A book with a collection of examples of general, elementary series.

Descrizione

Prefazione

Contenuto

A book with a collection of examples of general, elementary series.

Here follows a collection of examples of *general, elementary series*. The reader is also referred to Calculus 3b. The main subject is Power series; but first we must consider series in general. We shall in *Calculus 3c-3* return to the power series.

Finally, even if I have tried to write as careful as possible, I doubt that all errors have been removed. I hope that the reader will forgive me the unavoidable errors.

Leif Mejlbro

- Introduction

- Partial sums and telescopic series
- Simple convergence criteria for series
- The integral criterion
- Small theoretical examples
- Conditional convergence and Leibniz’s criterion
- Series of functions; uniform convergence

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Leif Mejlbro

*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 his retirement in 2003. He has twice been on leave, first time one year at the *Swedish Academy, Stockholm*, and second time at *the Copenhagen Telephone Company*, now part of the *Danish Telecommunication Company*, in both places doing research.

At the *Technical University of Denmark* he has during more than three decades given lectures in such various mathematical subjects as *Elementary Calculus, Complex Functions Theory, Functional Analysis, Laplace Transform, Special Functions, Probability Theory* and *Distribution Theory*, as well as some courses where *Calculus* and various *Engineering Sciences* were merged into a bigger course, where the lecturers had to cooperate in spite of their different background. He has written textbooks to many of the above courses.

His research in *Measure Theory* and *Complex Functions Theory* is too advanced to be of interest for more than just a few specialist, so it is not mentioned here. It must, however, be admitted that the philosophy of *Measure Theory* has deeply in
uenced his thinking also in all the other mathematical topics mentioned above.

After he retired he has been working as a consultant for engineering companies { at the latest for the *Femern Belt Consortium*, setting up some models for chloride penetration into concrete and giving some easy solution procedures for these models which can be applied straightforward without being an expert in *Mathematics*. Also, he has written a series of books on some of the topics mentioned above for the publisher *Ventus/Bookboon*.