Introduction to the theory of Fourier's series and integrals

Prejtace......Page 5
Contents......Page 7
Historical Introduction......Page 13
1 Rational And Iri~ational Numbers The System Of Real Numbers......Page 28
2 Infinil,e Sequences And Series......Page 41
3 Functions Of A Singi_je Variable Limits And Continuity......Page 61
4 The Definite Integral......Page 88
5 The Theory Of Infinite Series, Whose Terms Are Functions Of A Single Variable......Page 134
6 Definite Integrals Containing An Arbitrary Parameter......Page 181
7 Fourier's Series......Page 208
8 The Nature Of The Convergence Of Fourier's Series......Page 260
9 The Approximation Curves And Gibbs's Phenomenon In Fourier's Series *......Page 276
10 Fourier's Integrals......Page 295
Appendix I: Practical Harmonic Analysis And Periodogram Analysis......Page 307
Appendix Ii: Bibliography*......Page 314
List Of Authors Quoted......Page 330
General Index......Page 332