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An Introduction to Differential Geometry through Computation

An Introduction to Differential Geometry through Computation

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 fields is derived in Chapter 4. Chapter 5 develops the linear algebra of the dual space and the space of bi-linear functions and demonstrates how these concepts are used in defining differential one-forms... Show More


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