Calculus with Sage

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About this book: http://matrix.skku.ac.kr/Cal-Book/Web-Cover/index.htm

http://matrix.skku.ac.kr/cal-lab/Math-CAS.htm

Main Author : Sang-Gu Lee

Co-Authors : Eung-Ki Kim, Yoonmee Ham, Ajit Kumar, Robert A. Beezer, Quoc-Phong Vu,

Lois S. Simon, Suk-Geun Hwang, J.-D. Sim, ... (not more than 10)

Reviewers : Hyunsoo Kim, L. Shapiro, R. Sakthivel, K. Das, I. Hwang, J. Lee, ... (more than 10)

Calculus is the mathematical foundation for much of university mathematics, science, and engineering curriculum. For the mathematics student, it is a first exposure to rigorous mathematics. For the engineer, it is an introduction to the modeling and approximation techniques used throughout an engineering curriculum. And for the future scientist, it is the mathematical language that will be used to express many of the most important scientific concepts.

In the first part, that is for the beginners of calculus, we start with differential and integral calculus on functions of single variable and then study L'Hospital's theorem, concavity, convexity, inflection points, optimization problems, ordinary differential equations as applications of differential and integral calculus, parameter equations, polar coordinates, infinite sequences and infinite series accordingly. In the second part of calculus, we cover vector calculus that includes vectors, coordinate space, partial derivatives and multiple integrals. Concepts, definitions, terminology, and interpretation in calculus should be as current as possible. This book has many problems presenting calculus as the foundation of modern mathematics, science and engineering.

Many recent calculus textbooks are using Computer Algebra System (CAS) including a variety of visual tools in it. But in most cases its use by students is limited. Therefore, for this book, we have adapted a wonderful free and open-source program, Sage. With the new learning environment of universities, students will take a full advantage of 21st century state of the art technology to learn calculus easily and be better prepared for future careers. We can use Sage easily on popular web browsers such as Firefox or Chrome.

More content and related materials will be added to be viewed on the web. When you see or web address in the book, this means you will be able to find relevant information by clicking on the http://math1.skku.ac.kr/ address. This will save you a lot of work.

Finally, we would like to emphasize that a project of writing a calculus textbook which involves the use of technology and reflects the established traditions of teaching calculus as well as recent reforms team of dedicated people, and our effort is not an exception. We appreciate the valuable contributions of many of our colleagues to the project of writing this book.

2013. 8. 5.

CONTENTS

Introduction

Part I Single Variable Calculus

Chapter 1. Functions

Chapter 2. Limits and Continuity

Chapter 3. Derivatives

Chapter 4. Applications of Derivatives

Chapter 5. Integrals

Chapter 6. Applications of Integration

Chapter 7. Techniques of Integration

Chapter 8. Further Applications of Integration