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The fundamentals of mathematical analysis. Volume 2 /
The Fundamentals of Mathematical Analysis, Volume 2 is a continuation of the discussion of the fundamentals of mathematical analysis, specifically on the subject of curvilinear and surface integrals, with emphasis on the difference between the curvilinear and surface """"integral...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
London :
Pergamon Press,
1965.
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| Colección: | International series in pure and applied mathematics ;
v. 2. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; The Fundamentals of Mathematical Analysis; Copyright Page; Table of Contents; CHAPTER 15. SERIES OF NUMBERS; 1. Introduction; 2. The convergence of positive series; 3. The convergence of arbitrary series; 4. The properties of convergent series; 5. Infinite products; 6. The expansion of elementary functions in power series; 7. Approximate calculations using series; CHAPTER 16. SEQUENCES AND SERIES OF FUNCTIONS; 1. Uniform convergence; 2. The functional properties of the sum of a series; 3. Power series and series of polynomials
- 4. An outline of the history of seriesCHAPTER 17. IMPROPER INTEGRALS; 1. Improper integrals with infinite limits; 2. Improper integrals of unbounded functions; 3. Transformation and evaluation of improper integrals; CHAPTER 18. INTEGRALS DEPENDING ON A PARAMETER; 1. Elementary theory; 2. Uniform convergence of integrals; 3. The use of the uniform convergence of integrals; 4. Eulerian integrals; CHAPTER 19. IMPLICIT FUNCTIONS. FUNCTIONAL DETERMINANTS; 1. Implicit functions; 2. Some applications of the theory of implicit functions
- 3. Functional determinants and their formal propertiesCHAPTER 20. CURVILINEAR INTEGRALS; 1. Curvilinear integrals of the first kind; 2. Curvilinear integrals of the second kind; CHAPTER 21. DOUBLE INTEGRALS; 1. The definition and simplest properties of double integrals; 2. The evaluation of a double integral; 3 . Greenes formula; 4. Conditions for a curvilinear integral to be independent of the path of integration; 5. Change of variables in double integrals; CHAPTER 22. THE AREA OF A SURFACE. SURFACE INTEGRALS; 1. Two-sided surfaces; 2. The area of a curved surface
- 3. Surface integrals of the first type 4. Surface integrals of the second type; CHAPTER 23. TRIPLE INTEGRALS; 1. A triple integral and its evaluation; 2. Ostrogradski's formula; 3. Change of variables in triple integrals; 4. The elementary theory of a field; 5. Multiple integrals; CHAPTER 24. FOURIER SERIES; 1. Introduction; 2. The expansion of functions in Fourier series; 3. The Fourier integral; 4. The closed and complete nature of a trigonometrical system of functions; 5. An outline of the history of trigonometrical series
- CONCLUSION AN OUTLINE OF FURTHER DEVELOPMENTS IN MATHEMATICAL ANALYSISI. The theory of differential equations; II. Variational calculus; III. The theory of functions of a complex variable; IV. The theory of integral equations; V. The theory of functions of a real variable; VI. Functional analysis; Index; Other Titles in the Series