Mathematical Methods in Science and Engineering

Books

Mathematical methods form an essential foundation for the sciences and engineering. Two of the most pervasive areas in such fields are variational and matrix methods; variational methods provide the unifying mathematical framework at the heart of a wide variety of physical principles, while matrix methods provide the unifying mathematical language for expressing, solving, and interpreting physical systems in science and engineering.

The following two books have been published by Cambridge University Press and endeavor to consolidate, generalize, and unify variational methods as well as matrix, along with numerical and optimization, methods with a strong emphasis on applications in science and engineering. Click on either book to access additional information about each book as well as links to videos based on material in each book.

Additional Topics

Select the link(s) below for YouTube videos that cover additional (unpublished) mathematical methods in science and engineering topics.

Complex Variable Methods with Applications in Science and Engineering

Courses

Select the links below for YouTube videos that cover the material contained in the following courses:

Engineering Analysis (Matrix Methods, Complex Variables, and Variational Methods)

Numerical Methods for Partial Differential Equations and Computational Fluid Dynamics

About the Author:

Kevin W. Cassel is Professor of Mechanical and Aerospace Engineering and Professor of Applied Mathematics at the Illinois Institute of Technology (IIT). He is a Fellow of the American Society of Mechanical Engineers (ASME), an Associate Fellow of the American Institute of Aeronautics and Astronautics (AIAA), and his honors include Illinois Institute of Technology's University Excellence in Teaching Award (2008) and Ralph L. Barnett Excellence in Teaching Award (2015, 2007, 2001), the 2002 Alfred Noble Prize, and the Army Research Office Young Investigator Award (1998-2001). Professor Cassel has been a visiting researcher at the University of Manchester and University College London, and is a visiting professor at the University of Palermo, Italy. His research utilizes computational fluid dynamics in conjunction with advanced analytical methods to address problems in bio-fluids, unsteady aerodynamics, multiphase flow, and cryogenic fluid flow and heat transfer.

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