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1	Introduction to some modes of convergence : Theory and applications Bolibrzuch, Milosz January 2017 (has links) This thesis aims to provide a brief exposition of some chosen modes of convergence; namely uniform convergence, pointwise convergence and L1 convergence. Theoretical discussion is complemented by simple applications to scientific computing. The latter include solving differential equations with various methods and estimating the convergence, as well as modelling problematic situations to investigate odd behaviors of usually convergent methods. Modes of convergence uniform convergence pointwise convergence L1 convergence numerical methods differential equations big O notation central difference method topological space metric space bump function support Computational Mathematics Beräkningsmatematik Mathematical Analysis Matematisk analys