Analysis I

Analysis I is part one of the undergraduate series in analysis. This book is based on the courses given by the author at Heidelberg. It comprises of materials for a one and a half semester, and can be used as a textbook. The contents range from elementary calculus to fairly advanced topics in functional analysis, measure theory and differential geometry. The book covers ""The convergence of sequences, topological concepts including continuity, compactness and connectedness, Resp. differentiation in one variable, theorems of Arzela-Ascoli and Stone-Weierstra[beta] and analytic functions in several variables, as well as Riemann integral. This book, which demands minimum prerequisites, is intended for first year graduate students or undergraduates who want to pursue the Math or Physics fields.