Differential Equations and Their Applications With elements of array theory, special functions and integral transformations

This book deals with the material of differential equations, common and with some derivatives, which is usually covered in various university courses and consists of four parts. The first part is devoted to the ordinary differential equations (SDRs), while the second is dedicated to the differential equations with some derivatives (MDEs). The third part is dedicated to the complete transformations and in particular to the Laplace and Fourier transformations. Special emphasis is given to the use of these transformations for the calculation of integrals, as well as for the solution of differential and integral equations.In addition, the first part of the book includes a chapter dedicated to special functions and rectangular polynomials. The fourth part of the book is devoted to applications of differential equations, integral equations as well as special functions, which appear in various real problems such as problems of environmental engineering, fluid mechanics, hydraulics, statics, oscillations, etc.

In addition, an extensive appendix with the basics of array theory and linear algebraic systems has been included.

In more detail in this book is covered the material that concerns:

• in the basic concepts of differential equations
• in the main methods of solving first class SBS
• in the general theory and in the basic methods of solving upper order linear SBS
• in the basic methods of solving SBS systems
• in the solution of SDE with the method of dynamos
• in eigenvalue problems for SBS
• in Fourier series
• in the Gamma, Beta, Error, Bessel functions, as well as in the rectangular polynomials Legendre, Hermite, Chebyshev, Laguerre
• in d’Alembert ’s solution to the wave equation
• in the method of the characteristic equation for specific classes of MDE
• in the method of features for solving first-order MDE
• in the method of separating variables for solving MDE
• in the Laplace transform