Equations of Physics and Engineering   
      
   Hello:   
      
    How do you solve let say Bessel differential equations with order of an   
   integer and half?   
      
   We know that in the textbooks, we approach it via infinite series solutions.   
      
   In Volume 1 of my book, we use Riccati theorems to handle classical equations   
   of physics and engineering.   
      
   While some examples provided for Bessel and Associated Legendre differential   
   equations, using Riccati equations, but treatment of such equations postponed   
   to other volumes of author's series.   
      
   You will have a chance to examine all classical equations of physics, using   
   Riccati theorems provided in the book, and advance further.   
      
   I suppose it takes a decade such that, we eventually transform solving of   
   differential equations of classical type to Riccati DNA.   
      
   Applications are ranging from solving integrations to differential equations.   
   For example, as noted in DNA of mathematics book, the following function:   
      
   S1: (t+2)/(t*sqrt((t+1)*(2*t^2+b*(t+1))));   
      
   Where b is a non-zero real number, has integration of all rational functions.   
   However Maple, and Mathematica, expresses them with Elliptic functions.   
      
   These are integrations squeezed between Riccati and polynomials, and presented   
   normally as a class, depending on degree of polynomial.   
      
   Many such elliptic solving integrals with complete rational solutions will be   
   presented in the future volumes.   
      
   Sincerely   
      
   Dr.Mehran Basti   
   Retired mathematician   
      
   PS: Volume 1 will be ready by Christmas.   
      
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