Playing Around with GeoGebra - Copy

Jennifer Travis, Jul 20, 2015

Just learning my way around the system. Worksheets were chosen semi-randomly. (Begun at ICTCM 2015.)

Table of Contents

  1. Introduction to Derivatives
    1. Application of Derivatives
    2. Solids and volumes of revolution (rotation about y_axis)
    3. Curve Sketching with Derivatives
  2. Calculus 3
    1. Contour Plot
    2. Space Curve and TNB Frame
    3. Vector Fields and Line Integrals
    4. 2D Vector Fields
    5. Divergence and curl of a vector field 2D
    6. coeur
    7. Quadric Surfaces (3D applet) - JAVA
    8. 11.6 Quadric Surfaces

1.

Introduction to Derivatives

Useful stuff I have found.

  • 1. Application of Derivatives
  • 2. Solids and volumes of revolution (rotation about y_axis)
  • 3. Curve Sketching with Derivatives

1.1.

Application of Derivatives

Application of Derivatives[br][br]In Isaac Newton's day, one of the biggest problems was poor navigation at sea. Before calculus was developed, the stars were vital for navigation. Shipwrecks occurred because the ship was not where the captain thought it should be. There was not a good enough understanding of how the Earth, stars and planets moved with respect to each other. Calculus (differentiation and integration) was developed to improve this understanding. Differentiation and integration can help us to solve many types of real-world problems in our day to day life. We use the derivative to determine the maximum and minimum values of particular functions (e.g. cost, strength, amount of material used in a building, profit, loss, etc.). Derivatives are met in many engineering and science problems, especially when modelling the behaviour of moving objects.
Application of Derivatives
1. A rectangular sheet of tin 7cm x 5cm is to be made into a box without top, by cutting off squares from the corners and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?[br][br]2. A box with a square base has no top. If 100 sq. cm of material is used, what is the maximum possible volume for the box?
– sureshbabupp

1.2.

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1.3.

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2.

Calculus 3

  • 1. Contour Plot
  • 2. Space Curve and TNB Frame
  • 3. Vector Fields and Line Integrals
  • 4. 2D Vector Fields
  • 5. Divergence and curl of a vector field 2D
  • 6. coeur
  • 7. Quadric Surfaces (3D applet) - JAVA
  • 8. 11.6 Quadric Surfaces

2.1.

Contour Plot

This worksheet shows how to make contour plots for arbitrary function z=f(x,y) with predetermined intervals. The number of contour lines and its resolution can be specified. Moving the testpoint you can study the properties of the surface: contour lines, extrempunkten.
– Roman Chijner

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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