Transition to Analysis with Proof

ISBN-13: 9781138064065 / Angielski / Miękka / 2017 / 348 str.

Krantz, Steven

Opis

Transition to Real Analysis with Proof provides undergraduate students with an introduction to analysis including an introduction to proof. The text combines the topics covered in a transition course to lead into a first course on analysis. This combined approach allows instructors to teach a single course where two were offered.

 

Spis treści

Chapter 1 Basic Logic; Chapter 2 Methods of Proof; Chapter 3 Set TheoryChapter 4 Relations and Functions; Chapter 5 Essential Number Systems Chapter 6 Sequences; Chapter 7 Series of Numbers; Chapter 8 Basic Topology Open and Closed Sets; Chapter 9 Limits and Continuity of Functions; Chapter 10 Differentiation of Functions; Chapter 11 The Integral; APPENDIX: Construction of The Weierstrass Nowhere Differentiable Function; Chapter 12 Sequences and Series of Functions; APPENDIX: Proof of the Weierstrass Approximation Theorem; Chapter 13 Elementary Transcendental Functions APPENDIX I Elementary Number Systems Table NotationGlossary Bibliography, Index

O autorze

Steven G. Krantz is a professor at Washington University in St. Louis where he teaches mathematics. He received his Ph.D. from Princeton University and since then has taught at UCLA, Princeton University, and Pennsylvania State University. Dr. Krantz has written over 175 scholarly papers and more than 65 books. He is the founding editor of the Journal of Geometric Analysis. He was named a fellow of the American Mathematical Society and has received the Chauvenet Prize, Beckenbach Book Award, and Kemper Prize.