Basic Analysis I: Functions of a Real Variable

by Peterson, James K.

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Title Statements

Full title :Basic Analysis I : Functions of a Real Variable.

Edition Statements

Publication Date:2020.

Publication Statements

Publisher(s):CRC Press LLC
Place of Publication:Milton
Language:eng
Publication Date:2020.

Notes

Description based upon print version of record.

8.4.1 Homework

The Physical Object

Description:1 online resource (595 p.)

Edition Identifiers

ISBN:9781351679459, 1351679457, 9781351679442, 1351679449, 9781351679435, 1351679430, 9781315166254, 1315166259
DOI:10.1201/9781315166254
oclc:on1155319606
Dewey Decimal:515.8

Cover -- Half Title -- Title Page -- Copyright Page -- Dedication -- Abstract -- Acknowledgments -- Table of Contents -- I: Introduction -- 1: Introduction -- 1.1 Table of Contents -- II: Understanding Smoothness -- 2: Proving Propositions -- 2.1 Mathematical Induction -- 2.1.1 Homework -- 2.2 More Examples -- 2.3 More Abstract Proofs and Even Trickier POMIs -- 2.3.1 Homework -- 2.4 Some Contradiction Proofs -- 2.5 Triangle Inequalities. -- 2.5.1 A First Look at the Cauchy -- Schwartz Inequality -- 2.5.2 Homework -- 2.6 The Supremum and Infimum of a Set of Real Numbers -- 2.6.1 Bounded Sets

2.6.2 Least Upper Bounds and Greatest Lower Bounds -- 2.6.3 The Completeness Axiom and Consequences -- 2.6.4 Some Basic Results -- 2.6.5 Homework -- 3: Sequences of Real Numbers -- 3.1 Basic Definitions -- 3.2 The Definition of a Sequence -- 3.2.1 Homework -- 3.3 The Convergence of a Sequence -- 3.3.1 Proofs of Divergence -- 3.3.2 Uniqueness of Limits and So Forth -- 3.3.3 Proofs of Convergence -- 3.3.4 Homework -- 3.4 Sequence Spaces -- 3.4.1 Limit Theorems -- 3.4.2 Some Examples -- 3.4.3 Homework -- 4: Bolzano -- Weierstrass Results -- 4.1 Bounded Sequences with a Finite Range

4.2 Sequences…