| Item type | Current location | Collection | Call number | Copy number | Status | Date due | Barcode |
|---|---|---|---|---|---|---|---|
| E-Books | Biblioteca da FCTUNL Online | Não Ficção | QA304.HID FCT 95310 (Browse shelf) | 1 | Available |
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| QA303.SPR FCT 94691 Calculus of one variable | QA303.2.SPR FCT 81350 Calculus without derivatives | QA303.2.SPR FCT 81455 Applications of q-calculus in operator theory | QA304.HID FCT 95310 Differential calculus in normed linear spaces | QA305.SPR FCT 95555 Advances in automatic differentiation | QA308.SPR FCT 81793 A course on integration theory | QA308.SPR FCT 97234 Application of holomorphic functions in two and higher dimensions |
Colocação: Online
This book presents Advanced Calculus from a geometric point of view: instead of dealing with partial derivatives of functions of several variables, the derivative of the function is treated as a linear transformation between normed linear spaces. Not only does this lead to a simplified and transparent exposition of "difficult" results like the Inverse and Implicit Function Theorems but also permits, without any extra effort, a discussion of the Differential Calculus of functions defined on infinite dimensional Hilbert or Banach spaces.The prerequisites demanded of the reader are modest: a sound understanding of convergence of sequences and series of real numbers, the continuity and differentiability properties of functions of a real variable and a little Linear Algebra should provide adequate background for understanding the book. The first two chapters cover much of the more advanced background material on Linear Algebra (like dual spaces, multilinear functions and tensor products.) Chapter 3 gives an ab initio exposition of the basic results concerning the topology of metric spaces, particularly of normed linear spaces.The last chapter deals with miscellaneous applications of the Differential Calculus including an introduction to the Calculus of Variations. As a corollary to this, there is a brief discussion of geodesics in Euclidean and hyperbolic planes and non-Euclidean geometry.
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