No—the mathematics is identical (differential geometry hasn’t changed in 50 years). The improvements are in readability, clarity of figures, and error correction. If you only have the 1969 PDF, you can still learn. But the "new" PDF saves you headaches.
Pro tip: Use the PDF’s search function for terms like "Christoffel symbols of the second kind"—the new PDF has them hyperlinked in the index. schaum 39s outline differential geometry pdf new
Yes, through your university library’s e-book portal. Search for "McGraw-Hill Schaum's Outline Differential Geometry." If your library subscribes to O’Reilly Online Learning, you will get a fully searchable, high-resolution PDF. clarity of figures