  This set of lecture notes constitutes the free textbook project I initiated
towards the end of Summer 2015, while preparing for the Fall 2015 Analytical
Methods in Physics course I taught to upper level undergraduates at the
University of Minnesota Duluth. During Fall 2017, I taught Differential
Geometry and Physics in Curved Spacetimes at National Central University,
Taiwan; and this gave me an opportunity to expand on the text. Topics currently
covered include: complex numbers, matrix algebra, finite and infinite
dimensional vector spaces, calculus on the complex plane, special/approximation
methods in calculus, differential geometry in curved space(time)s, and partial
differential equations.
