Calculus

Lecture 1

Advanced Mathematics

CALCULUS(微积分)

For Business, Economics, and the Social and Life Sciences

Calculus

Algebra

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Overview

Functions(函数) Limits (极限) Differentiation (微分) Integration (积分)

Calculus Object Tool

Contents

Part I. Part II. Differentiation (Ch2) Applications of Differentiation (Ch3)

Part III. Integration (Ch5) Part IV. Techniques of Integration (Ch6)

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Outline

Part I. Review of functions and graphs (1.1---1.4)

Chapter 1 Functions, Graphs, Functions Graphs and Limits

Part II. Limits (1.5 ) Part III. Continuity (1.6)

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1

Lecture 1

Function

1.1-1.4 Review of Functions and Graphs

OBJECTIVE Review of elementary functions; Functions used in economics; Break-even Analysis;

A function is a correspondence between a first set, called the domain, and a second set, called the range, such that each member of the domain corresponds to exactly one member of the range.

Figure 1.1

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Interpretations of the function f(x).

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Example 1: Determine whether or not each

correspondence is a function. a) Microsoft Stock Domain July 14, 2011 July 15, 2011 July 16, 2011 July 17, 2011 This relationship is a function because each member of the b f h domain corresponds to only one member of the range.

Example 1 (continued):

b) Squaring Domain 3 4 5 –5 Range 9 16 25

Range $27.23 $27.36 $27.27 $27.50

This relationship is a function because each member of the domain corresponds to only one member of the range, even though two members of the domain correspond to 25.

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Finding Domain and Range

Example 1 (concluded):

c) Baseball Teams Domain Arizona Chicago Baltimore li Range Diamondbacks Cubs White Sox Orioles i l

Example 2: Find the domain: (1). f ( x) =

3 ; 2x − 5

(2). f ( x) = 4 + 3 x .

(1). The domain of f is {x| x is a real number and x ≠ 5/2}

(2). 4 + 3x ≥ 3x ≥ x 0

This...