Introduction to Analysis (4th Edition)

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9780132296380: Introduction to Analysis (4th Edition)

This text prepares readers for fluency with analytic ideas, such as real and complex analysis, partial and ordinary differential equations, numerical analysis, fluid mechanics, and differential geometry. This book is designed to challenge advanced readers while encouraging and helping readers with weaker skills. Offering readability, practicality and flexibility, Wade presents fundamental theorems and ideas from a practical viewpoint, showing readers the motivation behind the mathematics and enabling them to construct their own proofs.

 

ONE-DIMENSIONAL THEORY; The Real Number System; Sequences in R; Continuity on R; Differentiability on R; Integrability on R; Infinite Series of Real Numbers; Infinite Series of Functions; MULTIDIMENSIONAL THEORY; Euclidean Spaces; Convergence in Rn; Metric Spaces; Differentiability on Rn; Integration on Rn; Fundamental Theorems of Vector Calculus; Fourier Series

 

For all readers interested in analysis.

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From the Publisher:

Designed as a "bridge" between sophomore-level calculus to graduate-level courses that use analytic ideas, this text provides an unusually friendly, but rigorous treatment. It is friendly because the text helps link proofs together in a way that teaches students to think ahead: "Why this Theorem?"

From the Back Cover:

User-friendly--yet rigorous--in approach, this introduction to analysis meets readers where they are by providing extra support for those who like a slower, less detailed approach, but not getting in the way of those who want a quicker pace and deeper focus. It uses analogy and geometry to motivate and explain the theory, and precedes many complicated proofs with a "Strategy" which motivates the proof, shows why it was chosen, and why it should work. Examples follow many theorems, showing why each hypothesis is needed, allowing readers to remember the hypotheses by recalling the examples. Proofs are presented in complete detail, with each step carefully documented, and proofs are linked together in a way that teaches readers to think ahead. Physical interpretations are used to examine some concepts from a second or third point of view. Includes over 200 worked examples and over 600 exercises. Provides extensive coverage of multidimensional analysis.

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