Location

Brunswick, ME

Start Date

1-1-1990 12:00 AM

Description

Using Newton’s recently formulated laws of motion, Brook Taylor (1685–1721) discovered the wave equation by means of physical insight alone [1]. Daniel Bernouli (1700–1782) showed that an infinite summation of sinusoids can represent the general solution of the wave equation with given initial conditions [2]. Finally Jean Baptiste Joseph Fourier (1768–1830) showed that such an infinite sum, a Fourier series, can represent any discontinuous function under general conditions [3]. From this early work connecting the wave equation and the Fourier transform, much of engineering mathematics of wave motion and transformations has been developed.

Book Title

Review of Progress in Quantitative Nondestructive Evaluation

Volume

9A

Chapter

Minisymposium

Pages

29-36

DOI

10.1007/978-1-4684-5772-8_2

Language

en

File Format

application/pdf

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Jan 1st, 12:00 AM

History of the Wave Equation and Transforms in Engineering

Brunswick, ME

Using Newton’s recently formulated laws of motion, Brook Taylor (1685–1721) discovered the wave equation by means of physical insight alone [1]. Daniel Bernouli (1700–1782) showed that an infinite summation of sinusoids can represent the general solution of the wave equation with given initial conditions [2]. Finally Jean Baptiste Joseph Fourier (1768–1830) showed that such an infinite sum, a Fourier series, can represent any discontinuous function under general conditions [3]. From this early work connecting the wave equation and the Fourier transform, much of engineering mathematics of wave motion and transformations has been developed.