This thesis is intended to be an introductory mathematical presentation of analog computation. An attempt was made to explain in concise mathematical language, how an electronic analog computer works, why it works, and the simplicity of its use. The components of the computer are considered as operational blocks, each block performing an indicated operation. Hence, the electrical knowledge presented is meager. The methods of solution and the corresponding computer solutions obtained for several types of mathematical problems are presented; such as, the determination of the characteristic vectors and characteristic values of a given matrix. In each case, a 15-amplifier Heath Kit analog computer model number ES-400 was used. Since this type of computer contains no devices for multiplying variable quantities, the only types of problems that could be considered were those that can be represented by a system of linear, ordinary differential equations with constant coefficients. However, similar techniques are applicable to the analogous non-linear systems and systems with variable coefficients, on a fully-equipped analog computer. / Master of Science