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Related lectures (32)

Christoffel Symbols and Gravity Before Einstein

Introduces Christoffel symbols and gravity concepts before Einstein, discussing mathematical tensors and the Nobel Prize in Physics.

Objective function, Differentiability, The second order MOOC: Optimization: principles and algorithms - Unconstrained nonlinear optimization

Explores the role of first and second derivatives in function curvature and convexity.

Scalar Gravity: Einstein Equations

Introduces scalar gravity, covering covariant derivatives, Ricci tensor, Einstein Equivalence Principle, and the generalization of Newtonian gravity equations.

Derivatives and Continuity

Explores properties of functions with continuous partial derivatives in open subsets of Rn.

Symplectic Geometry Log in to Mediaspace to watch this video

Covers the background on symplectic geometry, focusing on symplectic manifolds and canonical structures.

Linear Shell Theory: Equilibrium and Energy Log in to Mediaspace to watch this video

Covers the expression of the Kirchhoff-Saint Venant energy in a covariant setting and explores equilibrium equations for spherical shells and linear shell theory.

Linear Shell Theory: Equilibrium Equations Log in to Mediaspace to watch this video

Covers the dimensional reduction of strain energy from 3D to 2D and linear shell theory equilibrium equations.

Covariant derivatives along curves Log in to Mediaspace to watch this video

Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.

Mechanics of Slender Structure: Shells III Log in to Mediaspace to watch this video

Explores the nonlinear theory of spherical shells, including Reissner's solution and Zoelly's solution for pressure buckling.

Geometric Meaning of Line Integrals Log in to Mediaspace to watch this video

Explores the geometric interpretation of line integrals in altimetric profiles of cycling stages.

Shells III: Nonlinear Theory and Pressure Buckling Log in to Mediaspace to watch this video

Explores the nonlinear theory of spherical shells and Zoelly's solution for pressure buckling, covering topics like strain measures and critical buckling pressure.

Directional Derivative: Definitions and Examples Log in to Mediaspace to watch this video

Covers the definition of directional derivative and provides illustrative examples.

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