A. Hinrichs: Analysis für Lehramt. Vorlesungsnotizen - 2016/17. Johannes Kepler Universität Linz
Learning Advanced Analysis with GeoGebra
Talk at GeoGebra Global Gathering 2017 July 18th, 2017
Table of Contents
- Differential calculus
- Vector field in IR²
- Gradient field of a Function for 2 Variables
- Vector field in IR³
- Directional derivative
- Path along maximum gradient
- Taylor polynomials
- Taylor polynomials for multivariable functions
- Local Extrema
- Lokale Extrema Copy
- Contour lines
- Integral calculus
- Curvilinear integral of a scalar field
- Curvilinear integral of a vector field in IR²
- Example: Curvilinear integral of a vector field
- Curvilinear integral of a vector field in IR³
- Fubini's theorem
- Multiple Integral
Vector field in IR²
A [b]vector field[/b] is given by [math]v(x,y) = (v_x, v_y)[/math].[br]The applet shows the vector field for [math]v(x,y) = (x, -y)[/math].[br][br][b]Task[br][/b]Cange the sliders for [br]- the coefficients a and b[br]- step s[br]- the length of the vectors.[br]The red point mark the lower and upper bounds of the vector field.[br][br]Choose other vector field, for example v(x,y) = (a·x² + y, -b·y)[br][br][i]Hint: The arrows are shortened by the factor l.[/i]
Curvilinear integral of a scalar field