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)
2013 Midterm Exam of Calculus 2 (pdf)
2013 Final Exam of Calculus 2 (pdf)
Calculus 1 http://matrix.skku.ac.kr/PBL/
Calculus 2 http://matrix.skku.ac.kr/PBL2/
Calculus Lab http://matrix.skku.ac.kr/Lab-Book/Sage-Lab-Manual-1.htm
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/
PS: Dear Ajit and Abhijit Champanerkar,