Abstract
In the following we wish to present many concrete examples, foregoing extensive technical details, whose solutions have contributed essentially to the development of a general theory of extremal problems. A glance at the organization of this chapter in the Contents shows the variety of different problems one encounters. In this connection, an especially central position is assumed by Section 37.4, where we discuss a number of fundamental ideas from the classical calculus of variations. The ideas of the calculus of variations have influenced the modern theory of extremal problems in an essential way, and knowledge of these classical ideas is indispensable for a thorough understanding of the modern development.
When I was a student it was fashionable to give courses called “Elementary Mathematics from the Higher Point of View” ... . But what I needed was a few courses called “Higher Mathematics from the Elementary Point of View.”
Joel Franklin
In the occupation with mathematical problems, a more important role than generalization is played—I believe—by specialization.
David Hilbert
There are two ways to teach mathematics. One is to take real pains toward creating understanding—visual aids, that sort of thing. The other is the old British system of teaching until you’re blue in the face.
James R. Newman, compiler of the 2,535 page The World of Mathematics, quoted in the New York Times, Sept. 30,1956
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Zeidler, E. (1985). Introductory Typical Examples. In: Nonlinear Functional Analysis and its Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5020-3_2
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