Real analysis and applications : including Fourier series and the calculus of variations /
| Main Author: | |
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| Format: | Book |
| Language: | English |
| Published: |
Providence, R.I. :
American Mathematical Society,
c2005.
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| Subjects: | |
| Online Access: | Table of contents |
Table of Contents:
- CH. 1. Numbers and logic
- Ch. 2. Infinity
- Ch. 3. Sequences
- Ch. 4. Subsequences
- Ch. 5. Functions and Limits
- Ch. 6. Composition of functions
- Ch. 7. Open and closed sets
- Ch. 8. Compactness
- Ch. 9. Existence of maximum
- Ch. 10. Uniform continuity
- Ch. 11. Connected sets and the intermediate value theorem
- Ch. 12. The cantor set and fractals
- Ch. 13. The derivate and the mean value theorem
- Ch. 14. The riemann integral
- Ch. 15. The fundamental theorem of calculus
- Ch. 16. Sequences of functions
- Ch. 17. The lebesgue theory
- Ch. 18. Infinite series
- Ch. 19. Absolute convergence
- Ch. 20. Power series
- Ch. 21. The exponential function
- Ch. 22. Volumes of n-balls and the gamma function
- Ch. 23. Fourier series
- Ch. 24. Strings and springs
- Ch. 25. Convergence of fourier series
- Ch. 26. Euler's equation
- Ch. 27. First integrals and the brachistochrone problem
- Ch. 28. Geodesics and great circles
- Ch. 29. Variational notation, higher order equations
- Ch. 30. Harmonic functions
- Ch. 31. Minimal surfaces
- Ch. 32. Hamilton's action and lagrange's equations
- Ch. 33. Optimal economic strategies
- Ch. 34. Utility of consumption
- Ch. 35. Riemannian geometry
- Ch. 36. NonEuclidean geometry
- Ch. 37. General relativity