Understanding Real Analysis 2nd Edition by Paul Zorn ISBN 1138033014 978-1138033016
Original price was: $50.00.$35.00Current price is: $35.00.
Understanding Real Analysis 2nd Edition by Paul Zorn – Ebook PDF Instant Download/Delivery: 1138033014 , 978-1138033016
Full download Understanding Real Analysis 2nd edition after payment
Product details:
ISBN 10: 1138033014
ISBN 13: 978-1138033016
Author: Paul Zorn
Understanding Real Analysis, Second Edition offers substantial coverage of foundational material and expands on the ideas of elementary calculus to develop a better understanding of crucial mathematical ideas. The text meets students at their current level and helps them develop a foundation in real analysis.
The author brings definitions, proofs, examples and other mathematical tools together to show how they work to create unified theory. These helps students grasp the linguistic conventions of mathematics early in the text. The text allows the instructor to pace the course for students of different mathematical backgrounds.
Understanding Real Analysis 2nd Table of contents:
1 Preliminaries: Numbers, Sets, Proofs, and Bounds
1.1 Numbers 101: The Very Basics
Integers, Rationals, and Reals
1.2 Sets101: Getting Started
1.3 Sets102: The Idea of a Function
Seeing Functions
All Kinds of Functions
New Functions from Old
Inverse Functions
Relations
1.4 Proofs 101: Proofs and Proof‐Writing
Mathematical Language and Literature
Proof Language: A Lexicon
1.5 Types of Proof
Direct Proof
Indirect Proof
Proof by Contradiction
Brute Force, Cases, Exhaustion, Enumeration
Proof by Induction
1.6 Sets103: Finite and Infinite Sets; Cardinality
Cardinality: The Idea
Working with Countable Sets
Uncountable Sets
1.7 Numbers 102: Absolute Values
Absolute Truths
1.8 Bounds
Getting Edgy: sup, lub, inf, and glb
Functions and Bounds
1.9 Numbers 103: Completeness
Nested Intervals
Rationals and Irrationals: Tightly Packed
2 Sequences and Series
2.1 Sequences and Convergence
Convergence and Divergence
Visualizing Sequences and Convergence
Properties of Sequences
2.2 Working with Sequences
New Sequences from Old
Divergence to Infinity
2.3 Subsequences
Basic Ideas
Properties of Subsequences
2.4 Cauchy Sequences
Cauchy Basics
Properties of Cauchy Sequences
2.5 Series 101: Basic Ideas
Series: The Basics
Detecting Convergence and Divergence
Absolute Convergence
2.6 Series 102: Testing for Convergence and Estimating Limits
Estimating Limits
2.7 Lim sup and lim inf: A Guided Discovery
3 Limits and Continuity
3.1 Limits of Functions
Defining Limits of Functions
Basic Properties of Limits
3.2 Continuous Functions
New Continuous Functions from Old
3.3 Why Continuity Matters: Value Theorems
3.4 Uniform Continuity
3.5 Topology of the Real Numbers
3.6 Compactness
4 Derivatives
4.1 Defining the Derivative
Different Views of the Derivative
Derivatives as Functions
Properties of Differentiable Functions
4.2 Calculating Derivatives
Derivatives of Elementary Functions
4.3 The Mean Value Theorem
Proving the Mean Value Theorem
Calculus Friends Revisited: Using the MVT
4.4 Sequences and Series of Functions
4.5 Taylor SerWere and TayUr’s Theorem: A Guided Discovery
5 lntegrals
5.1 The Riemann lntegral: Definition and Examples
Familiar ldeas Revisited
Expressions and calculations like
Defining the Integral
Illustrating the Definition
Which Functions are Riemann Integrable?
5.2 Properties of the Integral
Algebra with Integrals
Joinery
Antiderivatives and lntegrals: Toward a Fundamental Theorem
Using the Fundamental Theorem
5.3 Integrability
Criteria for lntegrability
lntegrability and Box Sums
5.4 Some Fundamental Theorems
People also search for Understanding Real Analysis 2nd :
understanding real analysis zorn pdf
understanding real analysis stephen abbott pdf
understanding real analysis pdf
understanding real analysis stephen abbott
understanding real analysis solutions