OSAKA UNIV. CBCMP

OSAKA UNIVERSITY CHEMISTRY - BIOLOGY COMBINED MAJOR PROGRAM

Mathematics 1

Outline

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

differentiation and integration and their basic applications. We start from

to introduce elementary functions such as trigonometric, exponential, logarithmic,

inverse trigonometric and hyperbolic functions and will learn their derivatives

and integration. Limits of functions, the convergence of sequences, Newton’s

method and Taylor expansions, length of curves, area and volume of revolutions

will also be covered.

 

1. Numbers and Functions,
2. Trigonometric functions, Inverse trigonometric functions
3. Exp-Log functions and Hyperbolic functions
4. Differentiation 1 (Definition, product rule, quotient rule, chain rule)
5. Differentiation 2 (Derivatives of Inverse function and implicit function)
6. L’ Hospital’s rule and Graph sketching
7. Intermediate value theorem, Mean value theorm
8. Polynomial equation and Newton’s method
9. Power series, Taylor expansion
10. Integration 1 (Definition, Fundamental theorem of calculus)
11. Integration 2 (Change variables, Integration by parts)
12. Integration 3 (Infinite integral)
13. Computation of Length, Area and Volume
14. Fourier expansions
15. Ordinary differential equations
16. Final Examination

 

This class is half of a joint class, together with “Exercise Session (Mathematics)”. Students must take both classes together.

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

Kentaro Ihara

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