DIFFERENTIAL EQUATIONS FOR ENGINEERS AND SCIENTISTS, VOL. 1

Differential equations play an extremely important role in almost all branches of Engineering, Mathematics, Physics, etc. and in particular in the study of Applied Mathematics.
Many Physical and Engineering problems, when formulated in mathematical terms, lead to differential equations. The motion of a simple pendulum, the orbit of planets, the vibrations of a mechanical system and the oscillations of an electrical system, just to mention a few are described in terms of differential equations.
In general terms, one dimension problems are described by Ordinary Differential Equations (O.D.E) while higher dimension problems are described by Partial Differential Equations (P.D.E). The Schrödinger’s equation in Quantum Mechanics and the Einstein’s Field equations in General Relativity are Partial Differential Equations. It seems that our world is governed by differential equations.
The subject of differential equations is a complex one. In this text we lay out fundamental concepts and definitions, investigate various types of first order differential equations, present methods of obtaining their general solution and finally show how to solve a variety of problems arising in Engineering, Physics, Geometry, Biology, and Economy by means of the corresponding differential equations.