Teaching Calculus

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  • Nikolay Brodskiy
  • Alexander Brodsky

Lecture 2012.02.24 Curvature: Geometric Point of View

YouTube Playlist

Image Title Description Files Demonstrations
Part 01 Curvature as numeric characteristic that reflects a geometric property of the curve in the given point. Notes
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Part 02 Deriving formula for the angle between tangent lines and for the length of the curve. Notes
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Part 03 To find the limit we substitute delta t equals zero into the formula. We get uncertainty 0/0 and have to use advanced techniques. Notes
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Part 04 How does Taylor's approach advances L'Hospital's Rule? Notes
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Part 05 Physical point of view helps us to find the derivative of the denominator. Notes
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Part 06 Computing the derivative of cosine inverse we get infinity. Notes
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Part 07 We get new formula for the curvature using area to find the angle between tangent lines. Notes
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Part 08 Deriving the formula for curvature. Notes
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