Spectrum of Hyperbolic Surfaces

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Related lectures (31)

Hyperbolic Geometry

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Coordinate Systems: Applications and Transformations

Explores coordinate systems, including polar and curvilinear coordinates, and their transformations.

General Physics: Mechanics

Covers mechanics concepts in different coordinate systems, explaining position, velocity, and acceleration vectors.

Coordinate Systems: Polar, Cylindrical, Spherical

Covers position, velocity, and acceleration in polar, cylindrical, and spherical coordinate systems.

Riemannian distance, geodesically convex sets

Covers the structure of Riemannian manifolds, geodesic convexity, and the Riemannian distance function.

Circular motion: Friction and Newton's Laws

Explores circular motion, friction, and Newton's laws in various coordinate systems.

Circular motion: Concepts and Calculations

Explores circular motion concepts, centripetal force, velocity, and acceleration in different coordinate systems, with a focus on auto racing and Formula 1 tire physics.

Polar Coordinates: Jacobian Matrix and Examples

Covers polar coordinates, the Jacobian matrix, and examples of calculating areas in polar coordinates.

Kinematics: Position, Velocity, Acceleration

Covers the fundamental concepts of kinematics, including position, velocity, and acceleration in different coordinate systems.

Rotating Vectors in Physics 1

Explores rotating vectors in physics, emphasizing the norm-angular speed relationship and various coordinate systems.

Coordinate Systems: Polar and Cylindrical

Explores position, velocity, and acceleration in polar and cylindrical coordinate systems, simplifying complex formulas for motion analysis.

Invariant Integral Operators

Explores invariant integral operators and their spectral properties on hyperbolic surfaces.

Coordinate Systems: Polar and Spherical

Covers polar and spherical coordinate systems, position vectors, equations of motion, and Frenet frame concepts.

Cylindrical and Spherical Coordinates, Rotations

Covers cylindrical and spherical coordinates, transformations between coordinate systems, and rotations in physics.

Laplacian Operator in Cartesian and Polar Coordinates

Explores the Laplacian operator in Cartesian and polar coordinates, showcasing its application through examples.

Coordinate Systems: Polar, Cylindrical, and Spherical

Explains polar, cylindrical, and spherical coordinates in physics, emphasizing their advantages in simplifying motion analysis.

Meromorphic Functions & Differentials

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.

Curves with Poritsky Property and Liouville Nets

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

Harmonic Forms: Main Theorem

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

Advanced Physics I: Kinematics and Coordinate Systems

Explores advanced physics topics like kinematics in 3D, non-Cartesian coordinates, and practical examples of collisions and snowball fights.

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