FreeComputerBooks.com
Links to Free Computer, Mathematics, Technical Books all over the World


 Title Mathematical Background: Foundations of Infinitesimal Calculus
 Author(s) Keith Duncan Stroyan
 Publisher: University of Iowa
 eBook PDF, 182 pages, 1.6 MB
 Language: English
 ISBN10: N/A
 ISBN13: N/A
 Share This:
Book Description
This book of mathematical 'background' shows how to fill in the mathematical details of the main topics from the course. These proofs are completely rigorous in the sense of modern mathematics  technically bulletproof.
We wrote this book of foundations in part to provide a convenient reference for a student who might like to see the "theorem  proof" approach to calculus.
This book also shows how the pathologies arise in the traditional approach (we left pointwise pathology out of the main text, but present it here for the curious and for comparison). Perhaps only math majors ever need to know about these sorts of examples, but they are fun in a negative sort of way.
About the Authors Keith Duncan Stroyan an American mathematician, currently professor at University of Iowa.
 Mathematical Logic  Set Theory, Model Theory, Computability, etc
 Calculus and Mathematical Analysis
 Mathematics
 Mathematical Background: Foundations of Infinitesimal Calculus (K. Stroyan)
 The Mirror Site (1)  PDF

Nonstandard Analysish (Jaap Ponstein, et al.)
This book is concerned with an attempt to introduce the infinitesimals and the other 'nonstandard' numbers in a naive, simpleminded way. Nevertheless, the resulting theory is hoped to be mathematically sound, and to be complete within obvious limits.

Yet Another Calculus Text: A Short Introduction with Infinitesimals
An introduction to calculus based on the hyperreal number system so it uses infinitesimal and infinite numbers freely. It aims primarily at readers who already have some familiarity with calculus.

Elementary Calculus: An Infinitesimal Approach (H. Jerome Keisler)
This firstyear calculus book is centered around the use of infinitesimals. It contains all the ordinary calculus topics, including the basic concepts of the derivative, continuity, and the integral, plus traditional limit concepts and approximation problems.

Foundations of Infinitesimal Calculus (H. Jerome Keisler)
This monograph is a companion to the Author's textbook. It can be used as a quick introduction to the infinitesimal approach to calculus for mathematicians, as background material for instructors, or as a text for an undergraduate seminar.

Introduction to Mathematical Analysis (Beatriz Lafferriere, et al)
The goal of this book is to provide students with a strong foundation in mathematical analysis. Such a foundation is crucial for future study of deeper topics of analysis. It will be reinforced through rigorous proofs.

Elementary Calculus (Michael Corral)
This textbook covers calculus of a single variable, is designed for students who have completed courses in highschool algebra, geometry, and trigonometry. Though designed for college students, it could also be used in high schools.

Calculus (Gilbert Strang)
This highly regarded calculus textbook is ideal as for selfstudy. Examples of apps of calculus to physics, engineering and economics are included, as well as many practice questions and illustrative diagrams to assist the reader's grasp of the material.

Applied Analysis (John K. Hunter, et al)
This book provides an introduction to those parts of analysis that are most useful in applications for graduate students. The material is selected for use in applied problems, and is presented clearly and simply but without sacrificing mathematical rigor.

Calculus: Theory and Applications (Kenneth Kuttler)
This is a book on single variable calculus including most of the important applications of calculus. It also includes proofs of all theorems presented, either in the text itself, or in an appendix. It also contains an introduction to vectors and vector products.

Advanced Calculus (Lynn H. Loomis, et al)
Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking.

Active Calculus (Matt Boelkins)
Rather than detailed explanations and worked out examples, this book uses activities intended to be done by the students in order to present the standard concepts and computational techniques of calculus.

Calculus (WikiBooks)
This wikibook aims to be a high quality calculus textbook through which users can master the discipline. Standard topics such as limits, differentiation and integration are covered, as well as several others.

Precalculus: An Investigation of Functions (David Lippman, et al)
Comprehensive and evenly paced, this book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas.
:






















