Real Functions in Several Variables: Volume IX

sformation of Integrals and Improper Integrals
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132 pages
Språk:
 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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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...

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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 IX, Transformation formulæ and improper integrals
  3. Transformation of plane and space integrals
    1. Transformation of a plane integral
    2. Transformation of a space integral
    3. Procedures for the transformation of plane or space integrals
    4. Examples of transformation of plane and space integrals/li>
  4. Improper integrals
    1. Introduction
    2. Theorems for improper integrals
    3. Procedure for improper integrals; bounded domain
    4. Procedure for improper integrals; unbounded domain
    5. Examples of improper integrals/li>
  5. 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
  6. Index