You're looking for a detailed report on "Differential Geometry and Its Applications" by John Oprea, and preferably a PDF version. Here's what I can offer:
Based on our review, we recommend the following:
Geometry of Curves
The book typically follows a logical progression that moves from 3D curves to more complex surfaces: : Frenet-Serret formulas and curvature.
Accessibility
: Unlike many dense graduate texts, Oprea’s writing is noted for its lucid style and contagious enthusiasm, making it approachable for science and engineering majors.
Practical Applications
: Unlike many pure math texts, Oprea focuses on real-world phenomena. It includes sections on: Soap film formation and minimal surfaces.