Applied Scientific Computing: With Python

Book Preface

This book represents a modern approach to teaching numerical methods—or scientific computing—to students with a broad range of primary interests. The underlying mathematical content is not new, of course, but the focus on applications and models (or modeling) is. Today’s mathematics or computer science students have a strong desire to see the relevance of what they are studying in a practical way. This is even more true for students of other STEM disciplines in their mathematics and computing classes.

In an introductory text such as this, it is difficult to give complete detail on the application of the methods to “real-world” engineering, or economics, or physical science, or social science applications but it is important to connect those dots. Throughout the book, we emphasize applications and include opportunities for both problem- and project-based learning through examples, exercises, and projects drawn from practical applications. Thus, the book provides a self-contained answer to the common question “why do I need to learn this?”

That is a question which we believe any student has a right both to ask and to expect a reasonable and credible answer, hence our focus on Applied Scientific Computing. The intention is that this book is suitable for an introductory first course in scientific computing for students across a range of major fields of study. Therefore, we make no pretense at a fully rigorous development of all the state-of-the-art methods and their analyses. The intention is to give a basic understanding of the need for, and methods of, scientific computing for different types of problems. In all cases, there is sufficient mathematical justification and practical evidence to provide motivation for the reader.

Any text such as this needs to provide practical guidance on coding the methods, too. Coding a linear system solver, for example, certainly helps the student’s understanding of the practical issues, and limitations, of its use. Typically students
find introductory numerical methods more difficult than their professors expect. Part of the reason is that students are expected to combine skills from different parts of their experience—different branches of mathematics, programming and other computer science skills, and some insight in applications fields. Arguably, these are independent skill sets and so the probabilities of success multiply.