Analysis II: Differential and Integral Calculus, Fourier Series, Holomorphic Functions
The choice of topics included in this book and their order is far from the traditional approach. Elementary considerations are mixed with deeper results and historical comments. The book starts with the theory of Riemann integrals but within a few pages the reader will find uniform convergence, Fourier series and power series. Chapter 5 (the first in the second volume) ends with approximation theorems (Weierstrass), Radon measures in R and C and Schwarz distributions. The remaining two chapters are devoted to an introduction to Lebesgue theory and harmonic analysis and holomorphic functions. The last chapter contains elementary facts on Fourier series, analytic functions and holomorphic functions (while facts depending on the Cauchy integrals over arbitrary curves are omitted) and it closes with a study of Fourier integrals. The final part of the book is called ‘Science, technology, arms’ and it contains almost fifty pages of the author’s description of the role of mathematics and applied mathematics in the development of the technical background to certain arms, like the A- and H-bombs.