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An Introduction to Analysis(4th)  무료배송

 
지은이 : wade
출판사 : Pearson
페이지수 : 682
ISBN : 978-0-13-615370-2
예상출고일 : 입금확인후 2일 이내
주문수량 :
도서가격 : 품절
     

 

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.

Preface


Part I. ONE-DIMENSIONAL THEORY


1. The Real Number System


1.1 Introduction


1.2 Ordered field axioms


1.3 Completeness Axiom


1.4 Mathematical Induction


1.5 Inverse functions and images


1.6 Countable and uncountable sets


2. Sequences in R


2.1 Limits of sequences


2.2 Limit theorems


2.3 Bolzano-Weierstrass Theorem


2.4 Cauchy sequences


*2.5 Limits supremum and infimum


3. Continuity on R


3.1 Two-sided limits


3.2 One-sided limits and limits at infinity


3.3 Continuity


3.4 Uniform continuity


4. Differentiability on R


4.1 The derivative


4.2 Differentiability theorems


4.3 The Mean Value Theorem


4.4 Taylor's Theorem and l'H�pital's Rule


4.5 Inverse function theorems


5 Integrability on R


5.1 The Riemann integral


5.2 Riemann sums


5.3 The Fundamental Theorem of Calculus


5.4 Improper Riemann integration


*5.5 Functions of bounded variation


*5.6 Convex functions


6. Infinite Series of Real Numbers


6.1 Introduction


6.2 Series with nonnegative terms


6.3 Absolute convergence


6.4 Alternating series


*6.5 Estimation of series


*6.6 Additional tests


7. Infinite Series of Functions


7.1 Uniform convergence of sequences


7.2 Uniform convergence of series


7.3 Power series


7.4 Analytic functions


*7.5 Applications


Part II. MULTIDIMENSIONAL THEORY


8. Euclidean Spaces


8.1 Algebraic structure


8.2 Planes and linear transformations


8.3 Topology of Rn


8.4 Interior, closure, boundary


9. Convergence in Rn


9.1 Limits of sequences


9.2 Heine-Borel Theorem


9.3 Limits of functions


9.4 Continuous functions


*9.5 Compact sets


*9.6 Applications


10. Metric Spaces


10.1 Introduction


10.2 Limits of functions


10.3 Interior, closure, boundary


10.4 Compact sets


10.5 Connected sets


10.6 Continuous functions


10.7 Stone-Weierstrass Theorem


11. Differentiability on Rn


11.1 Partial derivatives and partial integrals


11.2 The definition of differentiability


11.3 Derivatives, differentials, and tangent planes


11.4 The Chain Rule


11.5 The Mean Value Theorem and Taylor's Formula


11.6 The Inverse Function Theorem


*11.7 Optimization


12. Integration on Rn


12.1 Jordan regions


12.2 Riemann integration on Jordan regions


12.3 Iterated integrals


12.4 Change of variables


*12.5 Partitions of unity


*12.6 The gamma function and volume


13. Fundamental Theorems of Vector Calculus


13.1 Curves


13.2 Oriented curves


13.3 Surfaces


13.4 Oriented surfaces


13.5 Theorems of Green and Gauss


13.6 Stokes's Theorem


*14. Fourier Series


*14.1 Introduction


*14.2 Summability of Fourier series


*14.3 Growth of Fourier coefficients


*14.4 Convergence of Fourier series


*14.5 Uniqueness


Appendices


A. Algebraic laws


B. Trigonometry


C. Matrices and determinants


D. Quadric surfaces


E. Vector calculus and physics


F. Equivalence relations


References


Answers and Hints to Exercises


Subject Index


Symbol Index

"This book was used in my Analysis I class. I later had to prepare again for my masters certifying exam on Analysis and the primary reason I didn't use this book, even though I owned it, was the binding. By the end of my analysis course, it was practically in individual pages. The binding is atrocious - how can a $100+ book just be sort of glued together weakly that it falls apart after 1 semester of use.

The other reason I didn't use this book was that it goes through the 1-dimensional analysis pretty fast. My chosen analysis preparation book was also supposed to be my preparation for Royden's Real Analysis but I choose a book that covers the 1-dimensional analysis in twice the amount of pages and exercises taking a more detailed topology route. So, I'd advise a little bit of caution there if this is your path to graduate level Real Analysis.

However, with the 3rd edition out, our department threw out all the old 2nd edition books. I needed a multi-dimensional analysis text to prepare for my graduate PDE course and took 3 copies of the thrown ones out.

The reason I took 3 copies was that I knew the binding was going to fall apart and sure enough it did. It sort of breaks down into little booklets each that is glued to the spine. The pages on booklet peel off real easy and soon you have just pages instead of a book.

As for the multidimensional analysis it covers, it was very entertaining and fun to do. Chapter 13 becomes a little bit in the air as the exercises get a little tedious with calculate this integral with all sorts of surfaces enclosing it and not really much exercises requring a lot of threading of analysis ideas. I don't as of yet know if it has me prepared enough for Evan's PDE book but this was the only text conviniently showed up in the "free books" bin. But, I did have a nice linear and fun writing to it and I enjoyed it. Though not much as some of my other books."


"There HAS to be better texts out there in analysis. This book obscures simple concepts and neglects vital information for an introduction to analysis. I have suffered through this book, working VERY hard for three semesters. Nevertheless there are still concepts that I don't TRULY understand, which is largely attributable Wade's poor exposition of the topic. For example, the entire treatment of differentiability in Euclidean n-space, including the manner in which Wade introduces the definition, is pathetically motivated/explained. This makes it difficult to understand and convince yourself of other proofs/concepts which rely on a firm understanding of the previously studied material.

For a truly comprehensive introduction, I'd suggest Introduction to Analysis by Maxwell Rosenlicht. I bought this as a supplementary text to the courses I have taken, largely due to positive reviews, and was very pleased. I gained significant insight due to the presence of discussions spanning more than three sentences between each lemma, theorem, corollary, or remark, in complete contrast to Wade's book. Another plus is that it's around 10% of the cost."
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