For two-semester/three-quarter, first undergraduate courses in Advanced Calculus or Real Analysis.
This book is an easy, readable, intimidation-free analysis textbook. Ideas and methods of proof build upon each other and are explained thoroughly. This is the first text to cover both single and multivariable analysis in such a student friendly setting.
Features
NEW - Revised and reorganized content—Hundreds of small improvements enhance the presentation of material throughout the text.
Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
NEW - Added examples and explanations.
NEW - Reworded exercises.
Further enhances the precision of the instructions, making it easier for students to follow.
NEW - Expanded use of geometry and illustrations.
Enhances the visual appeal of the text and students' understanding and visualization.
NEW - Author website with additional topics.
New To This Edition
Revised and reorganized content—Hundreds of small improvements enhance the presentation of material throughout the text.
Provides students with more thorough treatments of existing material in a clearer, more readable, and student-friendly format.
Added examples and explanations.
Reworded exercises.
Further enhances the precision of the instructions, making it easier for students to follow.
Expanded use of geometry and illustrations.
Enhances the visual appeal of the text and students' understanding and visualization.
Author website with additional topics.
The chapter on Fourier Analysis is, for example, available now in this form.

lgli/2004 A Friendly Introduction to Analysis.pdf

lgrsnf/2004 A Friendly Introduction to Analysis.pdf

zlib/Mathematics/Analysis/Witold A. J. Kosmala/A Friendly Introduction to Analysis: Single and Multivariable_2189408.pdf

A Friendly Introduction to Analysis, Second Edition

Kosmala, Witold

Addison-Wesley Longman, Incorporated

Globe Fearon Educational Publishing

Longman Publishing

Cengage Gale

Adobe Press

United States, United States of America

2nd ed, Englewood Cliffs, N.J, 2003

2 edition, October 15, 2003

Second Edition, PS, 2004

0

lg1159261

{"edition":"2","isbns":["0130457965","0321724909","9780130457967","9780321724908"],"last_page":600,"publisher":"Pearson"}

Rev. ed. of: Advanced calculus. Upper Saddle River, N.J. : Prentice Hall, c1999.
Includes index.

Cover
S Title
A Friendly Introduction to Analysis
Copyright
© 2004, 1999 Pearson Education
ISBN 0-13-045796-5
Dedication
Contents
Preface
1 Purpose and Background
2 Design and Organization
3 Supplements
4 How the 2nd Edition Differs From the 1st Edition
5 Acknowledgments
1 Introduction
1.1 * Algebra of Sets
Exercises 1.1
1.2* Relations and Functions
Exercises 1.2
1.3* Mathematical Induction
Exercises 1.3
1.4* Proof Techniques
Exercises 1.4
1.5* Inverse Functions
Exercises 1.5
1.6* Finite and Infinite Sets
Exercises 1.6
1.7* Ordered Field and a Real Number System
Exercises 1.7
1.8* Some Properties of Real Numbers
Exercises 1.8
1,9* Review
1.10* Projects
Part 1. Fibonacci Numbers
Part 2. Lucas Numbers
Part 3. Mean of Real Numbers
2 Sequences
2.1 Convergence
Exercises 2.1
2.2 Limit Theorems
Exercises 2.2
2.3 Infinite Limits
Exercises 2.3
2.4 Monotone Sequences
Exercises 2.4
2.5 Cauchy Sequences
Exercises 2.5
2.6 Subsequences
Exercises 2.6
2.7* Review
2.8* Projects
Part 1. The Transcendental Number e
Part 2. Summable Sequences
3 Limits of Functions
3.1 Limit at Infinity
Exercises 3.1
3.2 Limit at a Real Number
Exercises 3.2
3.3 Sided Limits
Exercises 3.3
3.4* Review
3.5* Projects
Part 1. Monotone Functions
Part 2. Continued Fractions
4 Continuity
4.1 Continuity of a Function
Exercises 4.1
4.2* Discontinuity of a Function
Exercises 4.2
4.3 Properties of Continuous Functions
Exercises 4.3
4.4 Uniform Continuity
Exercises 4.4
4.5* Review
4.6* Projects
Part 1. Compact Sets
Part 2. Multiplicative, Subadditive, and Additive Functions
5 Differentiation
5.1 Derivative of a Function
Exercises 5.1
5.2 Properties of Differentiable Functions
Exercises 5.2
5.3 Mean Value Theorems
Exercises 5.3
5.4 Higher-Order Derivatives
Exercises 5.4
5.5 * L'Hopital's Rule
Exercises 5.5
5.6 * Review
5.7 * Projects
Part 1. Approximation of Derivatives
Part 2. Lipschitz Condition
Part 3. Functions of Bounded Variation
Part 4. Absolutely Continuous Functions
Part 5. Convex Functions
6 Integration
6.1 Riemann Integral
Exercises 6.1
6.2 Integrable Functions
Exercises 6.2
6.3 Properties of the Riemann Integral
Exercises 6.3
6.4 Integration in Relation to Differentiation
Exercises 6.4
6.5 Improper Integral
Exercises 6.5
6.6 * Special Functions
Exercises 6.6
6.7 * Review
6.8 * Projects
Part 1. Wallis 's Formula
Part 2. Euler's Summation Formula
Part 3. Laplace Transforms
Part 4. Inverse Laplace Transforms
7 Infinite Series
7.1 Convergence
Exercises 7.1
7.2 Tests for Convergence
Exercises 7.2
7.3 Ratio and Root Tests
Exercises 7.3
7.4 Absolute and Conditional Convergence
Exercises 7.4
7.5* Review
7.6 * Projects
Part 1. Summation by Parts
Part 2. Multiplication of Series
Part 3. Infinite Products
Part 4. Cantor Set
8 Sequences and Series of Functions
8.1 Pointwise Convergence
Exercises 8.1
8.2 Uniform Convergence
Exercises 8.2
8.3 Properties of Uniform Convergence
Exercises 8.3
8.4 Pointwise and Uniform Convergence of Series
Exercises 8.4
8.5 Power Series
Exercises 8.5
8.6 Taylor Series
Exercises 8.6
8.7 * Review
8.8 * Projects
Part 1. Limit Superior
Part 2. Irrationality of e
Part 3. An Everywhere Continuous but Nowhere Differentiable Function
Part 4. Equicontinuity
9 Vector Calculus
9.1* Cartesian Coordinates in R^3
Exercises 9.1
9.2* Vectors in R^3
Exercises 9.2
9.3* Dot Product and Cross Product
Exercises 9.3
9.4 Parametric Equations
Exercises 9.4
9.5* Lines and Planes in R^3
Exercises 9.5
9.6 Vector-Valued Functions
Exercises 9.6
9.7 Arc Length
Exercises 9.7
9.8 * Review
9.9 * Projects
Part 1. Inner Product
Part 2. Polar Coordinates
Part 3. Cantor Function
10 Functions of two Variables
10.1 Basic Topology
Exercises 10.1
10.2 Limits and Continuity
Exercises 10.2
10.3 Partial Derivatives
Exercises 10.3
10.4 Differentiation
Exercises 10.4
10.5 Directional Derivative
Exercises 10.5
10.6 Chain Rule
Exercises 10.6
10.7* Review
10.8* Projects
Part 1. Operator Method for Solving Differential Equations
Part 2. Separable and Homogeneous First-Order Differential Equations
11 Multiple Integration
11.1 Double Integral
Exercises 11.1
11.2 Iterated Integrals
Exercises 11.2
11.3 Integrals Over General Regions
Exercises 11.3
11.4 Line Integrals
Exercises 11.4
11.5 Vector Fields and Work Integrals
Exercises 11.5
11.6 Gradient Vector Field
Exercises 11.6
11.7 Green's Theorem
Exercises 11.7
11.8 * Stokes's and Gauss's Theorems
Exercises 11.8
11.9* Review
11.10* Projects
Part 1. Change of Variables for Double Integrals
Part 2. Exact Equations
Hints and Solutions to Selected Exercises
Greek Alphabet
Index of Symbols
Index

<p><p>this Book Is Designed To Be An Easily Readable, Intimidation-free Guide To Advanced Calculus. Ideas And Methods Of Proof Build Upon Each Other And Are Explained Thoroughly. This Is The First Book To Cover Both Single And Multivariable Analysis In Such A Clear, Reader-friendly Setting. Chapter Topics Cover Sequences, Limits Of Functions, Continuity, Differentiation, Integration, Infinite Series, Sequences And Series Of Functions, Vector Calculus, Functions Of Two Variables, And Multiple Integration. For Individuals Seeking Math Fun At A Higher Level. <p></p>

Designed for undergraduate courses in advanced calculus and real analysis, this book is an easily readable, intimidation-free advanced calculus textbook. Ideas and methods of proof build upon each other and are explained thoroughly

2014-03-22