Differential Geometry

Differential Geometry (UNSW). This is a collection of video lectures on Differential Geometry given by Professor N. J. Wildberger. The lectures present a systematic and sometimes novel development of classical differential geometry, going back to Euler, Monge, Dupin, Gauss and many others.

Differential geometry is the application of calculus and analytic geometry to the study of curves and surfaces, and has numerous applications to manufacturing, video game design, robotics, physics, mechanics and close connections with classical geometry, algebraic topology, the calculus of several variables and mostly notably Einstein's General Theory of Relativity.

Lecture 01 - Classical Curves
Lecture 02 - Introduction to GeoGebra
Lecture 03 - Parametrized Curves and Algebraic Curves
Lecture 04 - The Differential Calculus for Curves, via Lagrange!
Lecture 05 - Tangent Conics and Tangent Quadrics
Lecture 06 - Visualizing the Folium Surface with GeoGebra
Lecture 07 - Differential Geometry with Finite Fields
Lecture 08 - The Differential Calculus for Curves (II)
Lecture 09 - Projective View of Conics and Quadrics
Lecture 10 - Duality, Polarity and Projective Linear Algebra
Lecture 11 - Duality, Polarity and Projective Linear Algebra (II)
Lecture 12 - Metrical Structure and Curvature of a Parabola
Lecture 13 - Curvature for the General Parabola
Lecture 14 - Quadratic Curvature for Algebraic Curves
Lecture 15 - Quadratic Curvature for Algebraic Curves (cont.)