Notes on Ma 20 (Calculus), 6/16/08

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Notes on Ma 20 (Calculus for Economists) as of 16 June 2008:

So far we have discussed the following topics in class:

1. Introduction to Calculus and the Derivative.

2. Symbols used in denoting the derivative of a function.

3. Derivatives of some functions (with respect to x):

3.1. Derivative of y = c (where c is a constant)
3.2. Derivative of y = x (where y = f(x))
3.3. Derivative of y = cx^n (where c = constant, n = power) [Power Rule]

4. Rate of change, Instantaneous rate of change, Slope of a secant line, Slope of tangent line

5. Derivative of the sum and difference of functions:

(d/dx) [ f(x) + g(x)] = (d/dx) f(x) + (d/dx) g(x) = f ' (x) + g ' (x)
(d/dx) [f(x) - g(x)] = (d/dx) f(x) - (d/dx) g(x) = f ' (x) - g ' (x)

6. Interpretations of the derivative

6.1 Derivative as instantaneous rate of change.
6.2 Derivative as slope of a tangent line.

7. Derivative of y involving radicals: y = cx^n (where n can be fractions)

8. Limit definition of the derivative (Barnett et al., p. 165)

9. Definition of "Limit" (Barnett et al., p. 149)

Today (6/16/08) we will discuss the following topics:

1. One-sided limits

2. On the existence of a Limit (Barnett et al., p. 151)

3. Analyzing limits graphically (Barnett et al. pp. 151 - 152)

Tomorrow (6/17/08) we will discuss the Properties of Limits (Theorem 1, Barnett et al., p. 153 - 154) and the Limit of a Polynomial Function (Theorem 2, Barnett et al., pp. 154 - 157).


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