Topics in a Differential Equations Course

To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page.

Bessel Function of the First Kind	A Bessel function of the first kind is a solution to a particular nonlinear second-order differential equation. Bessel functions appear in many physics applications when solving classical partial differential equations in cylindrical coordinates.
Differential Equation	A differential equation is an equation that involves the derivatives of a function as well as the function itself.
Euler Forward Method	The Euler forward method is a numerical method for solving ordinary differential equations.
Fourier Transform	A Fourier transform is a generalization of complex Fourier series that expresses a function in terms of frequency components. Fourier transforms arise quite commonly not only in mathematics, but also in optics, signal processing, and many other areas of science and engineering.
Laplace Transform	The Laplace transform is an integral transform perhaps second only to the Fourier transform in its utility in solving physical problems. The Laplace transform is particularly useful in solving linear ordinary differential equations such as those arising in the analysis of electronic circuits.
Ordinary Differential Equation	An equality involving a function and its derivatives.
Partial Differential Equation	A partial differential equation is an equation involving a function and its partial derivatives.
Second-Order Ordinary Differential Equation	A second-order ordinary differential equation is an ordinary differential equation that contains derivatives of second order but of no higher orders.
Separation of Variables	Separation of variables is a method of solving differential equations.
Slope Field	A slope field is a particular visualization of a linear, first-order differential equation in which the derivative at a given point is represented by a line segment of the corresponding slope.