Introduction to Analysis
by Irena Swanson
Publisher: Reed College 2016
Number of pages: 323
In this course, students learn to write proofs while at the same time learning about binary operations, orders, fields, ordered fields, complete fields, complex numbers, sequences, and series. We also review limits, continuity, differentiation, and integration.
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by Simon J.A. Malham - Heriot-Watt University
From the table of contents: Order notation; Perturbation methods; Asymptotic series; Laplace integrals (Laplace's method, Watson's lemma); Method of stationary phase; Method of steepest descents; Bibliography; Notes; Exam formula sheet; etc.
by Felix Nagel - arXiv
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. The exposition in this first part includes relation and order theory as well as a construction of number systems.
by Vasily Nekrasov - Yetanotherquant.de
This is a very clear and user-friendly introduction to the Lebesgue measure theory. After reading these notes, you will be able to read any book on Real Analysis and will easily understand Lebesgue integral and other advanced topics.
by E. Goursat, O. Dunkel, E.R. Hedrick - Ginn & company
Goursat's three-volume 'A Course in Mathematical Analysis' remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition.