Contents: Linear Algebraic Equations; Finding the Square Root of a Positive Definite Matrix; Largest and Smallest Characteristic Roots; Linear Differential Equations with Constant Coefficients; Linear Differential Equations with Variable Coefficients; On the Determination of Characteristic Values for a Class of Sturm-Liouville Problems; Nonlinear Differential Equations; Asymptotic Behavior; Partial Differential Equations and Dynamic Programming; Partial Differential Equations and Invariant Imbedding; Maximum Altitude; Semigroups in Space; Variational Problems and Functional Equations; Allocation Processes, Lagrange Multipliers and the Maximum Transform;