This is where Andrew Pressley’s approach shines. He manages to strip away the unnecessary abstraction that often alienates undergraduates, presenting the material in a way that feels like a natural extension of the vector calculus courses students have already mastered.
Pressley explains Gaussian and Mean curvature in detail. These concepts help distinguish between different types of surfaces, such as spheres, cylinders, and saddles. elementary differential geometry pressley pdf
If you are struggling to find a legitimate copy of Pressley, or if you want a different pedagogical style, here are excellent alternatives: This is where Andrew Pressley’s approach shines