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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
  • Refereed publications at the AMS

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

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Tulsi Srinivasan
Azim Premji University
Reference #
OMN:202504.111461

Attributes

Posted date
2025-04-17 07:31:00
Revised date
2025-04-17 07:31:00
Level
   Undergraduate
Notes type
   JIBLM refereed Course Notes
Topic
   Introduction to Mathematics
      Introduction to Proofs
      Precalculus/Calculus
   Analysis
      Real Analysis

A First Course in College Calculus

A first course in calculus/analysis, the first part of the course motivates the study of sequences and their convergence through problems involving calculating the area under a graph and the slope of the tangent at a point on a graph. The second part draws on observations from the first about structural differences between the reals and the rationals, and starts with some axioms for the reals. These axioms are then used to study continuity and properties of continuous functions on the reals.

Course Notes and Supplementary Material (PDF format)

TypeFile (Size)Date
Course notes v1 PDF (212K) 04/17/25
Supplementary v1 PDF (192K) 04/17/25