Mathematical modeling can be thought of as a four step process: 1) Description of physical situation 2) Mathematical formulation of the physical situation 3) Solution of mathematical problem 4) Physical interpretation of the mathematical solution One of the key features of the set (2) is the combination of approximate forms of the basic mathematical equations of mathematical modeling with careful and precise analysis. The approximations are required to make any progress possible, while precision is needed to make the progress meaningful. This combination is often the most difficult and elusive. This book is aimed to highlight this issue by means of combination of physical intuition and accurate derivation of mathematical models with precise analysis and MATLAB applications. Models of natural science shows that the formulation of fundamental natural laws and of technological problems in the form of rigorous mathematical models is given frequently, even prevalently, in terms of nonlinear
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