Real Functions in Several Variables: Volume VII

Space Integrals

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148 pages
Jazyk:
 English
The topic of this series of books on "Real Functions in Several Variables" is very important in the description in e.g. Mechanics of the real 3-dimensional world that we live in.
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Poslední vydání
O autorovi

Leif Mejlbro was educated as a mathematician at the University of Copenhagen, where he wrote his thesis on Linear Partial Differential Operators and Distributions. Shortly after he obtained a position at the Technical University of Denmark, where he remained until h...

Description
Content

The topic of this series of books on "Real Functions in Several Variables" is very important in the description in e.g. Mechanics of the real 3-dimensional world that we live in. Therefore, we start from the beginning, modelling this world by using the coordinates of R3 to describe e.b. a motion in space.

The theory and methods of these volumes on "Real Functions in Several Variables" are applied constantly in higher Mathematics, Mechanics and Engineering Sciences. It is of paramount importance for the calculations in Probability Theory, where one constantly integrate over some point set in space.

It is my hope that this text, these guidelines and these examples, of which many are treated in more ways to show that the solutions procedures are not unique, may be of some inspiration for the students who have just started their studies at the universities.

  1. Preface
  2. Introduction to volume VII, The space integral
  3. The space integral in rectangular coordinates
    1. Introduction
    2. Overview of setting up of a line, a plane, a surface or a space integral
    3. Reduction theorems in rectangular coordinates
    4. Procedure for reduction of space integral in rectangular coordinates
    5. Examples of space integrals in rectangular coordinates
  4. The space integral in semi-polar coordinates
    1. Reduction theorem in semi-polar coordinates
    2. Procedures for reduction of space integral in semi-polar coordinates
    3. Examples of space integrals in semi-polar coordinates
  5. The space integral in spherical coordinates
    1. Reduction theorem in spherical coordinates
    2. Procedures for reduction of space integral in spherical coordinates
    3. Examples of space integrals in spherical coordinates
    4. Examples of volumes
    5. Examples of moments of inertia and centres of gravity
  6. Formulæ
    1. Squares etc
    2. Powers etc
    3. Differentiation
    4. Special derivatives
    5. Integration
    6. Special antiderivatives
    7. Trigonometric formulæ
    8. Hyperbolic formulæ
    9. Complex transformation formulæ
    10. Taylor expansions
    11. Magnitudes of functions
  7. Index