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An Introduction To Differential Geometry Through Computation, Mark E. Fels
An Introduction To Differential Geometry Through Computation, Mark E. Fels
Textbooks
The outline of the book is as follows. Chapter 1 reviews some basic facts about smooth functions from IRn to IRm, as well as the basic facts about vector spaces, basis, and algebras. Chapter 2 introduces tangent vectors and vector fields in IRn using the standard two approaches with curves and derivations. Chapter 3 reviews linear transformations and their matrix representation so that in Chapter 4 the push-forward as an abstract linear transformation can be defined and its matrix representation as the Jacobian can be derived. As an application, the change of variable formula for vector …