This guide to computational fluid mechanics introduces beginning graduate students to the subject's standard methods and common pitfalls.

Scientists and engineers often use algorithms without fully knowing what's happening inside them. This blind faith can lead to inefficient solutions and sometimes flat-out wrong ones. This book breaks open the algorithmic black boxes to help you understand how they work and why they can break down. Ideal for first-year graduate students, this book works to build both the intuitive understanding of underlying mathematical theory and useful skills for research. Examples worked out in detail provide a practical guide for using numerical methods in linear algebra, numerical analysis, and partial differential equations.

Developed during ten years of teaching experience, this book serves as a set of lecture notes for an introductory course on numerical computation, at the senior undergraduate level. These notes contain the material that can be covered in a semester, together with a few optional sections for additional reading. Rather than surveying a large number of algorithms, the book presents the most important computational methods and emphasizes the underlying mathematical ideas. In most chapters, graphs and drawings are relied on, to build up intuition. The notes are written in a rather colloquial style, presenting the subject matter in the same form as it can be explained in a classroom. For instructors, this will minimize the amount of effort required to prepare their blackboard presentations.As prerequisites, the book only relies on standard calculus, an introductory course on matrices, and some basic computer programming skills. As a new feature, these notes are supplemented by two sets of videos from the author's Youtube channel. These videos contain a complete set of live lectures given in Spring 2015, together with a complete set of short tutorials, from 5 to 15 minutes each.A set of homework problems is included at the end of each chapter. Homework projects cover a variety of applications, in connection with population dynamics, engineering, mechanics, image reconstruction, etc. A complete set of solutions is available for instructors, upon request.

Offers students a practical knowledge of modern techniques in scientific computing.

This work addresses the increasingly important role of numerical methods in science and engineering. It combines traditional and well-developed topics with other material such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions.