Book description
An accessible guide to developing intuition and skills for solving
mathematical problems in the physical sciences and engineering
Equations play a central role in problem solving across various
fields of study. Understanding what an equation means is an essential
step toward forming an effective strategy to solve it, and it also
lays the foundation for a more successful and fulfilling work
experience. Thinking About Equations provides an accessible
guide to developing an intuitive understanding of mathematical methods
and, at the same time, presents a number of practical mathematical
tools for successfully solving problems that arise in engineering and
the physical sciences.
Equations form the basis for nearly all numerical solutions, and the
authors illustrate how a firm understanding of problem solving can
lead to improved strategies for computational approaches. Eight
succinct chapters provide thorough topical coverage, including:
- Approximation and estimation
- Isolating important variables
- Generalization and special cases
- Dimensional analysis and scaling
- Pictorial methods and graphical solutions
- Symmetry to simplify equations
Each chapter contains a general discussion that is integrated with
worked-out problems from various fields of study, including physics,
engineering, applied mathematics, and physical chemistry. These
examples illustrate the mathematical concepts and techniques that are
frequently encountered when solving problems. To accelerate learning,
the worked example problems are grouped by the equation-related
concepts that they illustrate as opposed to subfields within science
and mathematics, as in conventional treatments. In addition, each
problem is accompanied by a comprehensive solution, explanation, and
commentary, and numerous exercises at the end of each chapter provide
an opportunity to test comprehension.
Requiring only a working knowledge of basic calculus and introductory
physics, Thinking About Equations is an excellent supplement
for courses in engineering and the physical sciences at the
upper-undergraduate and graduate levels. It is also a valuable
reference for researchers, practitioners, and educators in all
branches of engineering, physics, chemistry, biophysics, and other
related fields who encounter mathematical problems in their day-to-day
work.
Matt A. Bernstein, PhD, is Professor of Radiologic
Physics at the Mayo Clinic, where he holds appointments in the
Departments of Radiology and Biomedical Engineering. A Fellow of the
International Society for Magnetic Resonance in Medicine (ISMRM) and
Editorial Board member of Magnetic Resonance in Medicine, Dr.
Bernstein has published over sixty journal articles, mainly in the
field of MRI physics.
William A. Friedman, PhD, is Emeritus Professor at the
University of Wisconsin and Affiliate Professor at the University of
Washington. A Fellow of the American Physical Society, Dr. Friedman
has over forty years of academic experience and has authored more than
one hundred journal articles in the field of nuclear physics.
