Lectures related to Lie derivative

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

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

Covariant Derivatives and Christoffel Symbols

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

Linear Shell Theory: Equilibrium and Energy

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

Hodge Duality and Covariant Derivatives

Introduces Hodge duality, covariant derivatives, and key concepts in differential geometry.

Quantum Field Theory II: Maxwell Field and Symmetries

Covers the Maxwell field, symmetries, and making shifts in local and covariant derivatives.

Linear Shell Theory: Equilibrium Equations

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

Descent methods and line search: Second Wolfe condition

Explores the second Wolfe condition, guiding step sizes based on the directional derivative increase.

Acceleration and geodesics

Explains acceleration along curves and geodesics on manifolds, generalizing straight lines to spheres.

Covariant derivatives along curves

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

Descent methods and line search: First Wolfe condition

Introduces the First Wolfe condition to ensure a proportional decrease in the objective function relative to the step length.

Differentiating vector fields along curves: Examples and finite differences

Covers the differentiation of vector fields along curves with examples and finite differences.

Taylor expansions: second order

Explores Taylor expansions and retractions on Riemannian manifolds, emphasizing second-order approximations and covariant derivatives.

Mechanics of Slender Structure: Shells III

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

Objective function, Differentiability, the first order

Covers directional derivative, differentiability, and gradient matrices, emphasizing the first order.

Parallel Transport and Geodesics

Explores parallel transport along curves and geodesics maximizing proper time between points.

Comparing Tangent Vectors: Parallel Transport

Explores parallel transport along loops and covariant derivatives induced by metrics.

Geometric Meaning of Line Integrals

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

Differential Forms on Manifolds

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

Comparing Tangent Vectors: Parallel Transport

Explores the definition, existence, and uniqueness of parallel transport of tangent vectors on manifolds.