Exercises in Functional Analysis

This self-contained work on linear and metric structures focuses on studying continuity and its applications to finite- and infinite-dimensional spaces.

This clear and concise textbook provides a rigorous introduction to the calculus of variations, depending on functions of one variable and their first derivatives. It is based on a translation of a German edition of the book Variationsrechnung (Vieweg+Teubner Verlag, 2010), translated and updated by the author himself.

by Daniel Li (Author),‎ Hervé Queffélec (Author),‎ Danièle Gibbons (Translator),‎ Greg Gibbons (Translator)

by Daniel Li (Author),‎ Hervé Queffélec (Author),‎ Danièle Gibbons (Translator),‎ Greg Gibbons (Translator)

In a contemporary course in mathematical analysis, the concept of series arises as a natural generalization of the concept of a sum over finitely many elements, and the simplest properties of finite sums carry over to infinite series. Standing as an exception among these properties is the commutative law, for the sum of a series can change as a result of a rearrangement of its terms.