Thursday, April 14 (outline)
Projective Geometry- Calculus Beginnings
Cones and Conic Sections
Lines - Ratios, Rates, Proportions-Measurement.
- Average Speed and velocity
- Delta Notation
- More on Similar triangles
- Slopes of lines
Coordinates and Functions.
- 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.
Section 10.0 - ON-Line Quiz
- Functions rule relating variables
- function notation x -> f(x)
Tutorial on Functions (numerical & algebraic)
Tutorial on Functions (Visual/Graphical)
Static vs. Dynamic visualizations
Some Historical Problems of Visualization:
The parabola and squares.
- Ratio of Length of verticals :: ratio of squares on horizontals
Visualizing Algebra, Motion and Change
- time vs. position
- time vs velocity
Analytic geometry- Descartes and Fermat
Section 10.1 - Quiz
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)
Section 10.2 - Quiz