Mathematical Analysis

ForewordNotationI The Differentiation of Functions of One Variable § 1 Derivatives and Differentials of the First Order § 2 Derivatives and Differentials of Higher Orders. Taylor's Series § 3 The Application of Derivatives in Investigating Functions. Extrema § 4 Differential OperatorsII The Differentiation of Functions of n Variables § 1 Derivatives and Differentials of the First Order § 2 Derivatives and Differentials of Higher Orders. Taylor's Series § 3 Polynomials of Differential Operators § 4 The Differentiation of Mappings from En into Em § 5 Extrema § 6 Stationary PointsIII Composite and Implicit Functions of n Variables § 1 Transformation of Variables. Composite Functions § 2 Implicit Functions. Functions Depending on a Parameter § 3 Newton's Diagram § 4 The Representation of Functions of n Variables in the Form of SuperpositionsIV Systems of Functions and Curvilinear Coordinates in a Plane and in Space § 1 Mapping. Jacobians § 2 Curvilinear Coordinates in a Plane § 3 Curvilinear Coordinates in SpaceV The Integration of Functions § 1 The Indefinite Integral § 2 The Integration of Elementary Functions § 3 The Definite Integral § 4 The Integration of Functions of n Variables § 5 The Application of Definite Integrals to Problems of Geometry and MechanicsVI Improper Integrals. Integrals Dependent on a Parameter. Stieltjes' Integral § 1 Improper Integrals § 2 Limiting Process under the Sign of the Integral. Integrals Dependent on a Parameter § 3 The Stieltjes Integral for Functions of One Variable § 4 Integrals and Derivatives of Fractional OrdersVII The Transformation of Differential and Integral Expressions § 1 Transformation of Differential Expressions § 2 Transformation of Integral Expressions § 3 Formulae for Transformation of IntegralsAppendixes 1. Derivatives of Elementary Functions 2. The Expansion of Elementary Functions into Power Series 3. Integrals of Elementary Functions 4. Special Functions Defined by IntegralsReferencesIndexOther Titles in the Series