Problems in real analysis advanced calculus on the real axis

[...]... Fibonacci numbers, √ in order to approximate 2 Fibonacci also gave a rough definition for the concept of continued fractions that is intimately associated with difference equations, which are now intensively applied in the modeling of continuous phenomena A more precise definition was formulated by Cataldi around 1613 The method of recursion was significantly advanced with the invention of mathematical induction... is said to be nondecreasing (resp., increasing) if an ≤ an+1 (resp., an < an+1 ), for all n ≥ 1 The sequence (an )n≥1 is called nonincreasing (resp., decreasing) if the above inequalities hold with “≥” (resp., “>”) instead of “≤” (resp., “ . for instructors wishing to enrich their teach- ing with some carefully chosen problems and for individuals who are interested in solving difficult problems in mathematical analysis on the real axis. . by topic into eight chapters, each of them containing both sections of proposed problems with complete solutions and separate sections including auxiliary problems, their solutions being left. num- bered consecutively in each section, and we also indicate both the chapter and the section numbers. We have included at the beginning of chapters and sections quo- tations from the literature. They