0

UQ-Advanced calculus

Juan Carlos Ponce Campuzano, Aug 29, 2016

Differentiation
1. Partial derivatives and Tangent plane
2. Directional derivatives and Gradient
Integration
1. Line integral for planar curves
2. Line integrals of vector fields: Work & Circulation
3. Line integrals of vector fields: Flux
4. Double integral over a rectangle
5. Line integrals: Arc length & Area of fence
6. Surface integral of a vector field over a surface
Vector fields
1. Vector Fields in 2D
2. Vector fields 3D
3. Divergence and Curl calculator
4. Vector fields 3D
Velocity fields
1. Basic examples of velocity fields
Non-linear transformations
1. Parabolic transformation
2. Polar transformation

Information

Differentiation

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

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.

Integration

1. Line integral for planar curves
2. Line integrals of vector fields: Work & Circulation
3. Line integrals of vector fields: Flux
4. Double integral over a rectangle
5. Line integrals: Arc length & Area of fence
6. Surface integral of a vector field over a surface

Line integral for planar curves

Vector fields

1. Vector Fields in 2D
2. Vector fields 3D
3. Divergence and Curl calculator
4. Vector fields 3D

Vector Fields in 2D

Instructions:

1. Change the components of the vector field by typing, for example:

x^2sin(y) ,

sqrt(y^2+x)exp(x/y) 2. Change the Scale or Vectors density to provide a better visualisation of the vector field. 3. Zoom In or Out (or drag the plane) to change the domain.

Velocity fields

1. Basic examples of velocity fields

Basic examples of velocity fields

Non-linear transformations

1. Parabolic transformation
2. Polar transformation

Parabolic transformation

Instructions:

A transformation is defined by the equations

and

. 1. Drag the BLUE point defined on the boundary of the square (left-side). Observe the effect of the transformation on the right side. 2. Drag the RED point to change the position of the square. Observe the effect of the transformation on the right side.

0

UQ-Advanced calculus

Table of Contents

Information

1.

Differentiation

1.1.

Partial derivatives and Tangent plane

1.2.

2.

Integration

2.1.

Line integral for planar curves

2.2.

2.3.

2.4.

2.5.

2.6.

3.

Vector fields

3.1.

Vector Fields in 2D

Instructions:

3.2.

3.3.

3.4.

4.

Velocity fields

4.1.

Basic examples of velocity fields

5.

Non-linear transformations

5.1.

Parabolic transformation

Instructions:

5.2.