From Calculus to Analysis

Exercises embedded in the text with solutions at the end of each section Approaches the real numbers through infinite decimals Classroom tested with both mathematics and mathematics education majors This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers. In addition to the standard results of advanced calculus, the book contains several interesting applications of these results. The text is intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section Content Level » Upper undergraduate Keywords » Derivatives - Fourier Series - Number Theory - Real Variables - Set Theory Related subjects » Algebra - Analysis This Textbook Features Applications Including A Proof Of The Fundamental Theorem Of Algebra, Space Filling Curves, And The Theory Of Irrational Numbers. in Addition To The Standard Results Of Advanced Calculus, The Book contains Several Interesting Applications Of These Results. The Text Is Intended To Form A Bridge Between Calculus And Analysis. It Is Based On The Authors Lecture Notes Used And Revised Nearly Every Year Over The Last Decade. The Book Contains Numerous Illustrations And Cross References Throughout, As Well As Exercises With Solutions At The End Of Each Section Part I -- Limits -- Introduction To Continuity -- Sets Of Real Numbers -- Counting -- Continuity -- Derivatives And Their Applications -- The Riemann Integral -- The Logarithm And The Exponential Function -- Part Ii -- Convergence Of Sequences -- Series -- Trigonometric Functions And Applications -- Fourier Series -- Topology -- Appendices. By Steen Pedersen. Front Matter Pages i-xix Part I Front Matter Pages 1-2 Book Chapter Pages 3-43 Limits Book Chapter Pages 45-50 Introduction to Continuity Book Chapter Pages 51-68 Sets of Real Numbers Book Chapter Pages 69-75 Counting Book Chapter Pages 77-89 Continuity Book Chapter Pages 91-126 Derivatives and Their Applications Book Chapter Pages 127-155 The Riemann Integral Book Chapter Pages 157-173 The Logarithm and the Exponential Function Part II Front Matter Pages 174-175 Book Chapter Pages 177-204 Convergence of Sequences Book Chapter Pages 205-228 Series Book Chapter Pages 229-245 Trigonometric Functions and Applications Book Chapter Pages 247-279 Fourier Series Book Chapter Pages 281-295 Topology Back Matter Pages 297-342