Transition to Analysis with Proof

Description

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. The text opens with an introduction to basic logic and set theory, setting students up to succeed in the study of analysis. Each section is followed by graduated exercises that both guide and challenge students. The author includes examples and illustrations that appeal to the visual side of analysis. The accessible structure of the book makes it an ideal refence for later years of study or professional work.   Content: 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