Metric Tensor: Definition

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Second Fundamental Tensor

Explores the second fundamental tensor and its role in calculating normal curvature on surfaces.

Intersection of Manifolds in Exercise 8.2

Covers the intersection of manifolds in exercise 8.2 and fiscal year 8.8.

Covariant Derivatives and Christoffel Symbols

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

Special and General Relativity

Introduces special and general relativity, Einstein equations, and gravitational dynamics.

Differential Geometry of Surfaces

Covers linear pressure vessels and the basics of differential geometry of surfaces, including covariant and contravariant base vectors.

Scalar Product: Geometric Properties

Covers the definition and properties of the scalar product, including geometric interpretations and algebraic properties.

Partial Differentiation

Explores simple examples of partial differentiation, demonstrating how to calculate partial derivatives and gradients in various scenarios.

Vector Spaces and Scalar Products

Covers vector spaces, scalar products, norms, and forms of polarization in standard properties.

Implicit Surface Parametrizations

Explores implicit surface parametrizations and the use of metric tensors in surface parameterization.

Conformity and Compliancy in Geometry

Explores conformity and compliancy in geometry, emphasizing angle preservation and function conditions.