Day 72 in Mat120

Today:

• No new worksheet.

• No problems to return.

• No quiz opportunity.

• No problems to collect.

• Questions on old stuff?

• Section Review:
  • Today we'll look at early stuff (differentiation) plus middle stuff (integration); tomorrow, recent stuff.

  • Review (part II of III)
    • Function Zoo
      • known animals
      • Especially - linear functions

    • Unknown animals
      • Transformations
      • Compositions
      • Inverses
      • New types
        • Exponentials/Logarithms
        • Hyperbolic trig functions

    • Limits (in order to characterize continuity, and to get at the tangent line)

    • Derivatives

    • Integrals

  • Types of Problems:
    • Study of a function
      • Domain and Range
      • Intercepts (e.g. roots)
      • Symmetry
      • Asymptotes (including slant)
      • Continuity
      • Differentiability
      • Increasing/Decreasing intervals
      • Concavity and Inflection
      • Extrema
      • Graphing it (and its derivatives)

    • Calculate derivatives using
      • Limit definition
      • Formulas (product, chain, etc.)

    • Using derivatives
      • To find extrema
      • To find tangent lines
      • Especially: Optimization problems
      • Matching derivatives (to create smoothness, e.g. when should a pilot start descent?)
      • Higher derivatives
      • Rolle's theorem and Mean Value Theorem (tilted Rolle's)

    • Integrals
      • Started with real areas, approximating them with rectangles
        • Left rectangles
        • Right rectangles
        • Midpoint rectangles
        • Trapezoids (average of left and right)
      • Calculating net areas (positive and negative)
      • Calculating definite versus indefinite integrals. Key to solving them is based on antiderivatives - An antiderivative of f is a function which has f(x) as its derivative.
        • Antiderivatives are not unique - don't forget "C"
        • Fundamental theorem of calculus
      • Using symmetry to solve integrals
      • Calculating areas between curves
      • Integrals as things other than areas!
      • Integrating along the y-axis, rather than the x-axis

Next time: Final day of review