Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Acknowledgments -- Introduction -- Chapter 6 Integration -- 6.1 Rectangles -- 6.2 Riemann integrability -- 6.3 Jordan measurability -- 6.4 Successive integration -- 6.5 Examples of successive integration -- 6.6 Change of Variables Theorem: formulation and examples -- 6.7 Partitions of unity -- 6.8 Approximation of Riemann integrable functions -- 6.9 Proof of Change of Variables Theorem -- 6.10 Absolute Riemann integrability -- 6.11 Application of integration: Fourier transformation -- 6.12 Dominated convergence -- 6.13 Appendix: two other proofs of Change of Variables Theorem -- Chapter 7 Integration over Submanifolds -- 7.1 Densities and integration with respect to density -- 7.2 AbsoluteRiemann integrabilitywith respect to density -- 7.3 Euclidean d-dimensional density -- 7.4 Examples of Euclidean densities -- 7.5 Open sets at one side of their boundary -- 7.6 Integration of a total derivative -- 7.7 Generalizations of the preceding theorem -- 7.8 Gauss' Divergence Theorem -- 7.9 Applications of Gauss' Divergence Theorem -- Chapter 8 Oriented Integration -- 8.1 Line integrals and properties of vector fields -- 8.2 Antidifferentiation -- 8.3 Green's and Cauchy's Integral Theorems -- 8.4 Stokes' Integral Theorem -- 8.5 Applications of Stokes' Integral Theorem -- 8.6 Apotheosis: differential forms and Stokes' Theorem -- 8.7 Properties of differential forms -- 8.8 Applications of differential forms -- 8.9 Homotopy Lemma -- 8.10 Poincaré's Lemma -- 8.11 Degree of mapping -- Exercises -- Exercises for Chapter 6 -- Exercises for Chapter 7 -- Exercises for Chapter 8 -- Notation -- Index.