- Book Name: Differential Equations With Applications and Historical Notes
- Pages: 763
- Size: 4 MB
Differential Equations With Applications PDF Free
I have taken advantage of this new edition of my book on differential equations to add two batches of new material of independent interest:
First, a fairly substantial appendix at the end of Chapter 1 on the famous bell curve. This curve is the graph of the normal distribution function, with many applications in the natural sciences, the social sciences, mathematics—in statistics and probability theory—and engineering. We shall be especially interested how the differential equation for this curve arises from very simple considerations and can be solved to obtain the equation of the curve itself.
And second, a brief section on the van der Pol nonlinear equation and its historical background in World War II that gave it significance in the development of the theory of radar. This consists, in part, of personal recollections of the eminent physicist Freeman Dyson.
Finally, I should add a few words on the meaning of the cover design, for this design amounts to a bit of self-indulgence.
Differential Equations With Applications PDF Free Download
The chapter on Fourier series is there mainly to provide machinery needed for the following chapter on partial differential equations. However, one of the minor offshoots of Fourier series is to find the exact sum of the infinite series formed from the reciprocals of the squares of the positive integers (the first formula on the cover). This sum was discovered by the great Swiss mathematician Euler in 1736, and since his time, several other methods for obtaining this sum, in addition to his own, have been discovered. This is one of the topics dealt with in Sections 34 and 35 and has been one of my own minor hobbies in mathematics for many years.
However, from 1736 to the present day, no one has ever been able to find the exact sum of the reciprocals of the cubes of the positive integers (the second formula on the cover). Some years ago, I was working with the zeroes of the Bessel functions. I thought for an exciting period of several days that I was on the trail of this unknown sum, but in the end it did not work out. Instead, the trail deviated in an unexpected direction and yielded yet another method for finding the sum in the first formula. These ideas will be found in Section 4
Differential equations with applications pdf free download.