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Analysis I by Vicky Neale
The contents include: Introduction, Axioms for arithmetic in R, Properties of arithmetic in R, Ordering the real numbers, Inequalities and arithmetic, The modulus of a real number, The complex numbers, Upper and lower bounds, Supremum, infimum and completeness, Existence of roots, More consequences of completeness, Countability, More on countability, Introduction to sequences, Convergence of a sequence, Bounded and unbounded sequences, Complex sequences, Subsequences, Orders of magnitude, Monotonic sequences, Convergent subsequences, Cauchy sequences, Convergence for series, More on the Comparison Test, Ratio Test, Integral Test, Power series, Radius of convergence, Differentiation Theorem.
Author(s): Vicky Neale
114 Pages 
Foundations of Mathematical Analysis
This note covers Basic concepts in mathematical analysis and some complements, Real numbers and ordered fields, Cardinality, Topologies, Construction of some special functions.
Author(s): Fabio Bagagiolo
122 Pages
Mathematical Analysis Lecture Notes by Anil Tas
The contents include: The Real And Complex Number Systems, Sets And Functions, Basic Topology, Sequences And Series, Continuity, Sequences And Series Of Functions, Figures.
Author(s): Anil Tas
90 Pages
The contents include: Introduction, Axioms for arithmetic in R, Properties of arithmetic in R, Ordering the real numbers, Inequalities and arithmetic, The modulus of a real number, The complex numbers, Upper and lower bounds, Supremum, infimum and completeness, Existence of roots, More consequences of completeness, Countability, More on countability, Introduction to sequences, Convergence of a sequence, Bounded and unbounded sequences, Complex sequences, Subsequences, Orders of magnitude, Monotonic sequences, Convergent subsequences, Cauchy sequences, Convergence for series, More on the Comparison Test, Ratio Test, Integral Test, Power series, Radius of convergence, Differentiation Theorem.
Author(s): Vicky Neale
114 Pages
Introduction to Mathematical Analysis I
Goal in this set of lecture notes is to provide students with a strong foundation in mathematical analysis. The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels.
Author(s): Portland State University
NA Pages
Introduction To Mathematical Analysis
This book explains the following topics: Some Elementary Logic, The Real Number System, Set Theory, Vector Space Properties of Rn, Metric Spaces, Sequences and Convergence, Cauchy Sequences, Sequences and Compactness, Limits of Functions, Continuity, Uniform Convergence of Functions, First Order Systems of Differential Equations
Author(s): John E. Hutchinson
284 Pages
The Convenient Setting of Global Analysis
This book covers the following topics: Calculus of smooth mappings, Calculus of holomorphic and real analytic mappings, Partitions of unity, Smoothly realcompact spaces, Extensions and liftings of mappings, Infinite dimensional manifolds, Calculus on infinite dimensional manifolds, Infinite dimensional differential geometry, Manifolds of mappings and Further applications.
Author(s): Andreas Kriegl and Peter W. Michor
NA Pages