on from this book, and introduce students to graduate level real analysis. Together these books provide a concise guide to the subject at all levels, ideal for student preparation for exams.
Author: Martin Moskowitz Publisher: World Scientific Publishing Company ISBN: 9813100915 Category : Mathematics Languages : en Pages : 732
Book Description
This book begins with the basics of the geometry and topology of Euclidean space and continues with the main topics in the theory of functions of several real variables including limits, continuity, differentiation and integration. All topics and in particular, differentiation and integration, are treated in depth and with mathematical rigor. The classical theorems of differentiation and integration such as the Inverse and Implicit Function theorems, Lagrange's multiplier rule, Fubini's theorem, the change of variables formula, Green's, Stokes' and Gauss' theorems are proved in detail and many of them with novel proofs. The authors develop the theory in a logical sequence building one result upon the other, enriching the development with numerous explanatory remarks and historical footnotes. A number of well chosen illustrative examples and counter-examples clarify matters and teach the reader how to apply these results and solve problems in mathematics, the other sciences and economics.Each of the chapters concludes with groups of exercises and problems, many of them with detailed solutions while others with hints or final answers. More advanced topics, such as Morse's lemma, Sard's theorem , the Weierstrass approximation theorem, the Fourier transform, Vector fields on spheres, Brouwer's fixed point theorem, Whitney's embedding theorem, Picard's theorem, and Hermite polynomials are discussed in stared sections.
Author: Steven G. Krantz Publisher: American Mathematical Soc. ISBN: 0883853388 Category : Education Languages : en Pages : 183
Book Description
This is a book about complex variables that gives the reader a quick and accessible introduction to the key topics. While the coverage is not comprehensive, it certainly gives the reader a solid grounding in this fundamental area. There are many figures and examples to illustrate the principal ideas, and the exposition is lively and inviting. An undergraduate wanting to have a first look at this subject or a graduate student preparing for the qualifying exams, will find this book to be a useful resource.
Author: Tefera Worku Publisher: Research & Education Assoc. ISBN: 9780878919215 Category : Mathematics Languages : en Pages : 78
Book Description
REA’s Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Real Variables includes set theory and topology of the real number system, metric spaces, measure theory, measurable function, the Lebesgue integral, LP-spaces, Banach spaces, linear operators, and Hilbert space.
Author: Jiri Lebl Publisher: Lulu.com ISBN: 1365095576 Category : Languages : en Pages : 142
Book Description
This book is a polished version of my course notes for Math 6283, Several Complex Variables, given in Spring 2014 and Spring 2016 semester at Oklahoma State University. The course covers basics of holomorphic function theory, CR geometry, the dbar problem, integral kernels and basic theory of complex analytic subvarieties. See http: //www.jirka.org/scv/ for more information.
Author: Karo Maestro Publisher: Independently Published ISBN: 9781795627979 Category : Mathematics Languages : en Pages : 678
Book Description
This wonderful textbook, written by one of the preeminent teachers and researchers of analysis of the mid-20th century, gives a deep and comprehensive presentation of undergraduate real analysis of one and several variables that is accessible to any student with a good working knowledge of calculus and some experience with proofs, such as can be provided by a non-applied first linear algebra course or discrete mathematics course. The book lies midway in difficulty between the very basic analysis texts i.e. "baby real variables" texts that present a first course in rigorous single variable calculus and hard-edged real variables courses set in abstract metric spaces like Rudin and Pugh. It is also very broad in coverage. The republication of this book for the first time in nearly 50 years will provide an excellent choice for either a course text or self-study in undergraduate analysis.Several aspects of the book's unusual organization and content make it very deserving of low cost republication. Firstly, while it covers just about all the usual topics in any undergraduate analysis text-number systems, functions, limits of functions and sequences of one and several variables in ℝn, continuity, differentiation and integration of functions in ℝ, bounded sequences, metric spaces, basic point set topology, infinite series, power series, convergence tests, improper integrals, partial and total derivatives and multiple integrals- it has a number of unique aspects to the presentation that distinguish it from other textbooks. For example, a number of important concepts of analysis are covered in the starred sections and exercises that are not usually covered in these courses, such as point set topology, Riemann-Steijles integration, vector analysis and differential forms. Another excellent innovation that an entire opening chapter giving a far more detailed axiomatic description of the number systems without explicitly constructing them. While most analysis texts have such an opening section, Olmstead's is longer and more detailed then the ones found in most books with many substantial exercises. Another positive quality of the book is its' unusual midway level of difficulty. Calculus courses today are far weaker than they were when the standard textbooks such as Walter Rudin's Principles of Mathematical Analysis were published. As a result, a number of students beginning analysis today need a bit more foundational training in rigorous calculus before tackling functions in Euclidean spaces and abstract metric spaces. So usually students have to begin with a "baby real variables" text before moving on to analysis on metric spaces. Olmsted does a fine job in his early chapters of presenting the properties of the real numbers and a precise presentation of calculus on the real line. This allows the first half of the text to act as a "baby real variables" book i.e. a bridge between today's calculus courses and hard-edged classical analysis courses on metric spaces. As a result, students will only need one inexpensive text rather than two. Lastly, Olmsted contains "pragmatic" sections that discuss classical, more computational aspects of analysis that would be of great interest to applied mathematics, physics and engineering students. It's clear that Olmsted's book is an extraordinarily versatile textbook for undergraduate analysis courses at all levels. It will make a strong addition to the undergraduate analysis textbook literature and will be immensely useful to students and teachers alike as either a low-priced main textbook or as a supplement.
Author: John P. D'Angelo Publisher: Routledge ISBN: 1351416715 Category : Mathematics Languages : en Pages : 319
Book Description
Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.
Author: Steven G. Krantz Publisher: Springer Science & Business Media ISBN: 1461215889 Category : Mathematics Languages : en Pages : 301
Book Description
This book is written to be a convenient reference for the working scientist, student, or engineer who needs to know and use basic concepts in complex analysis. It is not a book of mathematical theory. It is instead a book of mathematical practice. All the basic ideas of complex analysis, as well as many typical applica tions, are treated. Since we are not developing theory and proofs, we have not been obliged to conform to a strict logical ordering of topics. Instead, topics have been organized for ease of reference, so that cognate topics appear in one place. Required background for reading the text is minimal: a good ground ing in (real variable) calculus will suffice. However, the reader who gets maximum utility from the book will be that reader who has had a course in complex analysis at some time in his life. This book is a handy com pendium of all basic facts about complex variable theory. But it is not a textbook, and a person would be hard put to endeavor to learn the subject by reading this book.
Author: John D. Paliouras Publisher: Courier Corporation ISBN: 0486493474 Category : Mathematics Languages : en Pages : 612
Book Description
Outstanding undergraduate text provides a thorough understanding of fundamentals and creates the basis for higher-level courses. Numerous examples and extensive exercise sections of varying difficulty, plus answers to selected exercises. 1990 edition.
Author: Steven G. Krantz
Author: Steven G. Krantz
Author: Martin Moskowitz
Author: Steven G. Krantz
Author: Tefera Worku
Author: Jiri Lebl
Author: Karo Maestro
Author: John P. D'Angelo
Author: Steven G. Krantz
Author: G. B. Folland
Author: John D. Paliouras