In this book you find the basic mathematics that is needed by engineers and university students .

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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

In this book you find the basic mathematics that is needed by engineers and university students . The author will help you to understand the meaning and function of mathematical concepts. The best way to learn it, is by doing it, the exercises in this book will help you do just that.

Topics as Elementary probability calculus, density functions and stochastic processes are illustrated.

This book requires knowledge of Calculus 1 and Calculus 2.

This is the eight book of examples from the *Theory of Probability*. In general, this topic is not my favourite, but thanks to my former colleague, Ole Jørsboe, I somehow managed to get an idea of what it is all about. We shall, however, in this volume deal with some topics which are closer to my own mathematical fields.

The prerequisites for the topics can e.g. be found in the *Ventus: Calculus 2* series and the *Ventus: Complex Function Theory* series, and all the previous *Ventus: Probability c1-c6*.

Unfortunately errors cannot be avoided in a first edition of a work of this type. However, the author has tried to put them on a minimum, hoping that the reader will meet with sympathy the errors which do occur in the text.

Leif Mejlbro

27th October 2009

- Generating functions; background
- Denition of the generating function of a discrete random variable
- Some generating functions of random variables
- Computation of moments
- Distribution of sums of mutually independent random variables
- Computation of probabilities
- Convergence in distribution

- The Laplace transformation; background
- Denition of the Laplace transformation
- Some Laplace transforms of random variables
- Computation of moments
- Distribution of sums of mutually independent random variables
- Convergence in distribution

- Characteristic functions; background
- Denition of characteristic functions
- Characteristic functions for some random variables
- Computation of moments
- Distribution of sums of mutually independent random variables
- Convergence in distribution

- Generating functions
- The Laplace transformation
- The characteristic function
- Index