Algebraic Calculus One by Norman J Wildberger

source: Wild Egg mathematics courses
This playlist will contain the videos from the Algebraic Calculus One course, which will set out a new way of understanding integral calculus.

23:38 Invitation to a more logical, solid and careful analysis
25:10 AlgCalcOne: Points and Lines in the Affine Plane
22:02 AlgCalcOne: Points and Lines in the Affine Plane b)
25:35 AlgCalcOne: Vectors, Displacement, and Centre of Mass
22:20 AlgCalcOne: Vectors Displacement and Centre of Mass b)
25:35 AlgCalcOne: Introduction to Signed Area b)
21:15 AlgCalcOne: Introduction to Signed Area
24:01 AlgCalcOne: The Cross Product and Meister's Formula b)
20:42 AlgCalcOne: The Cross Product and Meister's Formula
28:42 AlgCalcOne: Signed Areas of Triangles on Curves
27:53 AlgCalcOne: Data Structures and Polygonal Splines
36:19 AlgCalcOne: Parabolic Splines and Archimedes
27:20 AlgCalcOne: The Mystery of "Circular Area"
24:07 AlgCalcOne: Summation and Sums of Powers
32:11 AlgCalcOne: Faulhaber's Formula and Bernoulli Numbers
31:05 AlgCalcOne: Polynomials, Matrices and Pascal Arrays
33:22 AlgCalcOne: Vexels and Polynumbers via Multisets
24:47 AlgCalcOne: Curves from Antiquity
22:47 AlgCalcOne: Novel Algebraic Operations for Affine Geometry
19:12 AlgCalcOne: Affine Combinations and Barycentric Coords
18:43 AlgCalcOne: Curves in Modern Times 
30:28 AlgCalcOne: Galileo, Newton and motions of particles 
28:26 AlgCalcOne: De Casteljau Bezier Curves