Differential Calculus in Normed Linear Spaces

verfasst von: Kalyan Mukherjea

Verlag: Hindustan Book Agency

Buchreihe : Texts and Readings in Mathematics

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Inhaltsverzeichnis

Frontmatter

1. Preliminaries

Abstract

In this chapter I am going to catalogue some facts, most of which you have encountered already, perhaps in a different form. Many assertions will not be proved: either because their truth will be evident upon a few moments’ reflection or because they follow easily from results you have seen earlier in your mathematical education. My main purpose here is to set up the notations I will use and to familiarize you with my eccentricities.

Kalyan Mukherjea

2. Linear Spaces: New Spaces for Old

Abstract

As suggested by the title, this chapter is concerned with the “creation” of new linear spaces. Why is it necessary to devote an entire chapter to such an enterprise in order to learn Differential Calculus? In this preamble I hope to convince you that, indeed, this is essential.

Kalyan Mukherjea

3. Normed Linear Spaces, Metric Spaces

Abstract

Now that I have built up a suitably flexible algebraic framework for dealing with the linear spaces and transformations on them which arise in the study of differentiable functions between subsets of linear spaces of dimension greater than one, it is time to do some more spadework and develop the basic tools of analysis in linear spaces.

Kalyan Mukherjea

4. Calculus

Abstract

I have now done all the spadework necessary for building up a form of the Differential Calculus which will be applicable to functions between open subsets of Banach spaces.

Kalyan Mukherjea

5. Existence Theorems

Abstract

This chapter is devoted to establishing three basic existence theorems which lie at the foundations of the “three great differential theories” of Modern Mathematics: Differential Topology, Differential Geometry and Differential Equations.

Kalyan Mukherjea

6. Applications: Stationary values

Abstract

Large portions of mathematical physics, almost all of Classical Mechanics, the theory of Differential Equations and so on ad infinitum may be regarded as applications of what has been done in the last two chapters.

Kalyan Mukherjea

Backmatter

Titel: Differential Calculus in Normed Linear Spaces
verfasst von: Kalyan Mukherjea
Verlag: Hindustan Book Agency
Electronic ISBN: 978-93-86279-34-7
Print ISBN: 978-81-85931-76-0
DOI: https://doi.org/10.1007/978-93-86279-34-7

Springer Professional

Inhaltsverzeichnis

Frontmatter

1. Preliminaries

2. Linear Spaces: New Spaces for Old

3. Normed Linear Spaces, Metric Spaces

4. Calculus

5. Existence Theorems

6. Applications: Stationary values

Backmatter

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