Elementary Analysis: The Theory of Calculus (with Solutions)

Kenneth A. Ross, “Elementary Analysis: The Theory of Calculus (with Solutions)”
S***r | 2010 | ISBN: 1441928111 | 368 pages | File type: PDF | 64,5 7,5 mb

Created for students having no previous encounter with rigorous proofs, this text on analysis might be used instantly following standard calculus courses. It is extremely recommended for anybody planning to study advanced analysis, e.g., complex variables, differential equations, Fourier analysis, numerical analysis, a number of variable calculus, and statistics. It’s also recommended for future secondary school teachers.

A limited number of concepts involving the real line and functions on the real line are studied. Numerous abstract ideas, including metric spaces and ordered systems, are avoided. The least upper bound property is taken as an axiom along with the order properties of the real line are exploited throughout. A thorough treatment of sequences of numbers is used as a basis for studying standard calculus topics. Optional sections invite students to study such topics as metric spaces and Riemann-Stieltjes integrals.

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