Real Functions in One Variable  Simple 1...
Download for FREE in 4 easy steps...
This is a Premium eBook  get it free for 30 days
You can also read this in Bookboon.com Premium
Summary
This series consists of six book on the elementary part of the theory of real functions in one variable.
300+ Business books exclusively in our Premium eReader
 No adverts
 Advanced features
 Personal library
Users who viewed this item also viewed

Real Functions in One Variable  Simple 2...

Real Functions in One Variable  Elementary...

Real Functions in One Variable  Complex...

Real Functions in One Variable  Integrals...

Real Functions in One Variable

Real Functions of Several Variables  Guidelines..

Real Functions of Several Variables  Max, Vect...

Real Functions of Several Variables  Basic Con...
About the book
Description
This series consists of six book on the elementary part of the theory of real functions in one variable. It is basic in the sense that Mathematics is the language of Physics. The emhasis is laid on worked exammples, while the mathematical theory is only briefly sketched, almost without proofs. The reader is referred to the usual textbooks. The most commonly used formulæ are included in each book as a separate appendix.
Preface
In this volume I present some examples of Simple Differential Equations I, cf. also Calculus 1a, Functions of One Variable. Since my aim also has been to demonstrate some solution strategy I have as far as possible structured the examples according to the following form
A Awareness, i.e. a short description of what is the problem.
D Decision, i.e. a reflection over what should be done with the problem.
I Implementation, i.e. where all the calculations are made.
C Control, i.e. a test of the result.
This is an ideal form of a general procedure of solution. It can be used in any situation and it is not linked to Mathematics alone. I learned it many years ago in the Theory of Telecommunication in a situation which did not contain Mathematics at all. The student is recommended to use it also in other disciplines.
One is used to from high school immediately to proceed to I. Implementation. However, examples and problems at university level are often so complicated that it in general will be a good investment also to spend some time on the first two points above in order to be absolutely certain of what to do in a particular case. Note that the first three points, ADI, can always be performed.
This is unfortunately not the case with C Control, because it from now on may be difficult, if possible, to check one’s solution. It is only an extra securing whenever it is possible, but we cannot include it always in our solution form above.
It is my hope that 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.
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
Content
Preface
1. Some theorems constantly applied in the following
2. Separation of the variables
3. Linear differential equation of first order
4. The Existence and Uniqueness Theorem and other theoretical considerations
5. The Bernoulli differential equation
6. The setup of model equations
7. MAPLE programmes
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 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.
Embed
Embed Frame  Terms of UseThe embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the bookboon.com website.
The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook
If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on tbm@bookboon.com and seek permission.