| The mathematical solution of a physical problem usually involves thefollowing steps:1 The construction Of a mathematical model. At this step we must care- fully define the variables involved and select a consistent system of units. Tile actual mathematical equations describing the physical problem are usually mathematical realizations of physical laws or imposed constraints. Frequently, some simplifying assumptions are made at this stage in order to make the model simple enough to solve.Solution of the mathematical equations obtained in step 1. Ideally, wewould like to be able to find exact solutions of the equations, but inmany cases only approximate solutions are available. In this case,theoretical support for the existence and uniqueness of the solutionwould be reassuring.Interpretation of the solution of the mathematical problem in terms ofthe original physical situation. It is important that the mathematicalresults be consistent with physical intuition and laboratory evidence.If they are not, then the construction of the model must be criticallyreexamined. This book will be concerned mostly with step 2. We will begin by con-sidering briefly a few simple mathematical models of physical situations which willmotivate the topics to be covered in this book. Solutions to these models will be studiedlater. |
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