OSAKA UNIV. CBCMP

OSAKA UNIVERSITY CHEMISTRY - BIOLOGY COMBINED MAJOR PROGRAM

Mathematics 2

Outline

In this class, the students will learn the basic concept and techniques on

differentiation and integration for several variables functions

and their basic applications . We will start from a geometry of vectors,

and learn partial derivatives, gradient vectors, directional derivatives,

tangent planes, maximum/minimum. Further, line integrals, multiple integral

(mainly in case of 2-variable functions), the Green’s theorem will also be covered.

 

1. Introduction
2. Geometry of vectors I
3. Geometry of vectors II
4. Graphs of several variable functions
5. Partial derivatives
6. Gradients and tangent planes
7. Directional derivatives
8. Exercise Session
9. Chain rules
10. Maximum/Minimum, Lagrange’s method
11. Curve integrals I
12. Curve integrals II
13. Double integrals I
14. Double integrals II

15. Green’s Theorem

 

Textbook

Reference:

H. Jerome Keisler/Elementary Calculus—An infinitesimal approach, 3rd Edition/Dover/ISBN13: 978-0-486-48452-5

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Grading

Attendance 10 percents

Assignments  20 percents

Mid Examination 35 Percents

Final Examination  35 percents

Instructor

Associate Professor, International College

Yuuki Shiraishi

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