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Basic Calculus

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?

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Basic Calculus

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  1. Basic Calculus

  2. Outline • Differentiation as finding slope • Integration as finding area • Integration as inverse of differentiation

  3. 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) y2 y1 x1 x2

  4. Limit y2 y1 x1 x2

  5. Differentiation of x^2 y2 y1 x1 x2 Let’s find dy/dx at x=x1

  6. Differentiation of x^n

  7. Differentiating a sum of two functions of x

  8. Differentiation of

  9. Chain Rule

  10. Area under curve Y= f(x) a b x

  11. Approximation by Summation a b x

  12. Integration: Infinitesimal Approximation by Summation Divide into n stripes, and let n goes to infinity … a b x

  13. The Fundamental Theorem of Calculus • Integration is antiderivative:

  14. Explaining Fundamental Theorem of Calculus • Differentiating area gets curve • Differentiating curve gets slope Y= f(x) a b x

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