CONTENTS

Introduction

Part I   Single Variable Calculus

Part II  Multivariate Calculus

Main Author : Sang-Gu Lee

Co-Authors : Eung-Ki Kim, Yoonmee Ham, Ajit Kumar, Robert Beezer, Quoc-Phong Vu, Lois Simon, Suk-Geun Hwang.

Reviewers : Hyunsoo Kim, Jaedong Sim, Insung Hwang, Mohit Kumbhat, L. Shapiro, R. Sakthivel, K. Das,  Victoria Lang, ... .

Calculus is the mathematical foundation for much of the university curriculum in mathematics, science, and engineering. For the student of mathematics, it is often their first exposure to rigorous mathematics. For the future engineer, it is an introduction to the modeling and approximation techniques used throughout the engineering curriculum. It is the mathematical language that expresses many fundamental important concepts in science.

We begin our study of differential and integral calculus with functions of a single variable and topics such as L'Hospital's theorem, concavity, convexity, inflection points, optimization, simple ordinary differential equations, parametric equations, polar coordinates, infinite sequences and infinite series. We then turn to multivariate and vector calculus, covering vector-valued functions, coordinate systems, partial derivatives and multiple integrals. This book has many problems presenting calculus as the foundation of modern mathematics, science and engineering, using concepts, definitions, terminology, and interpretation of the given situation.

Many of today's calculus textbooks use computer algebra systems (CAS) and a variety of visualization tools. But in most cases, use of these aids by students is limited. Therefore, we have adopted the usage of a wonderful free and open-source mathematics visualization program, Sage. With the new learning environment at many universities, students can take full advantage this 21st-century, state-of-the-art technology to learn calculus easily in preparation for their future careers in any applicable area. Sage can be accessed easily on any web browser, without the need for additional software installation, and on smaller devices like tablets and smartphones. More content and related materials will be continually added to the website for the book. So when you see  CAS(             ) or a web address in the book, you will be able to find relevant information from http://matrix.skku.ac.kr/Cal-Book/   and http://math1.skku.ac.kr/  . This will save you from the burden of entering new examples manually, and you can quickly edit existing examples to explore new and varied problems.

Finally, we would like to emphasize that the creation of a technology-rich calculus textbook, which also reflects both the established traditions of calculus instruction and recent reforms, requires a team of dedicated people. Our effort is no exception. We greatly appreciate the valuable contributions of many of our colleagues to this project and the efforts of hundreds of contributors to the Sage software project as well. Good Job!! We also thanks to Hyunsoo Kim, Jaedong Sim, Insung Hwang, Mohit Kumbhat, L. Shapiro, R. Sakthivel, K. Das, Victoria Lang and  every mathematics professors at Sungkyunkwan university who carefully reviewed the preprint of this book for years.

2014. 2. 1.

2014 Midterm Exam of  Calculus(pdf)

2014 Final Exam of  Calculus(pdf)

2013 Midterm Exam of  Calculus(pdf)

2013 Final Exam of  Calculus(pdf)

Appendix

Calculus 1   http://matrix.skku.ac.kr/PBL/

Calculus 2  http://matrix.skku.ac.kr/PBL2/

Index

Copyright @ 2013 SKKU Matrix Lab.

Internet resources :

(New) Mobile Sage Grapher : http://matrix.skku.ac.kr/Mobile-Sage-G/sage-grapher.html

(New) Linear Algebra with Sage : http://matrix.skku.ac.kr/LA-Lab/

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From: Sang-Gu Lee
Sent: Wednesday, February 26, 2014 10:51 AM
Subject: Dear Manager at KyungMoonSa, Mr. Jong-Won KIM,

Dear Manager at KyungMoonSa, Mr. Jong-Won KIM, wean5895@empal.com

Hi~~
...  your new book < CALCULUS : ISBN 978-89-6105-458-4> ...

>>> Title: Calculus
>>> Publisher : KyungMoonSa,  S. Korea, ISBN 978-89-6105-458-4, 2014
Main Author : Sang-Gu Lee
Co-Authors : Eung-Ki Kim, Yoonmee Ham, Ajit Kumar, Robert Beezer, Quoc-Phong Vu, Lois Simon, Suk-Geun Hwang.
>>> The book is in color, 948 pages and cost in Korea is \$38.
http://matrix.skku.ac.kr/Cal-Book/
Cyberlab Manual : http://matrix.skku.ac.kr/Lab-Book/Sage-Lab-Manual.htm

Would you take a look on the following and reply to Prof. Abhijit Champanerkar.
I hope you let him know how he can order a book.

So he can directly order a book “ Title: Calculus (with Sage) ISBN 978-89-6105-458-4”

( I hope (sooner or later) you can make that one can order a book through the Amazon.com )

Best wishes,

Sang-Gu LEE
E-Mail : sglee at skku.edu  TEL : 82-31-290-7025, FAX : 82-31-290-7033

PS: Dear Ajit and Abhijit Champanerkar,

Hi. Thanks for your interest on the following book~~

>>> Title: Calculus
>>> Publisher : KyungMoonSa,  S. Korea, ISBN 978-89-6105-458-4, 2014
Main Author : Sang-Gu Lee
Co-Authors : Eung-Ki Kim, Yoonmee Ham, Ajit Kumar, Robert Beezer, Quoc-Phong Vu, Lois Simon, Suk-Geun Hwang.
>>> The book is in color, 948 pages and cost in Korea is \$38.
http://matrix.skku.ac.kr/Cal-Book/
Cyberlab Manual : http://matrix.skku.ac.kr/Lab-Book/Sage-Lab-Manual.htm

Also you may directly order a book to  Manager at KyungMoonSa, Mr. Jong-Won KIM  wean5895@empal.com    know your mailing address sooner or later.

Best wishes,
Sang-Gu

---------- Forwarded message ----------
From: Abhijit
Date: Tue, Feb 25, 2014 at 10:28 PM
Subject: Re: CALCULUS using SAGE
To: ...

Your book is really interesting and I want to see it for to try to use it in our calc lab.

Could you ask your publisher how I can get it in US.
I will email/contact the company once I know whom to contact.
They will respond to you much favourably than to me.

Abhijit

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Subject: Re: CALCULUS using SAGE

Congrats! Great to hear about it.

Regards,

Vikram
*****************************
Subject: Re: CALCULUS using SAGE

Hello
Glad to know that in the book open source software like Sage has been used.
I strongly believe that it will definitely help to give clarity of the subject to the students community.

Great work!
-Manjusha

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Subject: Re: CALCULUS using SAGE

Congrats on the release of your new book on Calculus. Looking forward to seeing a copy.
With best regards
George
*****************************
From: Vishnu Namboothiri K

Excellent! Hope to see the Indian version coming out soon.
Is a soft copy of the first few pages atleast available with you?

is the webpage http://matrix.skku.ac.kr/Cal-Book/ associated with one of the authors?

Regards

Vishnu
*******************************

Congrats. Great to know about it.

regards

Shanta
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> On Tue, Feb 25, 2014 at 8:53 AM, Abhijit cabhijit@gmail.com wrote:
>> Congratulations ~~
>>
>> How can I buy this in US ?
>>
>> Abhijit