Introduction to the Theory of Fourier's Series and Integrals (Classic Reprint)

Fourier sS eries and Integrals and theM athematical Theory of the Conduction of Heat, published in 1906. and now for some time out of print. Since 1906 so much advance has been made in the Theory ofF ourier sS eries and I ntegrals, as well as in the mathematical discussion of Heat Conduction, that it has seemed advisable to write a completely new work, and to issue the same in two volumes. The first volume, which now appears, is concerned with the Theory of Infinite Series and I ntegrals, with special reference to Fourier sS eries and I ntegrals. The second volume will be devoted to theM athematical Theory of the Conduction of Heat. No one can properly understand Fourier sS eries and Integrals without a knowledge of what is involved in the convergence of infinite series and integrals. With these questions is bound up the development of the idea of a limit and a function, and both are founded upon the modern theory of real numbers. The first three chapters deal with these matters. In Chapter IV. theD efinite Integral is treated from Riemann spoint of view, and special attention is given to the question of the convergence of infinite integrals. The theory of series whose terms are functions of a single variable, and the theory of integrals which contain an arbitrary parameter are discussed inC hapters V. and VI. It will be seen that the two theories are closely related, and can be developed on similar lines. The treatment ofF ourier sS eries inC hapter VII. depends on Dirichlet sI ntegrals. There, and elsewhere throughout the book, theS econd Theorem of Mean Value will be found an essential part of the argument.
(Typographical errors above are due to OCR software and don't occur in the book.)

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