Mathematical Methods for Scientists and Engineers: Linear and Nonlinear Systems
Provided here is a new approach to this subject, with emphasis on current topics, including non-linear systems and their role in diverse areas of modern scientific research including optics, condensed matter, astrophysics, vibration etc. A great portion of the book contains discussions of asymptomatic techniques used to study linear systems. This material has traditionally been taught at the graduate level only, but is now introduced at a lower level and is accessible to seniors as well as first year graduates concerned with mathematical methods for science and engineering methods. The text will also benefit physicists, engineers, scientists, and applied mathematicians.
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amplitude analysis approach approximation associated assume asymptotic becomes begin behavior bound calculation Chapter choose clear compute conclude Consider constant contribution correction damping dependence derivatives determined develop differential equation discussion displacement eigenvalues elements equal error establish evaluate exact Example EXERCISE expansion exponential expression factor Figure fixed point follows frequency function given by Equation gives harmonic increases indicate infinity initial conditions integral interested interval introduce leading limit cycle linear look matrix maximum means method motion multiply neglect nonlinear Note observe obtain origin oscillator parameter period perturbation phase positive possible powers problems radius region remains require result satisfies scale secular simple solution solve stable symbol techniques tends transformation variables vector write yields York zero