﻿ Diff Geometry Videos

# Diff Geometry

• ### DiffGeom1: Classical curves

The first lecture of a beginner's course on Differential Geometry! Given by Assoc Prof N J Wildberger of the School of Mathematics and Statistics at UNSW. Differential geometry is the application of calculus and analytic geometry to the study of curves an

• ### DiffGeom2: Introduction to GeoGebra

GeoGebra is a dynamic geometry package, available for free, which allows us to easily make planar geometric constructions which are dynamic (move-able), and investigate associated algebraic formulas and relations. This short lecture gives a brief introduc

• ### DiffGeom3: Parametrized curves and algebraic curves

This lecture discusses parametrization of curves. We start with the case of conics, going back to the ancient Greeks, and then move to more general algebraic curves, in particular Fermat's cubic, the Folium of Descartes and the Lemniscate of Bernoulli. We

• ### DiffGeom4: The differential calculus for curves, via Lagrange!

We rejuvenate the powerful algebraic approach to calculus that goes back to the work of Newton, Euler and particularly Lagrange, in his 1797 book: The Theory of Analytic Functions (english translation). The idea is to study a polynomial function p(x) by u

• ### DiffGeom5: Tangent conics and tangent quadrics

In this video we further develop and extend Lagrange's algebraic approach to the differential calculus. We show how to associate to a polynomial function y=p(x) at a point x=r not just a tangent line, but also a tangent conic, a tangent cubic and so on. O

• ### DiffGeom6: Visualizing the folium surface with GeoGebra

In this tutorial we explore the surface z=x^3+y^3+3xy using GeoGebra. The aim is to develop our skills using this dynamic geometry package, at the same time trying to use a two dimensional representation to understand a surface in three dimensions, with i

• ### DiffGeom7: Differential geometry with finite fields

With an algebraic approach to differential geometry, the possibility of working over finite fields emerges. This is another key advantage to following Newton, Euler and Lagrange when it comes to calculus! In this lecture we introduce the basics of finite