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Strogatz, S.H. Nonlinear Dynamics and Chaos: With Application to Physics, Biology, Chemistry, and Engineering (Westview, 2000).
The application to physics is immediate: "Among all possible groups we have chosen one in particular, in order to refer to it all physical phenomena, just as we choose three coordinate axes in order to refer to them a geometrical figure" (ibid., p. 291).
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Applications to Physics and Engineering.
The Calculus of Variations, with Applications to Physics and Engineering.
Strogatz, S. H. Nonlinear Dynamics and Chaos: with Applications to Physics, Biology, Chemistry and Engineering Perseus Books (1994).
Introduction to nonlinear dynamics, with applications to physics, engineering, biology, and chemistry.
Applications to physics: Maxwell's equations from the differential form perspective.
He produced a rich and satisfying theory for the pure mathematician and wrote extensively on differential geometry and group theory and its applications to physics.
Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, 2nd edition, Westview Press, 2014.
Emphasis is placed on explicit rates of convergence for chains used in applications to physics, biology, and statistics.
There are also several sections on interpretations by and applications to physics, which a project could focus on either a lot or very little depending on interest.
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