Calculus is pictures.

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My name is Andrew Lorent, I am a professor of mathematics at the University of Cincinnati. These online lectures are to support my sections of the Calc 1 and...

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Vibrating membranes on a disk.

Vibrating membranes on a rectangle.

Differential inclusions and the Aviles Giga functional

Regularity of differential inclusions in subspaces without rank-1 connections.

Sverak's regularity theorem part 2.

Sverak's regularity theorem for differential inclusions

Sobolev Poincare inequality

Sketch of Elliptic regularity

The three gradient problem

Intro to the finite gradient problem

The Tartar square

Introduction to the Tartar square

Quasiregular mappings in higher dimension and generalizations of Liouville's theorem

Intro to quasiregular mappings in higher dimensions and more on Liouville's theorem.

L^p bounds on the Hilbert transform part 2, and intro to L^p boundness of the Beurling transform.

L^p bounds on the Hilbert transform. Part 1

Intro to the Hilbert transform and the Plememlj formula

More on the Beltrami equation

Solving Betrami's equation

More estimates for a Cauchy type operator and weak Wirtinger derivatives.

L^p estimates on a Cauchy type transform

More on the Beurling transform.

Introduction to the Beurling transform

Intro to the Cauchy transform

A generalized Cauchy integral formula

Stoilow decomposition reduces to solving Beltrami equation

Conformal and anticonformal matrices, Wirtinger derivatives, the Beltrami equation and Stoilow.

Quasiregular mappings, the Beltrami coefficient and introduction to the Stoilow decomposition.

Regularity of Sobolev differential inclusions and introduction to Quasiregular mappings.

A weak quantitative Liouville theorem and introduction to Sobolev differential inclusions.