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Welcome to AMS Open Math Notes, a repository of freely downloadable mathematical works hosted by the American Mathematical Society as a service to researchers, faculty and students. Open Math Notes includes:

  • Draft works including course notes, textbooks, and research expositions. These have not been published elsewhere and are subject to revision.
  • Items previously published in the Journal of Inquiry-Based Learning in Mathematics, a refereed journal
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Visitors are encouraged to download and use any of these materials as teaching and research aids, and to send constructive comments and suggestions to the authors.

Open Math Notes Advisory Board:

  • Karen Vogtmann, Chair | University of Warwick
  • Tom Halverson | Macalester College
  • Andrew Hwang | College of the Holy Cross
  • Robert Lazarsfeld | Stony Brook University
  • Mary Pugh | University of Toronto


Peter Philip
LMU Munich
MR ID: 639375
Reference #


Posted date
2021-09-13 23:17:20
Revised date
2022-09-16 07:07:05
Notes type
   Standard Course Offering
      Real Analysis
      Point Set Topology

Analysis II: Topology and Differential Calculus of Several Variables

2nd part of 3-semester course on Calculus and Real Analysis: Convergence and function continuity are studied in normed and metric spaces as well as in abstract topological spaces (where net convergence is used). Topological notions of interest include separation, compactness, and connectedness. The part on advanced differential calculus includes the chain rule, Taylor's theorem, necessary and sufficient conditions for extrema, as well as constrained optimization.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v5 PDF (1.3M) 09/17/22