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Explores conformal transformations, including holomorphic functions and Moebius transformations.

Residue Theorem: Calculating Integrals on Closed Curves

Covers the application of the residue theorem in calculating integrals on closed curves in complex analysis.

Conformal Transformations: Theory and Applications

Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.

Homogeneous Coordinates and Curves

Explores homogeneous coordinates, curves, and unique solutions in Cartesian coordinates.

Conformal Applications: Theory and Examples

Covers the theory and examples of conformal applications, focusing on the concept of conformal mappings and Moebius transformations.

Parametrized Curves in 2D

Covers the concept of parametrized curves in 2D and their properties.

Geometrical Aspects of Differential Operators

Explores differential operators, regular curves, norms, and injective functions, addressing questions on curves' properties, norms, simplicity, and injectivity.

Conformal Transformations: Part 1

Covers the topic of conformal transformations, including translations, dilations, rotations, and the conformal algebra.

Curvature and Osculating Circle

Covers curvature, osculating circles, and the evolute of plane curves, with examples and equations.

Parametric Curves: Limaçon de Pascal

Introduces the Limaçon de Pascal, a parametric curve with unique properties.

Parametric Curves: Pascal's Limaçon

Introduces the Limaçon de Pascal, a curve described by a moving point on a circle.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Surface of Revolution

Explains the parametric equations of surfaces of revolution generated by curves in space.

AutoCAD: Basic Functions for Vault Plan

Covers the basic functions of AutoCAD for creating a vault plan, including tools, properties, and parametric modifications.

Perspective of a Sphere & a Circle

Explores conical sections, plane curves, and the perspective of a sphere and a circle.

Intersection between Sphere and Cone

Explores the intersection between a sphere and a cone using spherical and cylindrical coordinates.

Vectorworks Basics & Attributes

Covers the basics of Vectorworks software and attributes like fill types and shadow settings.

Lecture 5: Conformal Transformations

Explores Conformal Transformations, emphasizing scale transformations and correlation functions.