Apostol Calculus – An Applied and Visual Study Project

This repository is an applied and computational companion to the following books:

Tom M. Apostol, Calculus, Volume 1 and Calculus, Volume 2, Second Edition,
John Wiley & Sons, New York.

Publisher’s official page:
https://www.wiley.com/en-us/Calculus%2C+Volume+1%2C+2nd+Edition-p-9780471000051

This project was started on January 15, 2026 by Muhammed Ikbal Yilmaz.

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About the Book

At the very beginning of the first volume, Apostol writes:

"Calculus is more than a technical tool — it is a collection of fascinating and exciting ideas that have interested thinking men for centuries."

Apostol’s books are known for their careful, axiomatic development of calculus and for emphasizing ideas and structure rather than treating the subject as a collection of computational tricks.

The first volume develops one-variable calculus together with the necessary foundations of linear algebra. The second volume continues with multivariable calculus, differential equations, linear analysis, and probability.

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Purpose of This Repository

The purpose of this repository is not to reproduce the text of the books. Instead, it aims to provide a working environment where the material can be explored using computation and visualization.

In this repository:

• Concepts are examined through numerical experiments,
• Geometric ideas are supported by plots and figures,
• Calculations are checked using symbolic computation,
• Selected exercises are implemented and tested in code.

The notebooks are written primarily for personal study, but they are kept public in the hope that they may also be useful to others working through the same material.

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Copyright and Use of the Source

This repository does not contain the text of the books.

• No definitions, theorems, or explanations are copied from the source.
• Only references to chapter and exercise numbers are used.
• All code, explanations, and figures in this repository are original.

This project is not intended to replace the books, but to accompany them.

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Project Structure

• notebooks/ contains Jupyter notebooks, organized by volume and chapter.
• src/ contains reusable helper functions and numerical routines.
• tests/ contains automated tests for verifying computations.
• assets/ contains figures and other visual material.

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Tools

• Python
• NumPy
• SymPy
• Matplotlib
• Jupyter Lab
• PyTest

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How to Cite the Book

If you want to cite Apostol’s book in LaTeX / BibTeX, you can use the following entry:

@book{ApostolCalculus,
  author    = {Tom M. Apostol},
  title     = {Calculus, Volume 1},
  edition   = {Second},
  publisher = {John Wiley \& Sons},
  address   = {New York},
  year      = {1967},
  isbn      = {0-471-00005-1}
}