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Linear algebra c-4

Quadratic equations in two or three variables

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Language:  English
This series consists of six books on the elementary part of Linear Algebra. It is aiming at the users in Physics and the technical sciences.
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This series consists of six books on the elementary part of Linear Algebra. It is aiming at the users in Physics and the technical sciences. For that reason the emphasis has been laid on worked examples, while the mathematical theory is only briefly sketched without proofs. The reader is referred to the usual textbooks. In order not to overburden the text, tensors are not included in this particular series.

Here we collect all tables of contents of all the books on mathematics I have written so far for the publisher. In the rst list the topics are grouped according to their headlines, so the reader quickly can get an idea of where to search for a given topic.In order not to make the titles too long I have in the numbering added

a for a compendium

b for practical solution procedures (standard methods etc.)

c for examples.

The ideal situation would of course be that all major topics were supplied with all three forms of books, but this would be too much for a single man to write within a limited time.

After the rst short review follows a more detailed review of the contents of each book. Only Linear Algebra has been supplied with a short index. The plan in the future is also to make indices of every other book as well, possibly supplied by an index of all books. This cannot be done for obvious reasons during the rst couple of years, because this work is very big, indeed.

It is my hope that the present list can help the reader to navigate through this rather big collection of books.

Finally, since this list from time to time will be updated, one should always check when this introduction has been signed. If a mathematical topic is not on this list, it still could be published, so the reader should also check for possible new books, which have not been included in this list yet.

Unfortunately errors cannot be avoided in a rst 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

5th October 2008

  • Introduction

  1. Conic Sections
  2. Conical surfaces
  3. Rectilinear generators
  4. Various surfaces
  5. Conical surfaces
  6. Quadratic forms

  • Index

About the Author

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.