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Calculus and Analytic Geometry

SLMtitle.png Preliminaries

SLMobj.png 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


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.


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


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Case Study

Case 1






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Case Study
Understanding Government Tax Policy


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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


SLMact.gif 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

MU KEY.jpg Key Terms

SLMref.png References and Bibliography

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