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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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 III, Differentiable Functions in Several Variables
- Differentiable functions in several variables
- Differentiability
- The chain rule
- Directional derivative
- Cn-functions
- Taylor’s formula

- Some useful procedures
- Introduction
- The chain rule
- Calculation of the directional derivative
- Approximating polynomials
- Examples of differentiable functions
- Gradient
- The chain rule
- Directional derivative
- Partial derivatives of higher order
- Taylor’s formula for functions of several variables

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

- Index