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Vector Calculus

Juan Carlos Ponce Campuzano, Oct 18, 2015

Geometrical approach to Vector Calculus

Geometry of Euclidean Space and real-valued functions
1. Addition of vectors
2. Scalar multiplication
3. Vector product
4. Plotting 3D surfaces
5. Parametric surfaces
6. Klein bottle
7. Distance: Point to Plane
Differentiation
1. Partial derivatives and Tangent plane
2. Directional derivatives and Gradient
Vector-Valued Functions
1. Vector fields in 2D
2. Vector field 3D
3. Dynamic Frenet-Serret frame
4. Vector Fields
5. Divergence and Curl calculator
Double integrals
1. Double integral over a rectangle
Integrals over paths and surfaces
1. Path integral for planar curves
2. Area of fence Example 1
3. Line integral: Work
4. Line integrals: Arc length & Area of fence
5. Surface integral of a vector field over a surface
6. Line integrals of vector fields: Work & Circulation
7. Line integrals of vector fields: Flux
8. Line integral for planar curves

Information

1.

Geometry of Euclidean Space and real-valued functions

1.1.

Addition of vectors

Addition of two vectors.

Drag the vectors around. You can change the magnitude and direction of the vectors too. To show the parallelogram rule, place the vectors at the origin.

1.2.

1.3.

1.4.

1.5.

1.6.

1.7.

2.

Differentiation

1. Partial derivatives and Tangent plane
2. Directional derivatives and Gradient

2.1.

Partial derivatives and Tangent plane

This simulation shows the geometric interpretation of the partial derivatives of f(x,y) at point A in

. It also shows the tangent plane at that point. Things to try:

Drag the point A in the xy-plane or type specific values on the boxes.
Select the object you want to show: Tangent plane, f_x or f_y.
Use right click and drag the mouse to rotate the 3D view or click on View button.