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Vol. 27, pp. 1708–1718, August 1957. [9] A. Michaeli, “Equivalent edge currents for arbitrary aspects of observation,” IEEE Trans. , vol. 23, pp. 252–258, March 1984. [10] H. Ling, S. W. Lee, and R. Chou, “Shooting and bouncing rays: calculating the RCS of an arbitrarily shaped cavity,” IEEE Trans. , vol. 37, pp. 194–205, February 1989. [11] H. Ling, S. W. Lee, and R. Chou, “High-frequency RCS of open cavities with rectangular and circular cross sections,” IEEE Trans. , vol. 37, pp. 648–652, May 1989.

Doing so yields ∆x 4πǫ = a1 0 1 dx′ + · · · + aN (x1 − x′ ) + a2 N∆x (N−1)∆x 1 dx′ (x1 − x′ ) + a2 .. 10) which comprises a matrix system of the form ⎤⎡ ⎡ Z11 Z12 Z13 . . Z1N ⎥⎢ ⎢Z ⎢ 21 Z22 Z23 . . Z2N ⎥ ⎢ ⎥⎢ ⎢ ⎢ Z31 Z32 Z33 . . Z3N ⎥ ⎢ ⎥⎢ ⎢ ⎢ ⎢ . . .. ⎥ .. ⎥⎢ ⎢ . . ⎦⎣ ⎣ . . Z N 1 ZN 2 ZN 3 . . Z N N a1 ⎤ ⎡ ⎢ a2 ⎥ ⎥ ⎢ ⎥ ⎢ ⎢ a3 ⎥ ⎥=⎢ ⎥ .. ⎥ ⎢ ⎢ . ⎦ ⎣ aN b1 ⎤ b2 ⎥ ⎥ ⎥ b3 ⎥ ⎥ .. ⎥ ⎥ . 12) can be evaluated in closed form. 14) where xb = n∆x and xa = (n − 1)∆x . Note that the linear geometry of this problem yields a matrix that has a symmetric Toeplitz structure of the form ⎡ ⎢ ⎢ ⎢ ⎢ Z=⎢ ⎢ ⎢ ⎣ Z1 Z2 Z3 .

In this chapter we will introduce the Method of Moments (MOM), a technique that is used to convert integral equations into a linear system that can then be solved numerically using the computer. To begin, we will analyze a few simple electrostatic problems to provide a bit of context, and then formally define the MOM. Next, we will discuss the expansion of an unknown function by a sum of weighted basis functions, and compare and contrast point matching and the Method of Galerkin. In the chapters that follow, we will then discuss electrodynamic problems and numerical methods for solving a general system of linear equations.

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