Polyanin A. Handbook of Exact Solutions to Mathematical Equations 2024

Textbook in PDF format

This reference book describes the exact solutions of the following types of mathematical equations:
Algebraic and Transcendental Equations.
Ordinary Differential Equations.
Systems of Ordinary Differential Equations.
First-Order Partial Differential Equations.
Linear Equations and Problems of Mathematical Physics.
Nonlinear Equations of Mathematical Physics.
Systems of Partial Differential Equations.
Integral Equations.
Difference and Functional Equations.
Ordinary Functional Differential Equations.
Partial Functional Differential Equations.
The book pays special attention to equations found in various fields of natural and engineering sciences (in the theory of heat and mass transfer, wave theory, hydrodynamics, gas dynamics, combustion theory, elasticity theory, general mechanics, theoretical physics, nonlinear optics, biology, chemical engineering sciences, ecology, and others) and equations of a reasonably general form, which depend on free parameters or arbitrary functions.
The Handbook of Exact Solutions to Mathematical Equations generally has no analogs in world literature and contains a vast amount of new material. The exact solutions given in the book, being rigorous mathematical standards, can be used as test problems to assess the accuracy and verify the adequacy of various numerical and approximate analytical methods for solving mathematical equations, as well as for checking and comparing the effectiveness of exact anlytical methods