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Numerical Methods for Scientific Computing: The Definitive Manual for Math Geeks
Numerical methods are ubiquitous in scientific research, often working quietly behind the scenes in algorithmic black boxes. Practitioners who use such black boxes don’t always know what’s happening inside them, sometimes leading to inaccurate or inefficient solutions and occasionally flat-out wrong ones. This book breaks open the algorithms to explain how they work and why they can fail. It helps develop both an intuitive understanding of the underlying mathematical theory and practical skills for research.
This book teaches not only how to be a critical user of scientific computing algorithms but also a knowledgeable creator of them. Ideal as an introductory text for senior undergraduate and first-year graduate students, as a self-study for anyone with a working knowledge of multivariate calculus and linear algebra, and as a modern reference on numerical methods for researchers.
This revised edition, extensively rewritten and expanded, provides a comprehensive guide to using numerical methods in linear algebra, analysis, and differential equations. Examples and exercises are worked out in detail. This book includes extensive commentary and code for three essential scientific computing languages: Julia, Python, and MATLAB/Octave.
Special Functions of Mathematical Physics: A Tourist’s Guidebook
Strum a guitar. Bang a drum. The sound of one is a combination of sine functions and the other a combination of Bessel functions. While every scientist and engineer knows the sine function, not as many are familiar with Bessel functions or the broader class of special functions that frequently arise in mathematical physics. This book provides a guided tour through the important special functions and develops the mathematical tools and intuition for working with them.