Advanced Engineering Mathematics, Lecture 2.7: Bessel's equation
Автор: Professor Macauley
Загружено: 2017-05-09
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Advanced Engineering Mathematics, Lecture 2.7: Bessel's equation.
Bessel's equation is a 2nd order ODE that arises when solving the wave equation in polar or spherical coordinates, e.g., modeling the vibrations of a circular drum. It contains a parameter 'nu' that is an integer in the polar case (it represents the fundamental nodes of vibration) and a half-integer in the spherical case. The point x_0=0 is a regular singular point, and the Frobenius method yields two generalized power series solutions. When the parameter 'nu' is a non-integer, these are linearly independent. Otherwise, we only get one solution, called a "Bessel function of the 1st kind". Using either variation of parameters or reduction of order, a second solution can be derived, and is called a "Bessel function of the 2nd kind". These function are unbounded at the origin, so they do not arise as much when modeling waves.
Course webpage (with lecture notes, homework, worksheets, etc.): http://www.math.clemson.edu/~macaule/...
Prerequisite: http://www.math.clemson.edu/~macaule/...
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