Learning Advanced Analysis with GeoGebra
1. Differential calculus
1. Vector field in IR²
2. Gradient field of a Function for 2 Variables
3. Vector field in IR³
4. Directional derivative
5. Path along maximum gradient
6. Taylor polynomials
7. Taylor polynomials for multivariable functions
8. Local Extrema
9. Lokale Extrema Copy
10. Contour lines
2. Integral calculus
1. Curvilinear integral of a scalar field
2. Curvilinear integral of a vector field in IR²
3. Example: Curvilinear integral of a vector field
4. Curvilinear integral of a vector field in IR³
5. Fubini's theorem
6. Multiple Integral

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Learning Advanced Analysis with GeoGebra

Andreas Lindner, SAVAŞ ORHAN, 7 mar. 2018

Talk at GeoGebra Global Gathering 2017 July 18th, 2017

Conţinut

Differential calculus
1. Vector field in IR²
2. Gradient field of a Function for 2 Variables
3. Vector field in IR³
4. Directional derivative
5. Path along maximum gradient
6. Taylor polynomials
7. Taylor polynomials for multivariable functions
8. Local Extrema
9. Lokale Extrema Copy
10. Contour lines
Integral calculus
1. Curvilinear integral of a scalar field
2. Curvilinear integral of a vector field in IR²
3. Example: Curvilinear integral of a vector field
4. Curvilinear integral of a vector field in IR³
5. Fubini's theorem
6. Multiple Integral

Differential calculus

1. Vector field in IR²
2. Gradient field of a Function for 2 Variables
3. Vector field in IR³
4. Directional derivative
5. Path along maximum gradient
6. Taylor polynomials
7. Taylor polynomials for multivariable functions
8. Local Extrema
9. Lokale Extrema Copy
10. Contour lines

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]