Real analysis and applications : including Fourier series and the calculus of variations / Frank Morgan.

Includes index.

Includes bibliographical references and index.

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 derivative 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 [Sigma][subscript n=1][superscript [infinity]] a[subscript n] -- 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.