Sinossi
In a textbook for an undergraduate course in real analysis, Bridger recognizes that besides mathematics majors, such courses attract students of secondary teaching, physical sciences, and computer science and need more (and less) than a foundation for advanced graduate mathematics courses. The course shapes the way students think about mathematics, he says, and is often a student's introduction to precise reasoning and writing. His topics include the real numbers and completeness, an inverse function theorem and its application, the Riemann integral, and the complex numbers and Fourier series. Annotation ©2019 Ringgold, Inc., Portland, OR (protoview.com)
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Real Analysis
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American Mathematical Society, 2019
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ISBN 13: 9781470451448
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Real Analysis A Constructive Approach Through Interval Arithmetic
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Real Analysis : A Constructive Approach Through Interval Arithmetic
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Real Analysis
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Hardback. Condizione: New. Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering.The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material--including an introduction to complex variables and Fourier series--to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects--many with hints--at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout. Codice articolo LU-9781470451448
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Real Analysis : A Constructive Approach Through Interval Arithmetic
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Real Analysis (Hardcover)
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Hardcover. Condizione: new. Hardcover. Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. For example, at the very beginning, the real numbers are shown to exist because they are constructed from the rationals using interval arithmetic. This approach, with its clear analogy to scientific measurement with tolerances, is taken throughout the book and makes the subject especially relevant and appealing to students with an interest in computing, applied mathematics, the sciences, and engineering.The first part of the book contains all the usual material in a standard one-semester course in analysis of functions of a single real variable: continuity (uniform, not pointwise), derivatives, integrals, and convergence. The second part contains enough more technical material--including an introduction to complex variables and Fourier series--to fill out a full-year course. Throughout the book the emphasis on rigorous and direct proofs is supported by an abundance of examples, exercises, and projects--many with hints--at the end of every section. The exposition is informal but exceptionally clear and well motivated throughout. Presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: all existence proofs are direct, so showing that the numbers or functions in question exist means exactly that they can be explicitly calculated. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Codice articolo 9781470451448
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Real Analysis: A Constructive Approach Through Interval Arithmetic
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