One Variable Advanced Calculus

A treatment for a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work. It is assumed the reader is familiar enough with elementary functions.

**Tag(s):**
Mathematics

**Publication date**: 09 Mar 2014

**ISBN-10**:
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**ISBN-13**:
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**Paperback**:
287 pages

**Views**: 13,818

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**Post time**: 12 Apr 2008 10:14:26

One Variable Advanced Calculus

A treatment for a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work. It is assumed the reader is familiar enough with elementary functions.

Excerpts from the Introduction:

The difference between advanced calculus and calculus is that all the theorems are proved completely and the role of plane geometry is minimized. Instead, the notion of completeness is of preeminent importance. Silly gimmicks are of no significance at all. Routine skills involving elementary functions and integration techniques are supposed to be mastered and have no place in advanced calculus which deals with the fundamental issues related to existence and meaning. This is a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work.

Intended Audience:

An orderly development of the elementary functions is included but it is assumed the reader is familiar enough with these functions to use them in problems which illustrate some of the ideas presented.

The difference between advanced calculus and calculus is that all the theorems are proved completely and the role of plane geometry is minimized. Instead, the notion of completeness is of preeminent importance. Silly gimmicks are of no significance at all. Routine skills involving elementary functions and integration techniques are supposed to be mastered and have no place in advanced calculus which deals with the fundamental issues related to existence and meaning. This is a subject which places calculus as part of mathematics and involves proofs and definitions, not algorithms and busy work.

Intended Audience:

An orderly development of the elementary functions is included but it is assumed the reader is familiar enough with these functions to use them in problems which illustrate some of the ideas presented.

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About The Author(s)

Kenneth Kuttler is Professor in the Department of Mathematics at Brigham Young University. His primary area of research is Partial Differential Equations and Inclusions. He works on abstract methods for determining whether problems of this sort are well posed. Lately, he has been working on the mathematical theory of problems from contact mechanics including friction, wear, and damage. He has also been studying extensions to stochastic equations and inclusions.

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