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Differentiability and Tangent Planes
Explores differentiability in functions and tangent planes to surfaces.
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Explores directional derivatives, tangent planes, and normal vectors in surfaces.
Derivability Conditions
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Covariant derivatives along curves
Explores covariant derivatives along curves and second-order optimality conditions in vector fields and manifolds.
Acceleration and geodesicsMOOC: Introduction to optimization on smooth manifolds: first order methods
Explains acceleration along curves and geodesics on manifolds, generalizing straight lines to spheres.
Differentiating Vector Fields: DefinitionMOOC: Introduction to optimization on smooth manifolds: first order methods
Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.
Directional Derivative: Definitions and Examples
Covers the definition of directional derivative and provides illustrative examples.
Properties of Integrals
Covers properties of integrals and differentiation, focusing on exercise solutions and function behavior.
Implicit Functions
Covers directional derivatives, implicit functions, and the concept of the maximum.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

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