Cargando…
Mathematical analysis : differentiation and integration /
Mathematical Analysis: Differentiation and Integration is devoted to two basic operations of mathematical analysis, differentiation and integration. The problems directly connected with the operations of differentiation and integration of functions of one or several variables are discussed, together...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Pergamon Press,
1965.
|
| Colección: | International series of monographs in pure and applied mathematics, v. 81.
|
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Mathematical Analysis: Differentiation and Integration; Copyright Page; Table of Contents; FOREWORD; NOTATION; CHAPTER 1. 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 Operators; CHAPTER 2. 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 Points; CHAPTER 3. 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 Superpositions; CHAPTER 4. 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 Space
- CHAPTER 5. 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 Mechanics; CHAPTER 6. 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 Orders
- CHAPTER 7. THE TRANSFORMATION OF DIFFERENTIAL AND INTEGRAL EXPRESSIONS 1 Transformation of Differential Expressions; 2 Transformation of Integral Expressions; 3 Formulae for Transformation of Integrals; APPENDIXES; 1. Derivatives of Elementary Functions; 2. The Expansion of Elementary Functions into Power Series; 3. Integrals of Elementary Functions; 4. Special Functions Defined by Integrals; REFERENCES; INDEX; OTHER TITLES IN THE SERIES