| dc.description.abstract | A differential equation is a mathematical equation that relates some function with its
derivatives. In applications, the functions usually represent physical quantities, the derivatives
represent their rates of change, and the equation defines a relationship between the two.
Because such relations are extremely common, differential equations play a prominent role
in many disciplines including engineering, physics, economics, and biology. In pure
mathematics, differential equations are studied from several different perspectives, mostly
concerned with their solutions—the set of functions that satisfy the equation. Only the simplest
differential equations are solvable by explicit formulas; however, some properties of solutions
of a given differential equation may be determined without finding their exact form. If a self contained formula for the solution is not available, the solution may be numerically
approximated using computers. The theory of dynamical systems puts emphasis on qualitative
analysis of systems described by differential equations, while many numerical methods have
been developed to determine solutions with a given degree of accuracy. Differential equations
can be divided into several types. Apart from describing the properties of the equation itself,
these classes of differential equations can help inform the choice of approach to a solution.
Commonly used distinctions include whether the equation is: Ordinary/Partial, Linear/Non linear, and Homogeneous/Inhomogeneous. This book written primarily for graduate, or
advanced undergraduate, students of mathematics | en_US |
