Thursday, April 14 (outline)
Projective Geometry- Calculus Beginnings
The conics.
Cones and Conic Sections
FAPP video.
Lines - Ratios, Rates, Proportions-Measurement.
- Average Speed and velocity
- Delta Notation
- More on Similar triangles
- Slopes of lines
Parabolas
- Line of symmetry
- Coordinate graphs of quadratics relation
- Finding line of symmetry from data, from equation
- Secant lines and slopes
- Locatring the vertex. and slopes of secant lines.
Coordinates and Functions.
- Functions rule relating variables
- function notation x -> f(x)
Section 10.0 - ON-Line Quiz
Tutorial on Functions (numerical & algebraic)
Tutorial on Functions (Visual/Graphical)
Static vs. Dynamic visualizations
Winplot?
Ch. 10.1
Some Historical Problems of Visualization:
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The parabola and squares.
- Ratio of Length of verticals :: ratio of squares on horizontals
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Visualizing Algebra, Motion and Change
- time vs. position
- time vs velocity
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Analytic geometry- Descartes and Fermat
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Section 10.1 - Quiz
10.2
Four Problems Connecting the visual to the Numerical
- Area of a region.
- Tangent line
- Motion and distance traveled by a falling object
- Motion and position (cannon balls)
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Section 10.2 - Quiz