A supplementary text for undergraduate courses in the calculus of variations which provides an introduction to modern techniques in the field based on measure theoretic geometry. Varifold geometry is presented through and appraisal of Plateau's problem.
A supplementary text for undergraduate courses in the calculus of variations which provides an introduction to modern techniques in the field based on measure theoretic geometry. Varifold geometry is presented through and appraisal of Plateau's problem.
Functions on Euclidean Space Norm and inner Product Subsets of Euclidean Space Functions and Continuity Differentiation Basic Definitions Basic Theorems Partial Derivatives Inverse Functions Implicit Functions Notation Integration Basic Definitions Measure Zero and Content Zero Integrable Functions Fubinis Theorem Partitions of Unity Change of Variable Integration on Chains Algebraic Preliminaries Fields and Forms Geometric Preliminaries The Fundamental Theorem of Calculus Integration on Manifolds Manifolds Fields and Forms on Manifolds Stokes Theorem on Manifolds The Volume Element The Classical Theorems
Functions on Euclidean Space Norm and inner Product Subsets of Euclidean Space Functions and Continuity Differentiation Basic Definitions Basic Theorems Partial Derivatives Inverse Functions Implicit Functions Notation Integration Basic Definitions Measure Zero and Content Zero Integrable Functions Fubinis Theorem Partitions of Unity Change of Variable Integration on Chains Algebraic Preliminaries Fields and Forms Geometric Preliminaries The Fundamental Theorem of Calculus Integration on Manifolds Manifolds Fields and Forms on Manifolds Stokes Theorem on Manifolds The Volume Element The Classical Theorems
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