Syllabus system

2005年度上智大学シラバス

◆COLLEGE MATHEMATICS　－　（前）

NAGATA KIYOSHI

○講義概要

In this course, we aim to learn the essential concept and techniques of calculus by studying applications to topics in different areas.

○評価方法

出席状況(20%)、授業参画(10%)、前期学期末試験(定期試験期間中)(25%)、中間試験(20%)、小テスト等(25%)

○テキスト

Larry J. Goldstein/ David C. Lay/ David I. Schneid『Calculus and Its Applications』 Prentice Hall/Eigth Edition

○他学部・他学科生の受講

可

○授業計画

1	0. IntroductionNumbers, Equality and Inequalities, Interval notation, Monomials and Polynomials, Arithmetic of polynomials, etc.
2	1.Functions Properties of functions, Domain and range of value.
3	Some important functions: Linear functions, absolute value functions, positive and negative functions, composition of functions.
4	Zeros of functions: factorization and quadratic formula.
5	Exponents and Power functions.
6	Functions and Graphs of functions.
7	2. The DerivativeThe Slope of a Straight line. The Equation of Scant lines.
8	Intuitive approach of limit. Algebraic technique for evaluating limits.
9	Calculating some kind of limits.
10	Continuous functions. Differentiable functions.
11	Limits and the Derivatives.
12	Some Rules for Differentiation.
13	Calculation of Differential of some functions.
14	Calculation of Differential of some more functions.
15	The Derivatives as a Rate of Change.
16	4. Applications of the derivative Describing Graphs of functions.
17	The First, Second and n-th Derivative.
18	Curve Sketching (using first derivative).
19	Curve Sketching (using first and second derivative).
20	Curve Sketching (considering asymptote lines).
21	Relative maximum point and relative minimum point.
22	Optimization Problems.
23	Optimization Problems.
24	Applications of Calculus to Business and Economics.
25	5. The Exponential and Natural Logarithm Functions. Definitions of Exponential and Natural Logarithm functions.Inverse functions and their Derivatives.
26	Derivatives of Exponential and Natural Logarithm functions.
27	6. Applications of the Exponential and Natural Logarithm functions. Exponential Growth and Decay. Compound Interest.
28	Applications of the Natural Logarithm functions to Economics.