MUSTAFA A. AKCOGLU, PhD, is Professor Emeritus in the Department of Mathematics at the University of Toronto, Canada. He has authored or coauthored over sixty journal articles on the topics of ergodic theory, functional analysis, and harmonic analysis. PAUL F.A. BARTHA, PhD, is Associate Professor in the Department of Philosophy at The University of British Columbia, Canada. He has authored or coauthored journal articles on topics such as probability and symmetry, probabilistic paradoxes, and the general philosophy of science.DZUNG MINH HA, PhD, is Associate Professor in the Department of Mathematics at Ryerson University, Canada. Dr. Ha focuses his research in the areas of ergodic theory and operator theory.

"The authors do not shy away from doing the hard work involved in proving say, the change of variable theorem for integration, the inverse function theorem, and Stokes's theorem--work which is not generally seen in standard calculus books--and thus they are quite correct when they state that students need a firm grip on single-variable calculus and some linear algebra, and a good comfort level with the comprehension and construction of rigorous proofs. Includes many examples and an excellent selection of exercises." (CHOICE, November 2010)

• Preface ix1 Sets and Functions 32 Real Numbers 133 Vector Functions 274 Normed Vector Spaces 455 Derivatives 636 Diffeomorphisms and Manifolds 837 High-Order Derivatives 958 Multiple Integrals 999 Integration of Manifolds 11510 Stokes Theorem 131

MUSTAFA A. AKCOGLU, PhD, is Professor Emeritus in the Department of Mathematics at the University of Toronto, Canada. He has authored or coauthored over sixty journal articles on the topics of ergodic theory, functional analysis, and harmonic analysis. PAUL F.A. BARTHA, PhD, is Associate Professor in the Department of Philosophy at The University of British Columbia, Canada. He has authored or coauthored journal articles on topics such as probability and symmetry, probabilistic paradoxes, and the general philosophy of science.DZUNG MINH HA, PhD, is Associate Professor in the Department of Mathematics at Ryerson University, Canada. Dr. Ha focuses his research in the areas of ergodic theory and operator theory.

"The authors do not shy away from doing the hard work involved in proving say, the change of variable theorem for integration, the inverse function theorem, and Stokes's theorem--work which is not generally seen in standard calculus books--and thus they are quite correct when they state that students need a firm grip on single-variable calculus and some linear algebra, and a good comfort level with the comprehension and construction of rigorous proofs. Includes many examples and an excellent selection of exercises." (CHOICE, November 2010)

• Preface ix1 Sets and Functions 32 Real Numbers 133 Vector Functions 274 Normed Vector Spaces 455 Derivatives 636 Diffeomorphisms and Manifolds 837 High-Order Derivatives 958 Multiple Integrals 999 Integration of Manifolds 11510 Stokes Theorem 131

MUSTAFA A. AKCOGLU, PhD, is Professor Emeritus in the Department of Mathematics at the University of Toronto, Canada. He has authored or coauthored over sixty journal articles on the topics of ergodic theory, functional analysis, and harmonic analysis. PAUL F.A. BARTHA, PhD, is Associate Professor in the Department of Philosophy at The University of British Columbia, Canada. He has authored or coauthored journal articles on topics such as probability and symmetry, probabilistic paradoxes, and the general philosophy of science.DZUNG MINH HA, PhD, is Associate Professor in the Department of Mathematics at Ryerson University, Canada. Dr. Ha focuses his research in the areas of ergodic theory and operator theory.

"The authors do not shy away from doing the hard work involved in proving say, the change of variable theorem for integration, the inverse function theorem, and Stokes's theorem--work which is not generally seen in standard calculus books--and thus they are quite correct when they state that students need a firm grip on single-variable calculus and some linear algebra, and a good comfort level with the comprehension and construction of rigorous proofs. Includes many examples and an excellent selection of exercises." (CHOICE, November 2010)

• Preface ix1 Sets and Functions 32 Real Numbers 133 Vector Functions 274 Normed Vector Spaces 455 Derivatives 636 Diffeomorphisms and Manifolds 837 High-Order Derivatives 958 Multiple Integrals 999 Integration of Manifolds 11510 Stokes Theorem 131