Theory of Splines: Course Outline (MAT637)
Course Outline
The Cubic Spline: Existence, Uniqueness, and Best Approximation, Convergence, Equal Intervals, Approximate Differentiation and Integration, Curve Fitting, Approximate Solution of Differential Equations, Approximate Solution of Integral Equations, Additional Existence and Convergence Theorems. Intrinsic Properties of Cubic Splines: The minimum Norm Property, The Best Approximation Property, The Fundamental Identity, The First Integral Relation, Uniqueness, Existence, General Equations, Convergence of LowerOrder Derivatives, The Second Integral Relation, Raising the Order of Convergence, Convergence of HigherOrder Derivatives, Limits on the order of Convergence, Hilbert Space Interpretation, Convergence in Norm, Canonical Mesh Bases and Their Properties, Remainder Formulas, Transformations Defined by a Mesh, A Connection with Space Technology.
Recommended Book

Approximation Theory and Spline Functions byCall Number: 511.4 APPISBN: 9789400964686Publication Date: 20111019
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by Biebler, KarlErnst
Wodny, Michael
ISBN 9789814522236 
by Stepanets, A. I.
ISBN 9789067644273
Date of publication 2005 
by Dzyadyk, Vladislav K.
Shevchuk, Igor A.
Malyshev, Dmitry V. 
by Shirakova, Elena A.
ISBN 9781608052097
Date of publication 2011