eBook - PDF
The Fundamentals of Mathematical Analysis
- 541 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
The Fundamentals of Mathematical Analysis
About this book
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 ""integrals of first kind"" and ""integrals of second kind."" The discussions in the book start with an introduction to the elementary concepts of series of numbers, infinite sequences and their limits, and the continuity of the sum of a series. The definition of improper integrals of unbounded functions and that of uniform convergence of integrals are explained. Curvilinear integrals of the first and second kinds are analyzed mathematically. The book then notes the application of surface integrals, through a parametric representation of a surface, and the calculation of the mass of a solid. The text also highlights that Green's formula, which connects a double integral over a plane domain with curvilinear integral along the contour of the domain, has an analogue in Ostrogradski's formula. The periodic values and harmonic analysis such as that found in the operation of a steam engine are analyzed. The volume ends with a note of further developments in mathematical analysis, which is a chronological presentation of important milestones in the history of analysis. The book is an ideal reference for mathematicians, students, and professors of calculus and advanced mathematics.
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Table of contents
- Front Cover
- The Fundamentals of Mathematical Analysis
- Copyright Page
- Table of Contents
- CHAPTER 15. SERIES OF NUMBERS
- CHAPTER 16. SEQUENCES AND SERIES OF FUNCTIONS
- CHAPTER 17. IMPROPER INTEGRALS
- CHAPTER 18. INTEGRALS DEPENDING ON A PARAMETER
- CHAPTER 19. IMPLICIT FUNCTIONS. FUNCTIONAL DETERMINANTS
- CHAPTER 20. CURVILINEAR INTEGRALS
- CHAPTER 21. DOUBLE INTEGRALS
- CHAPTER 22. THE AREA OF A SURFACE. SURFACE INTEGRALS
- CHAPTER 23. TRIPLE INTEGRALS
- CHAPTER 24. FOURIER SERIES
- CONCLUSION AN OUTLINE OF FURTHER DEVELOPMENTS IN MATHEMATICAL ANALYSIS
- Index
- Other Titles in the Series
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Yes, you can access The Fundamentals of Mathematical Analysis by G. M. Fikhtengol'ts, I. N. Sneddon,M. Stark,S. Ulam in PDF and/or ePUB format, as well as other popular books in Mathematics & Calculus. We have over 1.5 million books available in our catalogue for you to explore.