Analytic Geometry and Calculus with Python

Fourth Edition (2026) · Stephen E. Moore · Department of Mathematics, University of Cape Coast, Ghana

🌐 Author's website: https://moorestephen.info/ 📘 Download the book (PDF): Analytic_Geometry_and_Calculus_with_Python_4th_Edition.pdf

This repository contains the book and all of its Python programs and Jupyter notebooks. It is free for students and teachers to use and share.

About the book

Analytic Geometry and Calculus with Python is a first-year university text. It covers coordinate geometry, circles, limits and continuity, differentiation and its applications, integration and its applications, parametric equations, polar coordinates and conic sections. It also teaches students to use Python to explore, check and apply the mathematics. No programming experience is assumed: Chapter 0 is a gentle introduction to Python.

Every Python listing in the book has been run. The output printed beneath it in the book is the real output of the program in this repository.

Each chapter contains:

• Learning objectives and a chapter summary
• worked examples by hand and in Python (NumPy, SymPy, Matplotlib, SciPy)
• highlighted Key Concept boxes (the ideas you must remember)
• Historical Notes on how the ideas developed, including Africa's contribution, from the Rhind papyrus to Euclid, Hypatia and Ibn al-Haytham
• In Context boxes that apply the mathematics to real situations: ride-hailing trip times and fares, telecom masts, population growth, rainfall, farms, bridges, satellites
• Watch Out boxes on common mistakes, and Check Your Understanding questions
• exercises in three kinds, Skills, Applications and Programming, with answers to selected exercises in Appendix B

A Chapter Map at the front of the book shows how the chapters depend on each other and suggests routes through the book for different courses.

Contents and code

Chapter	Code	Notebook	Programs
0. A First Course in Python for Calculus	code/ch00	Open in Colab	arithmetic, lists, loops, functions, NumPy, Matplotlib, SymPy
1. Coordinate Geometry	code/ch01	Open in Colab	distance, great-circle distance, midpoint, gradient, lines, angles, section formula, point–line distance, bisectors
2. Circles	code/ch02	Open in Colab	centre and radius, circle through three points, tangents, line–circle and circle–circle intersection, trilateration, Archimedes' π
3. Limits and Continuity	code/ch03	Open in Colab	numerical and symbolic limits, one-sided limits, the number e, squeeze theorem, discontinuities, bisection, ε–δ
4. The Derivative	code/ch04	Open in Colab	secants and tangents, first principles, rules, chain rule, implicit differentiation, population growth, numerical differentiation
5. Applications of the Derivative	code/ch05	Open in Colab	tangents and normals, related rates, best departure time for a trip, curve fitting, curve sketching, optimisation, Newton's method, l'Hôpital
6. Integration	code/ch06	Open in Colab	indefinite integrals, substitution, Riemann sums, the Fundamental Theorem, integration by parts, trapezium and Simpson's rules, quad
7. Applications of Integration	code/ch07	Open in Colab	area between curves, distance from speed data, rainfall, average value, volumes of revolution, arc length, survey areas, probability
8. Parametric Equations and Polar Coordinates	code/ch08	Open in Colab	parametric curves, projectiles, the cycloid, coordinate conversion, polar curves, polar slopes and areas
9. Conic Sections	code/ch09	Open in Colab	parabola, satellite dish, arch, ellipse, orbits, hyperbola, locating a lightning strike, classifying conics, eccentricity

Appendix A of the book is a Python quick reference. The program tools/check_answers.py recomputes the answers in Appendix B.

Each program code/chNN/name.py is self-contained. The file code/chNN/name.out next to it contains the output printed in the book, so you can check your results against it.

Getting started

You need Python 3 with NumPy, SymPy, Matplotlib and SciPy.

• No installation (works on a phone): click an Open in Colab link in the table above. Google Colab runs the notebook in your browser, and all the libraries are already installed. Run each cell with Shift + Enter.
• On a laptop: install Anaconda, which includes everything and works offline.
• With pip:

git clone https://github.com/moorekwesi/analytic-geometry-calculus-with-python.git
cd analytic-geometry-calculus-with-python
pip install -r requirements.txt

Run a single program, for example the best-departure-time problem from Chapter 5:

python code/ch05/ex5_03_bolt_travel_time.py

To run every program in the book, regenerating all outputs and saving all figures in figures/:

python run_all.py          # all chapters
python run_all.py ch05     # only Chapter 5

How to learn from this repository

1. Read a section of the book with the corresponding program or notebook open.
2. Type the code in yourself (or run it) and compare your output with the .out file.
3. Change something: a number, a function, a starting value. Predict what will happen first, then check.
4. Do the pen-and-paper exercises by hand first, then check them with Python.
5. Attempt at least one Programming exercise each week. Most of them start from one of these programs.

Editions

Edition	Year
First edition	2019
Second edition	2021
Third edition	2024
Fourth edition (with Python)	2026

Citing the book

S. E. Moore, Analytic Geometry and Calculus with Python, 4th ed., Department of Mathematics, University of Cape Coast, Ghana, 2026. Available at https://github.com/moorekwesi/analytic-geometry-calculus-with-python

Permissions and licence

You are free to use and share these materials for teaching and learning, as long as you give credit to the author.

• The book (course material), Analytic_Geometry_and_Calculus_with_Python_4th_Edition.pdf, is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International Licence (CC BY-NC-ND 4.0). You may download, print and share it free of charge, in its original form, provided you credit the author. You may not sell it, and you may not distribute modified versions of it. For other uses (translations, adapted editions, commercial printing), please contact the author via https://moorestephen.info/.
• The Python code (code/, notebooks/, tools/ and run_all.py) is licensed under the MIT Licence. You may use, copy, modify and distribute it freely, provided the copyright notice and licence text are kept.

Unless a source is given, the numerical data in the book's In Context boxes and in the programs (fares, trip times, tariffs and similar figures) are illustrative and invented for teaching.

Author

Stephen E. Moore, Department of Mathematics, University of Cape Coast, Ghana Website: https://moorestephen.info/

Corrections and suggestions are welcome: please open an issue.