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Analyse: Mit einer Einführung in den Beweis, 4., Steven Lay.-
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eBay-Artikelnr.:335706784459
Artikelmerkmale
- Artikelzustand
- Binding
- Hardcover
- Product Group
- Book
- Weight
- 1 lbs
- IsTextBook
- Yes
- ISBN
- 9780131481015
Über dieses Produkt
Product Identifiers
Publisher
Prentice Hall PTR
ISBN-10
0131481010
ISBN-13
9780131481015
eBay Product ID (ePID)
30770003
Product Key Features
Number of Pages
400 Pages
Publication Name
Analysis : with an Introduction to Proof
Language
English
Subject
Mathematical Analysis
Publication Year
2004
Features
Revised
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
0.9 in
Item Weight
28.4 Oz
Item Length
8.2 in
Item Width
9.5 in
Additional Product Features
Edition Number
4
Intended Audience
College Audience
LCCN
2004-060078
Reviews
"Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." — Aimo Hinkkanen,University of Illinois at Urbana"The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." — John Konvalina,University of Nebraska at Omaha, "Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." — Aimo Hinkkanen,University of Illinois at Urbana "The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." — John Konvalina,University of Nebraska at Omaha, "Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." -- Aimo Hinkkanen, University of Illinois at Urbana "The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." -- John Konvalina, University of Nebraska at Omaha, "Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." — Aimo Hinkkanen, University of Illinois at Urbana "The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." — John Konvalina, University of Nebraska at Omaha, "Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." Aimo Hinkkanen, University of Illinois at Urbana "The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." John Konvalina, University of Nebraska at Omaha, "Let me begin by saying that I really like this book, and I do not say that of very many books. What impresses me most is the level of motivation and explanation given for the basic logic, the construction of proofs, and the ways of thinking about proofs that this book provides in its first few sections. It felt that the author was talking to the reader the way I would like to talk to students. There was an air of familiarity there. All kinds of useful remarks were made, the type I would like to make in my lectures." - Aimo Hinkkanen, University of Illinois at Urbana"The writing style is suitable for our students. It is clear, logical, and concise. The examples are very helpful and well-developed. The topics are thoroughly covered and at the appropriate level for our students. The material is technically accurate, and the pedagogical material is effectively presented." - John Konvalina, University of Nebraska at Omaha
Dewey Edition
23/eng/20230113
Illustrated
Yes
Dewey Decimal
511.3/6
Edition Description
Revised edition
Table Of Content
Chapter 1. Logic and Proof. Section 1. Logical Connectives Section 2. Quantifiers Section 3. Techniques of Proof: I Section 4. Techniques of Proof: II 2. Sets and Functions. Section 5. Basic Set Operations Section 6. Relations Section 7. Functions Section 8. Cardinality Section 9. Axioms for Set Theory(Optional) 3. The Real Numbers. Section 10. Natural Numbers and Induction Section 11 Ordered Fields Section 12 The Completeness Axiom Section 13 Topology of the Reals Section 14 Compact Sets Section 15 Metric Spaces (Optional) 4. Sequences. Section 16 Convergence Section 17 Limit Theorems Section 18 Monotone Sequences and Cauchy Sequences Section 19 Subsequences 5. Limits and Continuity. Section 20 Limits of Functions Section 21 Continuous Functions Section 22 Properties of Continuous Functions Section 23 Uniform Continuity Section 24 Continuity in Metric Space (Optional) 6. Differentiation. Section 25 The Derivative Section 26 The Mean Value Theorem Section 27 L'Hospital's Rule Section 28 Taylor's Theorem 7. Integration. Section 29 The Riemann Integral Section 30 Properties of the Riemann Integral Section 31 The Fundamental Theorem of Calculus 8. Infinite Series. Section 32 Convergence of Infinite Series Section 33 Convergence Tests Section 34 Power Series 9. Sequences and Series of Functions. Section 35 Pointwise and uniform Convergence Section 36 Application of Uniform Convergence Section 37 Uniform Convergence of Power Series Glossary of Key Terms References. Hints for Selected Exercises. Index.
Synopsis
By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps readers transition from computationally oriented mathematics to abstract mathematics with its emphasis on proofs. Uses clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers. Offers a new boxed review of key terms after each section. Rewrites many exercises. Features more than 250 true/false questions. Includes more than 100 practice problems. Provides exceptionally high-quality drawings to illustrate key ideas. Provides numerous examples and more than 1,000 exercises. A thorough reference for readers who need to increase or brush up on their advanced mathematics skills., By introducing logic and by emphasizing the structure and nature of the arguments used, this book helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. It includes expositions and examples, helpful practice problems, numerous drawings, and selected hints and answers., For courses in undergraduate Analysis (an easy one) and Transition to Advanced Mathematics. This text helps fill in the groundwork students need to succeed in real analysis often considered the most difficult course in the undergraduate curriculum. By introducing logic and by emphasizing the structure and nature of the arguments used, Lay helps students move carefully from computationally oriented courses to abstract mathematics with its emphasis on proofs. Clear expositions and examples, helpful practice problems, numerous drawings, and selected hints/answers make this text readable and student-oriented, and teacher- friendly.
LC Classification Number
QA300.L427 2006
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