Basic Calculus. Outline Differentiation as finding slope Integration as finding area Integration as inverse of differentiation.

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Presentation transcript:

Basic Calculus

Outline Differentiation as finding slope Integration as finding area Integration as inverse of differentiation

Limit “Limit” as finding the slope of a curve –The slope of the curve y=mx+c is m. –How about the slope of the curve y=x^2? –Approximately, the slope at x1 is (y2-y1)/(x1-x2) x1x2 y1 y2

Limit x1x2 y1 y2

Differentiation of x^2 x1x2 y1 y2 Let’s find dy/dx at x=x1

Differentiation of x^n

Differentiating a sum of two functions of x

Differentiation of

Chain Rule

Area under curve x Y= f(x) ba

Approximation by Summation xba

Integration: Infinitesimal Approximation by Summation xba … Divide into n stripes, and let n goes to infinity

The Fundamental Theorem of Calculus Integration is antiderivative:

Explaining Fundamental Theorem of Calculus Differentiating area gets curve Differentiating curve gets slope x Y= f(x) ba