Mathematical Analysis I

Covers the basic topics of undergraduate real analysis.

**Tag(s):**
Mathematics

**Publication date**: 01 May 2004

**ISBN-10**:
193170502X

**ISBN-13**:
n/a

**Paperback**:
355 pages

**Views**: 30,507

Mathematical Analysis I

Covers the basic topics of undergraduate real analysis.

:santagrin: This book was suggested by Bradley Lucier

Book excerpts:

This text covers the basic topics of undergraduate real analysis including metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. The text also contains background material on set theory, the real numbers (including consequences of the completeness axiom), and Euclidean and vector spaces, taken from the author's Basic Concepts of Mathematics.

This text is designed to be used as early as possible in the undergraduate curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

Intended Audience:

This text is appropriate for any undergraduate course in real analysis or mathematical analysis, or for a preparatory class for beginning graduate students who will later advance to courses in measure theory and functional analysis. Lecturers can use the author's Basic Concepts of Mathematics, which contains expanded versions of Chapters 1 and 2 and Sections 1 through 10 of Chapter 3 of the present text, as supplementary background material for this text.

Reviews:

theassayer.org

Book excerpts:

This text covers the basic topics of undergraduate real analysis including metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. The text also contains background material on set theory, the real numbers (including consequences of the completeness axiom), and Euclidean and vector spaces, taken from the author's Basic Concepts of Mathematics.

This text is designed to be used as early as possible in the undergraduate curriculum; indeed, it was used for many years as the text for a two-semester class for second-year mathematics majors at the University of Windsor. If desired, the material can easily be specialized to n-dimensional (or even two-dimensional) Euclidean space.

Intended Audience:

This text is appropriate for any undergraduate course in real analysis or mathematical analysis, or for a preparatory class for beginning graduate students who will later advance to courses in measure theory and functional analysis. Lecturers can use the author's Basic Concepts of Mathematics, which contains expanded versions of Chapters 1 and 2 and Sections 1 through 10 of Chapter 3 of the present text, as supplementary background material for this text.

Reviews:

theassayer.org

:) "Zakon's 'Mathematical Analysis I' will show you how easy somethings can be by presenting the material in a nice, kind and very clear way with examples and everything you could expect to get a solid background on the subject. "

Tweet

About The Author(s)

No information is available for this author.

Book Categories

Computer Science
Introduction to Computer Science
Introduction to Computer Programming
Algorithms and Data Structures
Artificial Intelligence
Computer Vision
Machine Learning
Neural Networks
Game Development and Multimedia
Data Communication and Networks
Coding Theory
Computer Security
Information Security
Cryptography
Information Theory
Computer Organization and Architecture
Operating Systems
Image Processing
Parallel Computing
Concurrent Programming
Relational Database
Document-oriented Database
Data Mining
Big Data
Data Science
Digital Libraries
Compiler Design and Construction
Functional Programming
Logic Programming
Object Oriented Programming
Formal Methods
Software Engineering
Agile Software Development
Information Systems
Geographic Information System (GIS)

Mathematics
Mathematics
Algebra
Abstract Algebra
Linear Algebra
Number Theory
Numerical Methods
Precalculus
Calculus
Differential Equations
Category Theory
Proofs
Discrete Mathematics
Theory of Computation
Graph Theory
Real Analysis
Complex Analysis
Probability
Statistics
Game Theory
Queueing Theory
Operations Research
Computer Aided Mathematics

Supporting Fields
Web Design and Development
Mobile App Design and Development
System Administration
Cloud Computing
Electric Circuits
Embedded System
Signal Processing
Integration and Automation
Network Science
Project Management

Operating System
Programming/Scripting
Ada
Assembly
C / C++
Common Lisp
Forth
Java
JavaScript
Lua
Microsoft .NET
Rexx
Perl
PHP
Python
R
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors