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Laboratory Manual for Calculus with Sage
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274
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978-89-6105-557-4
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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 his engineering curriculum. And for future scientist, it is the mathematical language that will be used to express many of the most important scientific concepts.
In the first semester, that¡¯s 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, and ordinary differential equations as applications of differential and integral calculus accordingly. In the second semester of calculus, we cover vector calculus that includes parameter equations, polar coordinates, infinite sequences and infinite series, vectors and coordinate space which uses partial derivatives. Modeling and approximation in calculus should resemble the techniques and methods currently in use. Concepts, definitions, terminology, and interpretation in calculus should be as current as possible. This booklet has many problems to present calculus as the foundation of modern mathematics, science and engineering.
This booklet is a Lab Manual for Calculus with Sage-Math. Most of recent calculus textbooks are using Computer Algebra System(CAS) including a variety of visual tools in it. But its use was limited to students in most of cases. Therefore, in this book, we adapted a wonderful open-source program, SAGE, for our students.
With the new learning environment of universities, students will take a full advantage of 21C state of arts technology to learn calculus more easily and get better prepared for future job market. We can use the Sage-Math well 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 CAS or Web mark in the book, which means you will be able to find relevant informations by clicking
http://math1.skku.ac.kr/
address. That will save lots of your work.
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Calculus I
Chapter 1. Functions 1
Chapter 2. Limits and Continuity 11
Chapter 3. Theory of Differentiation 21
Chapter 4. Applications of Differentiation 39
Chapter 5. Integrals 63
Chapter 6. Applications of Integration 81
Chapter 7. Techniques of Integration 101
Calculus II
Chapter 8. Further Applications of Integration 123
Chapter 9. Parametric Equations and Polar Coordinates 133
Chapter 10. Infinite Sequences and infinite Series 163
Chapter 11. Vectors and the Geometry of Space 183
Chapter 12. Partial Derivatives and Local Maxima and Minima 211
Chapter 13. Vector Functions 213
Chapter 14. Vector Calculus 233
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