The theory and practice of compound interest. Topics include measurement of interest, accumulated value, present value, annuities certain, yield rates, amortization schedules, sinking funds, stocks, and bonds. General notion of stochastic processes, finite and infinite Markov chains, discrete and continuous Markov processes, stationary processes, random walk problems, birth and death processes, waiting line and serving problems, Brownian motion. Analytic functions, contour integration, residues, and applications to such topics as integral transforms, generalized functions and boundary value problems. The interplay between discrete and continuous mathematics is emphasized throughout.
Mathematical structure is revealed from equilibrium models in discrete and continuous systems.
Fourier analysis and its role in applied mathematics is developed, e.g., differential equations and approximations. Discrete aspects are emphasized in computational models. Metric spaces, topological spaces, compactness, connectedness. The programming model and simplex method of solution, duality and sensitivity analysis, transportation and assignment problems, shortest path and maximal flow problems, project networks including PERT and CPM, introduction to integer and nonlinear programming, dynamic programming and game theory. Emphasis on modeling and problem solving.