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Mathematical analysis --- Analyse mathématique --- 517.1 Mathematical analysis
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The transition from studying calculus in schools to studying mathematical analysis at university is notoriously difficult. In this second edition of Numbers and Functions, Dr Burn invites the student reader to tackle each of the key concepts in turn, progressing from experience through a structured sequence of several hundred problems to concepts, definitions and proofs of classical real analysis. The sequence of problems, which all have solutions supplied, draws students into constructing definitions and theorems for themselves. This natural development is informed and complemented by historical insight. The novel approach to rigorous analysis offered here is designed to enable students to grow in confidence and skill and thus overcome the traditional difficulties.
Mathematical analysis. --- Mathematics --- 517.1 Mathematical analysis --- Mathematical analysis
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The main emphasis of this volume is on harmonic and functional analysis. The papers include some of the latest research developments in this important field of mathematics.
Mathematical analysis --- Mathematics --- Math --- Science --- 517.1 Mathematical analysis
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This proceedings volume contains papers of research of expository nature, and is addressed to research workers and advanced graduate students in mathematics. Some of the papers are the written and expanded texts of lectures delivered at the conference, whereas others have been included by invitation.
Mathematical analysis --- Approximation theory --- Functional analysis --- 517.1 Mathematical analysis
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This practical introduction encapsulates the entire content of teaching material for UK honours degree courses in mathematics, physics, chemistry and engineering, and is also appropriate for post-graduate study. It imparts the necessary mathematics for use of the techniques, with subject-related worked examples throughout. The text is supported by challenging problem exercises (and answers) to test student comprehension. Index notation used in the text simplifies manipulations in the sections on vectors and tensors. Partial differential equations are discussed, and special functions introduced
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This Proceedings Volume contains 32 articles on various interesting areas ofpresent-day functional analysis and its applications: Banach spaces andtheir geometry, operator ideals, Banach and operator algebras, operator andspectral theory, Frechet spaces and algebras, function and sequence spaces.The authors have taken much care with their articles and many papers presentimportant results and methods in active fields of research. Several surveytype articles (at the beginning and the end of the book) will be very usefulfor mathematicians who want to learn ""what is go
Analyse fonctionnnelle --- Functional analysis --- Mathematical analysis --- 517.1 Mathematical analysis
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The new edition of this highly acclaimed textbook contains several major additions, including more than four hundred new exercises (with hints and answers). To match the mathematical preparation of current senior college and university entrants, the authors have included a preliminary chapter covering areas such as polynomial equations, trigonometric identities, coordinate geometry, partial fractions, binomial expansions, induction, and the proof of necessary and sufficient conditions. Elsewhere, matrix decompositions, nearly-singular matrices and non-square sets of linear equations are treated in detail. The presentation of probability has been reorganised and greatly extended, and includes all physically important distributions. New topics covered in a separate statistics chapter include estimator efficiency, distributions of samples, t- and F-tests for comparing means and variances, applications of the chi-squared distribution, and maximum likelihood and least-squares fitting. In other chapters the following topics have been added: linear recurrence relations, curvature, envelopes, curve-sketching, and more refined numerical methods.
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Introductory Analysis addresses the needs of students taking a course in analysis after completing a semester or two of calculus, and offers an alternative to texts that assume that math majors are their only audience. By using a conversational style that does not compromise mathematical precision, the author explains the material in terms that help the reader gain a firmer grasp of calculus concepts.* Written in an engaging, conversational tone and readable style while softening the rigor and theory* Takes a realistic approach to the necessary and accessible level of abstra
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Professor H. S. Wall wrote Creative Mathematics with the intention of leading students to develop their mathematical abilities, to help them learn the art of mathematics, and to teach them to create mathematical ideas. Creative Mathematics, according to Wall, 'is not a compendium of mathematical facts and inventions to be read over as a connoisseur of art looks over paintings. It is, instead, a sketchbook in which readers try their hands at mathematical discovery.' The book is self contained, and assumes little formal mathematical background on the part of the reader. Wall is earnest about developing mathematical creativity and independence in students. Wall developed Creative Mathematics over a period of many years of working with students at the University of Texas -Austin. In less than two hundred pages, he takes the reader on a stimulating tour starting with numbers, and then moving on to simple graphs, the integral, simple surfaces, successive approximations, linear spaces of simple graphs, and concluding with mechanical systems. The student who has worked through Creative Mathematics will come away with heightened mathematical maturity.
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For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.
Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis