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263 pages

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The present book describes the state-of-art in the middle of the 20th century, concerning first order differential equations of known solution formulæ.

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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 present book describes the state-of-art in the middle of the 20th century, concerning first order differential equations of known solution formulæ. Among the topics can be found exact differential forms, homogeneous differential forms, integrating factors, separation of the variables, and linear differential equations, Bernoulli's equation and Riccati's equation. All topics are illustrated by examples.

*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*.

- Some necessary auxiliary results
- First order differential equations and differential forms
- Separation of the variables
- The linear differential equation of first order
- Bernoulli’s equation
- Riccati’s equation
- The homogeneous case
- The homogeneous case where L(x, y) and M(x, y) are polynomials of degree 1
- Some simple implicit given differential equations
- Summary of solution methods and formulæ