Online Public Access Catalogue (OPAC)
Library,Documentation and Information Science Division

“A research journal serves that narrow

borderland which separates the known from the unknown”

-P.C.Mahalanobis

XV, 375 p. online resource. - (Universitext, ) Content notes : Calculus for Functions of One Variable -- Prerequisites -- Limits and Continuity of Functions -- Differentiability -- Characteristic Properties of Differentiable Functions. Differential Equations -- The Banach Fixed Point Theorem. The Concept of Banach Space -- Uniform Convergence. Interchangeability of Limiting Processes. Examples of Banach Spaces. The Theorem of Arzela-Ascoli -- Integrals and Ordinary Differential Equations -- Topological Concepts -- Metric Spaces: Continuity, Topological Notions, Compact Sets -- Calculus in Euclidean and Banach Spaces -- Differentiation in Banach Spaces -- Differential Calculus in \$\$\mathbb\$\$ d -- The Implicit Function Theorem. Applications -- Curves in \$\$\mathbb\$\$ d. Systems of ODEs -- The Lebesgue Integral -- Preparations. Semicontinuous Functions -- The Lebesgue Integral for Semicontinuous Functions. The Volume of Compact Sets -- Lebesgue Integrable Functions and Sets -- Null Functions and Null Sets. The Theorem of Fubini -- The Convergence Theorems of Lebesgue Integration Theory -- Measurable Functions and Sets. Jensen’s Inequality. The Theorem of Egorov -- The Transformation Formula -- and Sobolev Spaces -- The Lp-Spaces -- Integration by Parts. Weak Derivatives. Sobolev Spaces -- to the Calculus of Variations and Elliptic Partial Differential Equations -- Hilbert Spaces. Weak Convergence -- Variational Principles and Partial Differential Equations -- Regularity of Weak Solutions -- The Maximum Principle -- The Eigenvalue Problem for the Laplace Operator. Differential equations, partial. Analysis. Partial Differential Equations.

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