Numerical Methods: An Inquiry-Based Approach With Python

Abstract

This book is an inquiry-based approach to a first semester undergraduate Numerical Methods or Numerical Analysis course. The book covers floating point arithmetic, function approximation via Taylor series, numerical root finding, numerical differentiation and integration, an introduction to computational optimization, several methods from numerical linear algebra, several methods from ordinary differential equations, and an introduction to numerical partial differential equations. As an inquiry-based book this is a not a traditional text with complete exposition. Instead, this book contains collections of exercises that guide the student through the building and analysis of numerical algorithms. A heavy emphasis is put on numerical experimentation instead of mathematical proof. Each chapter ends with collections of challenging exercises and projects. Students are encouraged to work every example and exercise in the book to gain full understanding of the material. The primary programming language for this book is Python with an emphasis on using numpy, matplotlib, and scipy to solve computational problems. The intended student audience is sophomore to junior level STEM majors with a background in Calculus, Linear Algebra, and Differential equations.