Mathematical Analysis: A Concise Introduction [Schroder] 9780470107966

Bridging the gap between calculus and further abstract topics this book presents a well organized and much needed introduction to the foundations of analysis. It is composed of three sections: the analysis of functions of one real variable, including an introduction to the Lebesgue integral; how the appropriate abstractions lead to a powerful and widely applicable theoretical foundation for all branches of applied mathematics; an outlook to applied subjects in which analysis is used.

頁數：578
版次：第1版
年份：2008年
規格：精裝/單色
ISBN：9780470107966

PART I. ANALYSIS OF FUNCTIONS OF A SINGLE REAL VARIABLE.
2. Sequences of Real Numbers.
3. Continuous Functions.
4. Differentiable Functions.
5. The Riemann Integral I.
6. Series of Real Numbers I.
7. Some Set Theory.
8. The Riemann Integral II.
9. The Lebesgue Integral.
10. Series of Real Numbers II.
11. Sequences of Functions.
12. Transcendental Functions.
13. Numerical Methods 203.
PART II. ANALYSIS IN ABSTRACT SPACES.
14. Integration on Measure Spaces.
15. The Abstract Venues for Analysis.
16. The Topology of Metric Spaces.
17. Differentiation in Normed Spaces.
18. Measure, Topology and Differentiation.
19. Manifolds and Integral Theorems.
20. Hilbert Spaces.
PART III. APPLIED ANALYSIS.
21. Physics Background.
22. Ordinary Differential Equations.
23. The Finite Element Method.
Conclusion and Outlook. 
APPENDICES A. Logic.
APPENDICES B. Set Theory.
APPENDICES C. Natural Numbers, Integers and Rational Numbers.