Analysis I, Softcover reprint of the original 1st ed. 2004 Convergence, Elementary functions Universitext Series

I Sets and Functions.- §1. Set Theory.- §2. The logic of logicians.- II - Convergence: Discrete variables.- §1. Convergent sequences and series.- §2. Absolutely convergent series.- §3. First concepts of analytic functions.- III - Convergence: Continuous variables.- §1. The intermediate value theorem.- §2. Uniform convergence.- §3. Bolzano-Weierstrass and Cauchy’s criterion.- §4. Differentiable functions.- §5. Differentiable functions of several variables.- Appendix to Chapter III.- 1 - Cartesian spaces and general metric spaces.- 2 - Open and closed sets.- 3 - Limits and Cauchy’s criterion in a metric space; complete spaces.- 4 - Continuous functions.- 5 - Absolutely convergent series in a Banach space.- 6 - Continuous linear maps.- 7 - Compact spaces.- 8 - Topological spaces.- IV Powers, Exponentials, Logarithms, Trigonometric Functions.- §1. Direct construction.- §2. Series expansions.- §3. Infinite products.- §4. The topology of the functions Arg(z) and Log z.

Roger Godement (October 1, 1921 - July 21, 2016) is known for his work in functional analysis, and also his expository books. He started as a student at the École normale supérieure in 1940, where he became a student of Henri Cartan. He started research into harmonic analysis on locally compact abelian groups, finding a number of major results; this work was in parallel but independent of similar investigations in the USSR and Japan. Work on the abstract theory of spherical functions published in 1952 proved very influential in subsequent work, particularly that of Harish-Chandra. The isolation of the concept of square-integrable representation is attributed to him. The Godement compactness criterion in the theory of arithmetic groups was a conjecture of his. He later worked with Jacquet on the zeta function of a simple algebra. He was an active member of the Bourbaki group in the early 1950s, and subsequently gave a number of significant Bourbaki seminars. He also took part in the Cartan seminar. He also wrote texts on Lie groups, abstract algebra and mathematical analysis.

Prefers ideas to calculations Explains the ideas without parsimony of words Based on 35 years of teaching at Paris University Blends mathematics skilfully with didactical and historical considerations Includes supplementary material: sn.pub/extras