This book is for physics students interested in the mathematics they use and for mathematics students interested in seeing how some of the ideas of their discipline find realization in an applied setting. The presentation tries to strike a balance between formalism and application, between abstract and concrete. The interconnections among the various topics are clarified both by the use of vector spaces as a central unifying theme, recurring throughout the book, and by putting ideas into their historical context. Enough of the essential formalism is included to make the presentation self-contained.
The book is divided into eight parts: The first covers finite- dimensional vector spaces and the linear operators defined on them. The second is devoted to infinite-dimensional vector spaces, and includes discussions of the classical orthogonal polynomials and of Fourier series and transforms. The third part deals with complex analysis, including complex series and their convergence, the calculus of residues, multivalued functions, and analytic continuation. Part IV treats ordinary differential equations, concentrating on second-order equations and discussing both analytical and numerical methods of solution. The next part deals with operator theory, focusing on integral and Sturm--Liouville operators. Part VI is devoted to Green's functions, both for ordinary differential equations and in multidimensional spaces. Parts VII and VIII contain a thorough discussion of differential geometry and Lie groups and their applications, concluding with Noether's theorem on the relationship between symmetries and conservation laws.
Intended for advanced undergraduates or beginning graduate students, this comprehensive guide should also prove useful as a refresher or reference for physicists and applied mathematicians. Over 300 worked-out examples and more than 800 problems provide valuable learning aids.
Numerous enhancements and revision are incorporated into this new edition. For example, fiber bundle techniques are used to introduce differential geometry. This more elegant and intuitive approach naturally connects differential geometry with not only the general theory of relativity, but also gauge theories of fundamental forces.
Some praise for the previous edition:
PAGEOPH Pure and Applied Geophysics]
Review by Daniel Wojcik, University of Maryland
"This volume should be a welcome addition to any collection. The book is well written and explanations are usually clear. Lives of famous mathematicians and physicists are scattered within the book. They are quite extended, often amusing, making nice interludes. Numerous exercises help the student practice the methods introduced. ... I have recently been using this book for an extended time and acquired a liking for it. Among all the available books treating mathematical methods of physics this one certainly stands out and assuredly it would suit the needs of many physics readers."
ZENTRALBLATT MATH
Review by G.Roepstorff, University of Aachen, Germany
..". Unlike most existing texts with the same emphasis and audience, which are merely collections of facts and formulas, the present book is more systematic, self-contained, with a level of presentation that tends to be more formal and abstract. This entails proving a large number of theorems, lemmas, and corollaries, deferring most of the applications that physics students might be interested in to the example sections in small print. Indeed, there are 350 worked-out examples and about 850 problems. ... A very nice feature is the way the author intertwines the formalism with the life stories and anecdotes of some mathematicians and physicists, leading at their times. As is often the case, the historical view point helps to understand and appreciate the ideas presented in the text. ... For the physics studen
Описание: Can we coexist with the other life forms that have evolved on this planet? Are there realistic alternatives to fossil fuels that would sustainably provide for human society's energy needs and have fewer harmful effects? How do we deal with threats such as emergent diseases? Mathematical models--equations of various sorts capturing relationships between variables involved in a complex situation--are fundamental for understanding the potential consequences of choices we make. Extracting insights from the vast amounts of data we are able to collect requires analysis methods and statistical reasoning.This book on elementary topics in mathematical modeling and data analysis is intended for an undergraduate ``liberal arts mathematics''-type course but with a specific focus on environmental applications. It is suitable for introductory courses with no prerequisites beyond high school mathematics. A great variety of exercises extends the discussions of the main text to new situations and/or introduces new real-world examples. Every chapter ends with a section of problems, as well as with an extended chapter project which often involves substantial computing work either in spreadsheet software or in the ${\tt R}$ statistical package.
Автор: Joshi Название: Introduction to Mathematical Portfolio Theory ISBN: 1107042313 ISBN-13(EAN): 9781107042315 Издательство: Cambridge Academ Рейтинг: Цена: 9029.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A concise yet comprehensive guide to the mathematics of portfolio theory from a modelling perspective, with discussion of the assumptions, limitations and implementations of the models as well as the theory underlying them. Aimed at advanced undergraduates, this book can be used for self-study or as a course text.
Автор: Grimmett, Geoffrey (director Of Research And Professor Emeritus Of Mathematical Statistics, Director Of Research And Professor Emeritus Of Mathematica Название: Probability and random processes ISBN: 0198847602 ISBN-13(EAN): 9780198847601 Издательство: Oxford Academ Рейтинг: Цена: 13266.00 р. Наличие на складе: Поставка под заказ.
Описание: Probability is a core topic in science and life. This successful self-contained volume leads the reader from the foundations of probability theory and random processes to advanced topics and it presents a mathematical treatment with many applications to real-life situations.
Автор: M. Asghar Bhatti Название: Practical Optimization Methods ISBN: 1461267919 ISBN-13(EAN): 9781461267911 Издательство: Springer Рейтинг: Цена: 11398.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book, on the other hand, is the first text to use Mathematica to develop a thorough understanding of optimization algorithms, fully exploiting Mathematica`s symbolic, numerical and graphic capabilities.
Автор: Galina Filipuk, Andrzej Kozlowski Название: Analysis with Mathematica®: Volume 1: Single Variable Calculus ISBN: 3110590131 ISBN-13(EAN): 9783110590135 Издательство: Walter de Gruyter Цена: 11148.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: A computer algebra system such as Mathematica is able to do much more than just numerics: This text shows how to tackle real mathematical problems from basic analysis. The reader learns how Mathematica represents domains, qualifiers and limits to implement actual proofs – a requirement to unlock the huge potential of Mathematica for a variety of applications.
Автор: Edward P C Kao Название: An Introduction to Probability: With MATHEMATICA(R) ISBN: 9811245436 ISBN-13(EAN): 9789811245435 Издательство: World Scientific Publishing Рейтинг: Цена: 19800.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main objective of this text is to facilitate a student's smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
Автор: Edward P C Kao Название: An Introduction to Probability: With MATHEMATICA(R) ISBN: 9811246785 ISBN-13(EAN): 9789811246784 Издательство: World Scientific Publishing Рейтинг: Цена: 8712.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The main objective of this text is to facilitate a student's smooth learning transition from a course on probability to its applications in various areas. To achieve this goal, students are encouraged to experiment numerically with problems requiring computer solutions.
Автор: Magrab Название: An Engineer`s Guide to Mathematica® ISBN: 1118821262 ISBN-13(EAN): 9781118821268 Издательство: Wiley Рейтинг: Цена: 12664.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Free Mathematica 10 Update Included! Now available from www. wiley.
Описание: This is a textbook on classical polynomial and rational approximation theory for the twenty-first century. Aimed at advanced undergraduates and graduate students across all of applied mathematics, it uses MATLAB to teach the field’s most important ideas and results.
Approximation Theory and Approximation Practice, Extended Edition differs fundamentally from other works on approximation theory in a number of ways: its emphasis is on topics close to numerical algorithms; concepts are illustrated with Chebfun; and each chapter is a PUBLISHable MATLAB M-file, available online.
The book centers on theorems and methods for analytic functions, which appear so often in applications, rather than on functions at the edge of discontinuity with their seductive theoretical challenges. Original sources are cited rather than textbooks, and each item in the bibliography is accompanied by an editorial comment. In addition, each chapter has a collection of exercises, which span a wide range from mathematical theory to Chebfun-based numerical experimentation.
Автор: Singer Название: Mathematical Creativity and Mathematical Giftedness ISBN: 3319731556 ISBN-13(EAN): 9783319731551 Издательство: Springer Рейтинг: Цена: 12196.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book discusses the relationships between mathematical creativity and mathematical giftedness. It gathers the results of a literature review comprising all papers addressing mathematical creativity and giftedness presented at the International Congress on Mathematical Education (ICME) conferences since 2000. How can mathematical creativity contribute to children’s balanced development? What are the characteristics of mathematical giftedness in early ages? What about these characteristics at university level? What teaching strategies can enhance creative learning? How can young children’s mathematical promise be preserved and cultivated, preparing them for a variety of professions? These are some of the questions addressed by this book. The book offers, among others: analyses of substantial learning environments that promote creativity in mathematics lessons; discussions of a variety of strategies for posing and solving problems; investigations of students’ progress throughout their schooling; and examinations of technological tools and virtual resources meant to enhance learning with understanding. Multiple perspectives in the interdisciplinary fields of mathematical creativity and giftedness are developed to offer a springboard for further research. The theoretical and empirical studies included in the book offer a valuable resource for researchers, as well as for teachers of gifted students in specialized or inclusive settings, at various levels of education.
Описание: This book provides a lively and accessible introduction to the numerical solution of stochastic differential equations with the aim of making this subject available to the widest possible readership. It presents an outline of the underlying convergence and stability theory while avoiding technical details. Key ideas are illustrated with numerous computational examples and computer code is listed at the end of each chapter. The authors include 150 exercises, with solutions available online, and 40 programming tasks.Although introductory, the book covers a range of modern research topics, including It? versus Stratonovich calculus, implicit methods, stability theory, nonconvergence on nonlinear problems, multilevel Monte Carlo, approximation of double stochastic integrals, and tau leaping for chemical and biochemical reaction networks.An Introduction to the Numerical Simulation of Stochastic Differential Equations is appropriate for undergraduates and postgraduates in mathematics, engineering, physics, chemistry, finance, and related disciplines, as well as researchers in these areas. The material assumes only a competence in algebra and calculus at the level reached by a typical first-year undergraduate mathematics class, and prerequisites are kept to a minimum. Some familiarity with basic concepts from numerical analysis and probability is also desirable but not necessary.
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