Author	Courant, Richard. author
Title	Introduction to Calculus and Analysis I [electronic resource] / by Richard Courant, Fritz John
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 1999
Connect to	http://dx.doi.org/10.1007/978-3-642-58604-0
Descript	XXIII, 661 p. 184 illus. online resource

From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)

1 Introduction -- 2 The Fundamental Ideas of the Integral and Differential Calculus -- 3 The Techniques of Calculus -- 4 Applications in Physics and Geometry -- 5 Taylorโs Expansion -- 6 Numerical Methods -- 7 Infinite Sums and Products -- 8 Trigonometric Series -- 9 Differential Equations for the Simplest Types of Vibration -- List of Biographical Dates

1. Mathematics
2. Functions of real variables
3. Special functions
4. Mathematics
5. Real Functions
6. Special Functions