Mathematics Metric Tensor Fields This post explores the concept of metric tensor fields on smooth manifolds.
Mathematics Exterior Algebra This post examines the concept of the exterior algebra of a vector space.
Mathematics Differentials This post examines the idea of the differential of a function, relating it to concepts from differential geometry.
Mathematics Notes on Line and Surface Integrals This post explores line and surface integrals, relating the classical formulations to concepts from differential geometry such as the pullback of differential forms and volume forms.
Mathematics Cotangent Spaces This post explores the concept of the cotangent space at a point on a smooth manifold.
Mathematics Topological Spaces This post motivates the definition of a topological space using the concept of a filter.
Mathematics Tangent Bundles This post contains a detailed explanation of the concept of the tangent bundle on a smooth manifold.
Mathematics Tangent Spaces This post contains a detailed explanation of the concept of the tangent space at a point on a smooth manifold.
Mathematics Total Derivatives This post contains a detailed explanation of the concept of the total derivative of a continuous function. It attempts to explain the total derivative in a way which relates it to concepts from differential geometry (such as tangent spaces).
