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This book concerns the practical solution of Partial Differential Equations (PDE). It reflects an interdisciplinary approach to problems occurring in natural Environmental Phenomena: the hydrosphere, atmosphere, cryosphere, lithosphere, biosphere and ionosphere. It assumes the reader has gained some intuitive knowledge of their solution properties and now wants to solve PDE?s for real, in the context of practical problems as they arise in real situations. The practical aspect of this book is the infused focus on computation. It presents two major discretization methods ? Finite Difference and Finite Element. The blend of theory, analysis, and implementation practicality supports solving and understanding complicated problems. It is divided into three parts. Part I is an overview of Finite Difference Methods. Part II focuses on Finite Element Method, including an FEM tutorial. Part III deals with Inverse Methods, an introduction to formal approaches to practical problems