Functions of a Real Variable

Start reading → Derivatives

1. Front matter
   1. Introduction
   2. To the reader
2. IDerivatives
   1. Derivatives
   2. § 1. First derivative36
   3. § 2. The mean value theorem21
   4. § 3. Derivatives of higher order8
   5. § 4. Convex functions of a real variable23
3. IIPrimitives and integrals
   1. Primitives and integrals
   2. § 1. Primitives and integrals28
   3. § 2. Integrals over non-compact intervals9
   4. § 3. Derivatives and integrals of functions depending on a parameter18
4. IIIElementary functions
   1. Elementary functions
   2. § 1. Derivatives of the exponential and circular functions9
   3. § 2. Expansions of the exponential and circular functions and of the functions associated with them1
   4. Historical Note
5. IVDifferential equations
   1. Differential equations
   2. § 1. Existence theorems29
   3. § 2. Linear differential equations25
   4. Historical Note
6. VLocal study of functions
   1. Local study of functions
   2. § 1. Comparison of functions on a filtered set38
   3. § 2. Asymptotic expansions12
   4. § 3. Asymptotic expansions of functions of a real variable24
   5. § 4. Application to series with positive terms13
   6. App. 0. Hardy Fields. (H) Functions21
7. VIGeneralized Taylor expansions euler-maclaurin summation formula
   1. Generalized Taylor expansions euler-maclaurin summation formula
   2. § 1. Generalized Taylor expansions21
   3. § 2. Eulerian expansions of the trigonometric functions and Bernoulli numbers5
   4. § 3. Bounds for the remainder in the euler-maclaurin summation formula
   5. Historical Note
8. VIIThe gamma function
   1. The gamma function
   2. § 1. The gamma function in the real domain8
   3. § 2. The gamma function in the complex domain6
   4. Historical Note
9. Indexes
   1. Index of notation
   2. Index