Analytical Study of Space

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Related lectures (30)

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Analytical Geometry in Space: Chapter 8

Covers Chapter 8 on Analytical Geometry in Space, focusing on coordinate systems and equations of lines.

Rotating Vectors in Physics 1

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

Relative Positions: Examples

Covers examples of relative positions in a 2D space, focusing on equations involving x and y coordinates.

Vector Calculus: 3D Orientation and Cross Product

Covers 3D orientation, cross product, and volume calculations using mixed product in vector calculus.

Continuum Mechanics: Introduction

Introduces the fundamental concepts of Continuum Mechanics and discusses the density of flux and mass conservation.

Rotation in Two Dimensions

Explores rotation in two dimensions, covering vector products, angular momentum, and kinetic energy of solids.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Surfaces in Space

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

Turbulence: Numerical Flow Simulation

Explores turbulence characteristics, simulation methods, and modeling challenges, providing guidelines for choosing and validating turbulence models.

Covariant Derivatives and Christoffel Symbols

Covers accelerated and inertial coordinate systems, Jacobian, volume elements, covariant derivatives, Christoffel symbols, Lorentz case, and metric tensor properties.