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While there are several excellent books dealing with numerical analysis and analytical theory, students and faculty in numerical applications to ocean dynamics have to sift through hundreds of references. This monograph is an attempt to partly rectify this situation. Major chapters (II, III and IV) deal first with the basics and then go on to various applications. Instead of covering the vast field of ocean dynamics, this book focuses on transport equations (diffusion and advection), shallow water phenomena - tides, storm surges and tsunamis; three-dimensional time dependent oceanic motion; natural oscillations; and steady state phenomena. The aim of this book is two-fold; it gives an introduction to the application of finite-difference methods to ocean dynamics, and it also reviews more complex methods.