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Analysis with an introduction to proof 5th Edition by Steven R Lay ISBN 1292040246 9781292040240

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Analysis with an introduction to proof Fifth Edition, Pearson New International Edition Lay Digital Instant Download

Author(s): Lay, Steven R
ISBN(s): 9781292040240, 1292040246
Edition: Fifth edition, Pearson new international edition
File Details: PDF, 5.16 MB
Year: 2013
Language: english
SKU: EB-32705280 Category: Tags: ,

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Product details:

ISBN 10: 1292040246 
ISBN 13: 9781292040240
Author: Steven R Lay

For courses in undergraduate Analysis and Transition to Advanced Mathematics. Analysis with an Introduction to Proof, Fifth Edition 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 emphasizing the structure and nature of the arguments used, this text 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, student-oriented, and teacher- friendly.

Analysis with an introduction to proof 5th Table of contents:

Part I: LOGIC AND PROOFS

  • Chapter 1: Logic and Proofs
    • 1.1 Sentential Logic
    • 1.2 Quantifiers
    • 1.3 Techniques of Proof: I
    • 1.4 Techniques of Proof: II
    • 1.5 Proofs Involving Sets

Part II: SETS AND FUNCTIONS

  • Chapter 2: Sets and Functions
    • 2.1 Basic Concepts of Set Theory
    • 2.2 Operations on Sets
    • 2.3 Functions
    • 2.4 Indexed Families of Sets
    • 2.5 Countable and Uncountable Sets

Part III: THE REAL NUMBERS

  • Chapter 3: The Real Numbers
    • 3.1 Axioms for the Real Numbers
    • 3.2 Algebraic Properties of R
    • 3.3 Order Properties of R
    • 3.4 The Completeness Axiom
    • 3.5 Applications of the Completeness Axiom
    • 3.6 Cauchy Sequences

Part IV: SEQUENCES

  • Chapter 4: Sequences
    • 4.1 Convergence
    • 4.2 Limit Theorems
    • 4.3 Monotone Sequences and Cauchy Sequences
    • 4.4 Subsequences
    • 4.5 Lim Sup and Lim Inf
    • 4.6 Series of Real Numbers

Part V: LIMITS AND CONTINUITY

  • Chapter 5: Limits and Continuity
    • 5.1 Limits of Functions
    • 5.2 Continuous Functions
    • 5.3 Properties of Continuous Functions
    • 5.4 Uniform Continuity
    • 5.5 The Cantor Set and Related Topics

Part VI: DIFFERENTIATION

  • Chapter 6: Differentiation
    • 6.1 The Derivative
    • 6.2 The Mean Value Theorem
    • 6.3 L’Hospital’s Rule
    • 6.4 Taylor’s Theorem

Part VII: INTEGRATION

  • Chapter 7: Integration
    • 7.1 The Riemann Integral
    • 7.2 Properties of the Riemann Integral
    • 7.3 The Fundamental Theorem of Calculus
    • 7.4 Improper Integrals

Part VIII: SEQUENCES AND SERIES OF FUNCTIONS

  • Chapter 8: Sequences and Series of Functions
    • 8.1 Uniform Convergence
    • 8.2 Uniform Convergence and Continuity
    • 8.3 Uniform Convergence and Integration
    • 8.4 Uniform Convergence and Differentiation
    • 8.5 Power Series
    • 8.6 Taylor Series

Part IX: METRIC SPACES

  • Chapter 9: Metric Spaces

    • 9.1 Definitions and Examples
    • 9.2 Open and Closed Sets
    • 9.3 Convergence, Completeness, and Compactness
    • 9.4 Continuous Functions

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