Lectures related to Plane curve

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Curves with Poritsky Property and Liouville Nets

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

Surfaces in Space

Explores surfaces in space, including paraboloids, spheres, and hyperboloids, and their equations and intersections.

Geometric Areas: Integrals and Regions

Covers the calculation of areas using integrals for geometric regions defined by curves and parametric equations.

Residue Theorem: Calculating Integrals on Closed Curves

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

Geometrical Aspects of Differential Operators

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

Curves and Surfaces

Covers the representation of plane curves and the nature of obtained curves.

Curves in Space: Parametric Equations and Surfaces

Covers the equations for curves and surfaces in space, including parametric and particular surfaces.

Curvilinear Coordinates: Calculations and Examples

Covers curvilinear coordinates and area calculations using double integrals with examples of different curves.

Implicit Curves: Analysis & Regular Points

Covers implicit curves, regular and critical points, convexity, concavity, and inflection points.

Curvature and Osculating Circle

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

Dandelin Theorem: Ellipse Construction

Explores ellipse construction using the Dandelin theorem and properties of conics in space.

Differential Geometry: Parametric Curves & Surfaces

Introduces the basics of differential geometry for parametric curves and surfaces, covering curvature, tangent vectors, and surface optimization.

Geometry: Course Overview & 5 Regular Polyhedra

Explores geometry basics, 5 regular polyhedra construction, and their link to ancient physics and planets.

Arc Length Approximation

Explores arc length calculation for curves and polygons inscribed in circles using trigonometry and parametric equations.

Introduction to Rhino Surfaces and Meshes

Introduces working with surfaces, polysurfaces, and solids in Rhino, covering rendering, material editing, and mesh creation.

Closed Curves and Topological Spaces

Explores closed curves in topological spaces, emphasizing their properties and significance in mathematics.

Topology of Riemann Surfaces

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Parametric Curves and Derivatives

Explores parametric curves, derivatives, equivalence of paths, and local behavior of functions.