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Advanced Mathematics for Applications by Andrea Prosperetti

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2

Some Simple Preliminaries

 

This chapter collects in a simplified form some ideas and techniques extensively used in Part I of the book. This material will be revisited in greater detail in later chapters, but the brief summary given here may be helpful to readers who do not have the time or the inclination to tackle the more extensive treatments.

§2.1 continues the considerations of the final section of the previous chapter and further explains the fundamental idea underlying the method of eigenfunction expansions. While this method may be seen as an extension of the elementary “separation of variables” procedure (cf. §3.10), the geometric view advocated here provides a powerful aid to intuition and should greatly facilitate an understanding ...

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