Lectures related to Seventh Class: Analysis III

Curves with Poritsky Property and Liouville Nets

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

Surface of Revolution

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

Surfaces in Space

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

Curves in Space: Parametric Equations and Surfaces

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

Residue Theorem: Calculating Integrals on Closed Curves

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

Green Theorem: Analyzing Potential Derivatives

Explores potential derivatives, Green theorem, simple curves, and adherence in open domains.

Curves and Surfaces

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

Topology of Riemann Surfaces

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

Introduction to Rhino: Surfaces and Meshes

Introduces the fundamentals of working with NURBS and surfaces in Rhino, covering tools for creating curves, surfaces, and meshes.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Curves in the Oriented Plane

Explores curves in the oriented plane, discussing orientation, vector spaces, equivalence relations, and curvature of regular curves.

Double-layered Timber Plate Shell Tutorial

Covers a tutorial on creating a double-layered timber plate shell using Rhino3D and Grasshopper.

Indoor Comfort Analysis

Introduces indoor comfort analysis using Rhinoceros and Grasshopper tools.

Introduction to Rhino Surfaces and Meshes

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

Curvilinear Coordinates: Calculations and Examples

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

Geometric Areas: Integrals and Regions

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

Surfaces in R^3: Curves and Regular Surfaces

Covers curves in R^2, regular surfaces in R^3, and geometric properties of edges.

Gothic Surfaces: Curvature, Development, and Stereotomy

Delves into the geometric principles of Gothic architecture, focusing on surface curvature and stereotomy techniques.

Surfaces in Geometry II

Explores geometric surfaces, rules between shapes, and architectural applications.

Differential Geometry: Parametric Curves & Surfaces

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