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Unlike classical differential geometry books like Kreyzig, this is a relatively modern differential geometry textbook. What differentiates this book most from other differential geometry textbooks is that this book contains a lot of very useful physics applications like a cycloidal pendulum (Huygens pendulum). I found this textbook to be extremely helpful when studying classical mechanics. In addition, there are some professors who teach curves and surfaces in a very rigorous way in Mathematical Analysis II (Analisi Matematica II), which would make this book the perfect fit.

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