With a fresh geometric approach that incorporates more than 250
illustrations, this textbook sets itself apart from all others in
advanced calculus. Besides the classical capstones--the change of
variables formula, implicit and inverse function theorems, the integral
theorems of Gauss and Stokes--the text treats other important topics in
differential analysis, such as Morse's lemma and the Poincare' lemma.
The ideas behind most topics can be understood with just two or three
variables. This invites geometric visualization; the book incorporates
modern computational tools to give visualization real power.
Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps, such as the role of the derivative as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.
Using 2D and 3D graphics, the book offers new insights into fundamental elements of the calculus of differentiable maps, such as the role of the derivative as the local linear approximation to a map and its role in the change of variables formula for multiple integrals. The geometric theme continues with an analysis of the physical meaning of the divergence and the curl at a level of detail not found in other advanced calculus books.
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