Line Integrals and Surface Integrals

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190 pages

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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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About the author

*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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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.

- Preface
- Introduction to volume VIII, The line integral and the surface integral
- The line integral
- Introduction
- Reduction theorem of the line integral
- Procedures for reduction of a line integral
- Examples of the line integral in rectangular coordinates
- Examples of arc lengths and parametric descriptions by the arc length

- The surface integral
- The reduction theorem for a surface integral
- Procedures for reduction of a surface integral
- Examples of surface integrals
- Examples of surface area

- Formulæ
- Squares etc
- Powers etc
- Differentiation
- Special derivatives
- Integration
- Special antiderivatives
- Trigonometric formulæ
- Hyperbolic formulæ
- Complex transformation formulæ
- Taylor expansions
- Magnitudes of functions

- Index