Multivariable Calculus, Applications and Theory

Starts with the necessary linear algebra and then uses it as a framework upon which to build multivariable calculus. Many applications are presented, some of these are very difficult but worthwhile. Hard sections are starred in the table of contents.

**Tag(s):**
Mathematics

**Publication date**: 19 Aug 2011

**ISBN-10**:
n/a

**ISBN-13**:
n/a

**Paperback**:
466 pages

**Views**: 20,254

Multivariable Calculus, Applications and Theory

Starts with the necessary linear algebra and then uses it as a framework upon which to build multivariable calculus. Many applications are presented, some of these are very difficult but worthwhile. Hard sections are starred in the table of contents.

Update 02/07/2017:

The original book's URL at Kenneth Kutler's homepage in the Department of Mathematics at Brigham Young University is no longer accessible. There are other copies lying around the internet, but I couldn't be sure about the legality of these copies. Thus, I decided not link to them and remove this book entry instead.

Update 10/08/2017:

The book has been made publicly accessible again at Kenneth Kutler's homepage in the Department of Mathematics at Brigham Young University. The download link has been updated.

Excerpts from the Introduction:

Multivariable calculus is just calculus which involves more than one variable. To do it properly, you have to use some linear algebra. Otherwise it is impossible to understand. This book presents the necessary linear algebra and then uses it as a framework upon which to build multivariable calculus. This is not the usual approach in beginning courses but it is the correct approach, leaving open the possibility that at least some students will learn and understand the topics presented. For example, the derivative of a function of many variables is a linear transformation. If you don't know what a linear transformation is, then you can't understand the derivative because that is what it is and nothing else can be correctly substituted for it. The chain rule is best understood in terms of products of matrices which represent the various derivatives. The concepts involving multiple integrals involve determinants. The understandable version of the second derivative test uses eigenvalues, etc.

The purpose of this book is to present this subject in a way which can be understood by a motivated student. Because of the inherent difficulty, any treatment which is easy for the majority of students will not yield a correct understanding. However, the attempt is being made to make it as easy as possible.

Many applications are presented. Some of these are very difficult but worthwhile. Hard sections are starred in the table of contents. Most of these sections are enrichment material and can be omitted if one desires nothing more than what is usually done in a standard calculus class. Stunningly difficult sections having substantial mathematical content are also decorated with a picture of a battle between a dragon slayer and a dragon, the outcome of the contest uncertain. These sections are for fearless students who want to understand the subject more than they want to preserve their egos. Sometimes the dragon wins.

The original book's URL at Kenneth Kutler's homepage in the Department of Mathematics at Brigham Young University is no longer accessible. There are other copies lying around the internet, but I couldn't be sure about the legality of these copies. Thus, I decided not link to them and remove this book entry instead.

Update 10/08/2017:

The book has been made publicly accessible again at Kenneth Kutler's homepage in the Department of Mathematics at Brigham Young University. The download link has been updated.

Excerpts from the Introduction:

Multivariable calculus is just calculus which involves more than one variable. To do it properly, you have to use some linear algebra. Otherwise it is impossible to understand. This book presents the necessary linear algebra and then uses it as a framework upon which to build multivariable calculus. This is not the usual approach in beginning courses but it is the correct approach, leaving open the possibility that at least some students will learn and understand the topics presented. For example, the derivative of a function of many variables is a linear transformation. If you don't know what a linear transformation is, then you can't understand the derivative because that is what it is and nothing else can be correctly substituted for it. The chain rule is best understood in terms of products of matrices which represent the various derivatives. The concepts involving multiple integrals involve determinants. The understandable version of the second derivative test uses eigenvalues, etc.

The purpose of this book is to present this subject in a way which can be understood by a motivated student. Because of the inherent difficulty, any treatment which is easy for the majority of students will not yield a correct understanding. However, the attempt is being made to make it as easy as possible.

Many applications are presented. Some of these are very difficult but worthwhile. Hard sections are starred in the table of contents. Most of these sections are enrichment material and can be omitted if one desires nothing more than what is usually done in a standard calculus class. Stunningly difficult sections having substantial mathematical content are also decorated with a picture of a battle between a dragon slayer and a dragon, the outcome of the contest uncertain. These sections are for fearless students who want to understand the subject more than they want to preserve their egos. Sometimes the dragon wins.

Tweet

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.

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
Rexx
Microsoft .NET
Perl
PHP
R
Python
Rebol
Ruby
Scheme
Tcl/Tk

Miscellaneous
Sponsors