Preliminaries

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Calculus and Analytic Geometry

Preliminaries

	Learning Objectives
After reading this chapter, you are expected to learn about: Meaning and pronunciation of frequently used symbols. Additive and multiplicative properties of real numbers Definition of absolute value and intervals Definition and graphs of function

INTRODUCTION

Calculus is the mathematics of motion and change. Where there is a motion or growth, where variable forces are at work producing acceleration, calculus is what is applied there and this was the beginning of the subject.

Before we start with the actual course, it is essential that we fulfil some prerequisites. In this chapter, we revise the properties of real numbers and absolute values. Further, we define the notion of intervals and neighbourhoods that are special subsets of real numbers. We shall also revise functions, their types and graphs.

SYMBOLS AND NOTATIONS

As Mathematics is a language of symbols, in the course of Calculus, we will come across many symbols and notations. So let us first tabulate those, which are frequently used.

Symbol	Meaning (+ pronunciation)
[math] \forall [/math]	for all, for every
[math] \exists [/math]	there exists
[math] \in [/math]	belongs to
[math] \notin [/math]	does not belong to
[math] \ni [/math]	such that
iff or [math]\Leftrightarrow[/math]	if and only if
[math] \Rightarrow [/math]	implies
ε	epsilon
δ	delta
nbd	neighbourhod
N(a,δ)	δ − nbd of a or (a − δ,a + δ)
N * (a,δ)	deleted δ − nbd of a or (a − δ,a + δ) − {a}
[math] \mathbb{R}^{+} [/math]	positive real numbers

Case Study

Case 1

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Case Study

Understanding Government Tax Policy

Results

True or False Quiz

• Microeconomics and Macroeconomics
  • are two differnt aspects of economic theory.
    • True
  • are two different terms used in the economic theory which however are same in terms of their meaning and reference.
    • False

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Activity

Try to observe how your mother or father are utilizing their monthly income in order to meet the daily reqirements of the family. Discuss with them that how changes in economic variables like inflation, slowdown of economic activity, appreciation or depreciation of domestic currency (for example Rupee) is impacting their household budgeting decision. Try to analyze and record what in your view is aspect of Microeconomic theory and what is the aspect of macroeconomic theory

Key Terms

References and Bibliography

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