Real analysis and applications :
Morgan, Frank.
Real analysis and applications : including Fourier series and the calculus of variations / Frank Morgan. - Providence, R.I. : American Mathematical Society, c2005. - x, 197 p. : ill. ; 27 cm.
Includes index.
Includes bibliographical references and index.
Numbers and logic -- Infinity -- Sequences -- Subsequences -- Functions and limits -- Composition of functions -- Open and closed sets -- Compactness -- Existence of maximum -- Uniform continuity -- Connected sets and the intermediate value theorem -- The cantor set and fractals -- The derivative and the mean value theorem -- The Riemann integral -- The fundamental theorem of calculus -- Sequences of functions -- The Lebesgue theory -- Infinite series [Sigma][subscript n=1][superscript [infinity]] a[subscript n] -- Absolute convergence -- Power series -- The exponential function -- Volumes of n-balls and the gamma function -- Fourier series -- Strings and springs -- Convergence of Fourier series -- Euler's equation -- First integrals and the brachistochrone problem -- Geodesics and great circles -- Variational notation, higher order equations -- Harmonic functions -- Minimal surfaces -- Hamilton's action and Lagrange's equations -- Optimal economic strategies -- Utility of consumption -- Riemannian geometry -- NonEuclidean geometry -- General relativity. Ch. 1. Ch. 2. Ch. 3. Ch. 4. Ch. 5. Ch. 6. Ch. 7. Ch. 8. Ch. 9. Ch. 10. Ch. 11. Ch. 12. Ch. 13. Ch. 14. Ch. 15. Ch. 16. Ch. 17. Ch. 18. Ch. 19. Ch. 20. Ch. 21. Ch. 22. Ch. 23. Ch. 24. Ch. 25. Ch. 26. Ch. 27. Ch. 28. Ch. 29. Ch. 30. Ch. 31. Ch. 32. Ch. 33. Ch. 34. Ch. 35. Ch. 36. Ch. 37.
9780821891858
2005054563
Mathematical analysis--Textbooks.
Calculus of variations--Textbooks.
Functions of real variables--Textbooks.
Fourier series--Textbooks.
QA315 / .M58 2005
515
Real analysis and applications : including Fourier series and the calculus of variations / Frank Morgan. - Providence, R.I. : American Mathematical Society, c2005. - x, 197 p. : ill. ; 27 cm.
Includes index.
Includes bibliographical references and index.
Numbers and logic -- Infinity -- Sequences -- Subsequences -- Functions and limits -- Composition of functions -- Open and closed sets -- Compactness -- Existence of maximum -- Uniform continuity -- Connected sets and the intermediate value theorem -- The cantor set and fractals -- The derivative and the mean value theorem -- The Riemann integral -- The fundamental theorem of calculus -- Sequences of functions -- The Lebesgue theory -- Infinite series [Sigma][subscript n=1][superscript [infinity]] a[subscript n] -- Absolute convergence -- Power series -- The exponential function -- Volumes of n-balls and the gamma function -- Fourier series -- Strings and springs -- Convergence of Fourier series -- Euler's equation -- First integrals and the brachistochrone problem -- Geodesics and great circles -- Variational notation, higher order equations -- Harmonic functions -- Minimal surfaces -- Hamilton's action and Lagrange's equations -- Optimal economic strategies -- Utility of consumption -- Riemannian geometry -- NonEuclidean geometry -- General relativity. Ch. 1. Ch. 2. Ch. 3. Ch. 4. Ch. 5. Ch. 6. Ch. 7. Ch. 8. Ch. 9. Ch. 10. Ch. 11. Ch. 12. Ch. 13. Ch. 14. Ch. 15. Ch. 16. Ch. 17. Ch. 18. Ch. 19. Ch. 20. Ch. 21. Ch. 22. Ch. 23. Ch. 24. Ch. 25. Ch. 26. Ch. 27. Ch. 28. Ch. 29. Ch. 30. Ch. 31. Ch. 32. Ch. 33. Ch. 34. Ch. 35. Ch. 36. Ch. 37.
9780821891858
2005054563
Mathematical analysis--Textbooks.
Calculus of variations--Textbooks.
Functions of real variables--Textbooks.
Fourier series--Textbooks.
QA315 / .M58 2005
515