Calculus Without Limits

Introduces differentiability as a local property without using limits. The course is designed for life science majors who have a precalculus background, and whose primary interest lies in the applications of calculus.

**Tag(s):**
Mathematics

**Publication date**: 05 Jul 1999

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
n/a

**Views**: 16,205

**Type**: N/A

**Publisher**:
n/a

**License**:
n/a

**Post time**: 02 Nov 2009 04:28:00

Calculus Without Limits

Introduces differentiability as a local property without using limits. The course is designed for life science majors who have a precalculus background, and whose primary interest lies in the applications of calculus.

License Reminder:

Excerpts from the Book:

Karl Heinz Dovermann wrote:(C)Copyright 1999 by the author. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior written permission of the author. Printed in the United States of America.

Excerpts from the Book:

Karl Heinz Dovermann wrote:These notes are written for a one-semester calculus course which meets three times a week and is, preferably, supported by a computer lab. The course is designed for life science majors who have a precalculus background, and whose primary interest lies in the applications of calculus. We try to focus on those topics which are of greatest importance to them and use life science examples to illustrate them. At the same time, we try of stay mathematically coherent without becoming technical. To make this feasible, we are willing to sacrifice generality. There is less of an emphasis on by hand calculations. Instead, more complex and demanding problems find their place in a computer lab. In this sense, we are trying to adopt several ideas from calculus reform. Among them is a more visual and less analytic approach. We typically explore new ideas in examples before we give formal definitions.

In one more way we depart radically from the traditional approach to calculus. We introduce differentiability as a local property without using limits. The philosophy behind this idea is that limits are the a big stumbling block for most students who see calculus for the first time, and they take up a substantial part of the first semester. Though mathematically rigorous, our approach to the derivative makes no use of limits, allowing the students to get quickly and without unresolved problems to this concept. It is true that our definition is more restrictive than the ordinary one, and fewer functions are differentiable in this manuscript than in a standard text. But the functions which we do not recognize as being differentiable are not particularly important for students who will take only one semester of calculus. In addition, in our opinion the underlying geometric idea of the derivative is at least as clear in our approach as it is in the one using limits.

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