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A First Course in Real Analysis by Protter and Morrey

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  1. Continuity and Limits, 30-58
  2. Basic Properties of Functions on ℝ, 59-82
  3. Elementary Theory of Differentiation, 83-97
  4. Elementary Theory of Integration, 98-129
  5. Elementary Theory of Metric Spaces, 130-172
  6. Differentiation in ℝ, 173-193
  7. Integration in ℝ, 194-210
  8. Infinite Sequences and Infinite Series, 211-262
  9. Fourier Series, 263-284
  10. Functions Defined by Integrals; Improper Integrals, 285-304
  11. The Riemann—Stieltjes Integral and Functions of Bounded Variation, 305-328
  12. Contraction Mappings, Newton’s Method, and Differential Equations, 329-340
  13. Implicit Function Theorems and Lagrange Multipliers, 341-373
  14. Functions on Metric Spaces; Approximation, 374-412
  15. Vector Field Theory; the Theorems of Green and Stokes