Real Functions in Several Variables: Volume II

Continuous Functions in Several Variables

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142 pages
Idioma:
 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 II, Continuous Functions in Several Variables
  3. Continuous functions in several variables
    1. Maps in general
    2. Functions in several variables
    3. Vector functions
    4. Visualization of functions
    5. Implicit given function
    6. Limits and continuity
    7. Continuous functions
    8. Continuous curves
    9. Connectedness
    10. Continuous surfaces in R3
    11. Main theorems for continuous functions
  4. A useful procedure
    1. The domain of a function
  5. Examples of continuous functions in several variables
    1. Maximal domain of a function
    2. Level curves and level surfaces
    3. Continuous functions
    4. Description of curves
    5. Connected sets
    6. Description of surfaces
  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