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Numerical Methods and Analysis with Python

Frontmatter

Introduction

Main

1. Root-finding
2. Linear Algebra and Simultaneous Equations
3. Polynomial Collocation and Approximation
4. Derivatives and Definite Integrals
5. Optimization
- 5.1. Finding the Minimum of a Function of One Variable Without Using Derivatives
- 5.2. Finding the Minimum of a Function of Several Variables
6. Initial Value Problems for Ordinary Differential Equations
7. Future Topics

Some Templates for Exercises

1. Root Finding by Interval Halving, Exercise 1 template
2. Root Finding by Interval Halving, Exercise 2 template

Python Tutorial

1. Introduction to the Python Tutorial
2. Getting Python Software for Scientific Computing
3. Suggestions and Notes on Python and Jupyter Notebook Usage
4. Python Basics
5. Notes on Python Coding Style
6. Python Variables, Including Lists and Tuples, and Arrays from Package Numpy
7. Decision Making With if, else, and elif
8. Defining and Using Python Functions
9. Iteration with for
10. Iteration with while
11. Code Files, Modules, and an Integrated Development Environment
12. Recursion (vs iteration)
13. Plotting Graphs with Matplotlib
14. Numpy Array Operations and Linear Algebra
15. Package Scipy and More Tools for Linear Algebra
16. Summation and Integration
17. Random Numbers, Histograms, and a Simulation
18. Formatted Output and Some Text String Manipulation
19. Classes, Objects, Attributes, Methods: Very Basic Object-Oriented Programming in Python
20. Exceptions and Exception Handling

Appendices

1. Introduction to the appendices
2. Notebook for generating the module numerical_methods
3. Linear algebra algorithms using 0-based indexing and semi-open intervals
4. Some Possible Projects
5. Bibliography
6. Revision Notes and Plans
7. Notes for authors

.ipynb

Future Topics

7. Future Topics#

This chapter was last revised on December 5, 2025.

It is a collection of very preliminary versions of sections on new topics.

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6.11. Introduction to Implicit Methods and Stiff Equations — Future Topic

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7.1. Special Methods for ODE IVPs of Second Order and Conservative Systems

By Brenton LeMesurier, with contributions from Stephen Roberts

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