He also found Maclaurin series for J n( x) with integer values of n. In 1732 ( Saint Petersburg), Leonhard Euler (1707-1783) employed Bessel functions of both zero and integral orders in an analysis of vibrations of a stretched membrane. He also discovered that the equation J 0( x) = 0 has infinuitely many zeroes. He used the function of zero order J 0( x) as a solution to the problem of an oscillatingĬhain suspended at one end. Introduction to Linear Algebra with Mathematica GlossaryĪlthough Johann Bernoulli (1667-1748) came in 1694 to an equation that is a particular case of what we call now the Bessel equation, it was his son who actually introduced it.ĭaniel Bernoulli (1700-1782) is generally credited with being the first to introduce the concept of Bessels functions in 1732 ( Saint Petersburg). Return to Part VII of the course APMA0340 Return to the main page for the second course APMA0340 Return to the main page for the first course APMA0330 Return to Mathematica tutorial for the second course APMA0340 Return to Mathematica tutorial for the first course APMA0330 Return to computing page for the second course APMA0340 Return to computing page for the first course APMA0330 Laplace equation in spherical coordinates.Numerical solutions of Laplace equation.Laplace equation in infinite semi-stripe.Boundary Value Problems for heat equation.Part VI: Partial Differential Equations.Part III: Non-linear Systems of Ordinary Differential Equations.Part II: Linear Systems of Ordinary Differential Equations.
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