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From the reviews: ´´Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)´´ - The Mathematical Gazette (75.1991.471).

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Richard Courant was born in 1888 in a small town of what is now Poland, and died in New Rochelle, N.Y. in 1972. He received his doctorate from the legendary David Hilbert in Göttingen, where later he founded and directed its famed mathematics Institute, a Mecca for mathematicians in the twenties. In 1933 the Nazi government dismissed Courant for being Jewish, and he emigrated to the United States. He found, in New York, what he called ´´a reservoir of talent´´ to be tapped. He built, at New York University, a new mathematical Sciences Institute that shares the philosophy of its illustrious predecessor and rivals it in worldwide influence. For Courant mathematics was an adventure, with applications forming a vital part. This spirit is reflected in his books, in particular in his influential calculus text, revised in collaboration with his brilliant younger colleague, Fritz John. (P.D. Lax) Fritz John was born on June 14, 1910, in Berlin. After his school years in Danzig (now Gdansk, Poland), he studied in Göttingen and received his doctorate in 1933, just when the Nazi regime came to power. As he was half-Jewish and his bride Aryan, he had to flee Germany in 1934. After a year in Cambridge, UK, he accepted a position at the University of Kentucky, and in 1946 joined Courant, Friedrichs and Stoker in building up New York University the institute that later became the Courant Institute of Mathematical Sciences. He remained there until his death in New Rochelle on February 10, 1994. John´s research and the books he wrote had a strong impact on the development of many fields of mathematics, foremost in partial differential equations. He also worked on Radon transforms, illposed problems, convex geometry, numerical analysis, elasticity theory. In connection with his work in latter field, he and Nirenberg introduced the space of the BMO-functions (bounded mean oscillations). From the reviews: ´´These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that.´´Newsletter on Computational and Applied Mathematics, 1991´´...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

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44,99 € *

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From the reviews: ´´These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easyto understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that.´´Newsletter on Computational and Applied Mathematics, 1991´´...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

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A compact introduction to this active and powerful area of research, combining basic theory, core techniques, and recent applications.

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This book presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the so-called L2 $\bar{\delta}$-method. Exercises are included throughout, which makes this text ideal for a one- or two-semester graduate course. This textbook presents a unified approach to compact and noncompact Riemann surfaces from the point of view of the L² -method, a powerful technique used in the theory of several complex variables. The work features a simple construction of a strictly subharmonic exhaustion function and a related construction of a positive-curvature Hermitian metric in a holomorphic line bundle, topics which serve as starting points for proofs of standard results such as the Mittag-Leffler, Weierstrass, and Runge theorems; the Riemann Roch theorem; the Serre duality and Hodge decomposition theorems; and the uniformization theorem. The book also contains treatments of other facts concerning the holomorphic, smooth, and topological structure of a Riemann surface, such as the biholomorphic classification of Riemann surfaces, the embedding theorems, the integrability of almost complex structures, the Schönflies theorem (and the Jordan curve theorem), and the existence of smooth structures on second countable surfaces. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course. Although some previous experience with complex analysis, Hilbert space theory, and analysis on manifolds would be helpful, the only prerequisite for this book is a working knowledge of point-set topology and elementary measure theory. The work includes numerous exercises many of which lead to further development of the theory and presents (with proofs) streamlined treatments of background topics from analysis and topology on manifolds in easily-accessible reference chapters, making it ideal for a one- or two-semester graduate course.

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A must-read for mathematicians, scientists and engineers who want to understand difference equations and discrete dynamics Contains the most complete and comprehenive analysis of the stability of one-dimensional maps or first order difference equations. Has an extensive number of applications in a variety of fields from neural network to host-parasitoid systems. Includes chapters on continued fractions, orthogonal polynomials and asymptotics. Lucid and transparent writing style

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This text provides a framework in which the main objectives of the field of uncertainty quantification (UQ) are defined and an overview of the range of mathematical methods by which they can be achieved. Complete with exercises throughout, the book will equip readers with both theoretical understanding and practical experience of the key mathematical and algorithmic tools underlying the treatment of uncertainty in modern applied mathematics. Students and readers alike are encouraged to apply the mathematical methods discussed in this book to their own favorite problems to understand their strengths and weaknesses, also making the text suitable for a self-study. Uncertainty quantification is a topic of increasing practical importance at the intersection of applied mathematics, statistics, computation and numerous application areas in science and engineering. This text is designed as an introduction to UQ for senior undergraduate and graduate students with a mathematical or statistical background and also for researchers from the mathematical sciences or from applications areas who are interested in the field. T. J. Sullivan was Warwick Zeeman Lecturer at the Mathematics Institute of the University of Warwick, United Kingdom, from 2012 to 2015. Since 2015, he is Junior Professor of Applied Mathematics at the Free University of Berlin, Germany, with specialism in Uncertainty and Risk Quantification.

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In its expanded new edition, this book covers boundary layers, multiple scales, homogenisation, slender body theory, symbolic computing, discrete equations and more. Includes exercises derived from current research, drawn from a range of application areas.

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42,99 € *

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´´This book is the first volume of a two-volume textbook for undergraduates and is indeed the crystallization of a course offered by the author at the California Institute of Technology to undergraduates without any previous knowledge of number theory. For this reason, the book starts with the most elementary properties of the natural integers. Nevertheless, the text succeeds in presenting an enormous amount of material in little more than 300 pages.´´--MATHEMATICAL REVIEWS

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