Dimensional Analysis Across the Landscape of Physics

Aimed at students throughout the undergraduate Physics curriculum, this textbook emphasizes the utility of dimensional analysis techniques in research applications, with examples ranging from famous papers in the historical literature to recent advances, and includes an extensive array of worked examples and end-of-chapter problems.

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Dimensional Analysis Across the Landscape of Physics introduces readers to the powerful idea that almost all physical quantities in science and engineering can be described using only five base dimensions: mass, length, time, charge, and temperature, and combinations thereof. Starting with the basics of how this foundational intellectual concept arises, it illustrates the use of dimensional analysis in approaching the solutions to textbook-level problems in physics and adjacent fields, ranging from introductory courses, through the advanced undergraduate curriculum, to advanced Physics electives.

It covers the core curricular topics of classical mechanics, electricity and magnetism, thermal physics, and quantum mechanics. It includes examples of the use of dimensional analysis applied to topics from other related fields such as geosciences, meteorology, engineering, and biophysics to emphasize the utility of such methods across the proverbial landscape of physics. There is also coverage of more specialized topics, such as advanced quantum mechanics, particle physics, field theory, condensed matter physics, and astrophysics and gravitation.

Many worked examples are included, as well as an extensive array of end-of-chapter problems, with a solution manual available to instructors. In addition to covering the standard topics in the undergraduate curriculum, the book explores how dimensional analysis has been used (and continues to be used) in research across all fields of physics, citing examples from the historical literature and from very recent research results. The work includes extensive references to the original papers for further study, as well as useful ancillary material, including a dimensional analysis 'dictionary', brief introductions to data-fitting, and connections to metrology. There is an emphasis throughout on the use of modern symbolic programming to streamline the process of the solving systems of linear equations needed for a dimensional analysis approach, with several Mathematica© templates provided for reader use.