04802nam 2200661 a 450 991013957440332120170814175819.01-283-28114-797866132811421-118-09685-11-118-09686-X1-118-09684-3(CKB)2550000000052915(EBL)697633(OCoLC)761321872(SSID)ssj0000540647(PQKBManifestationID)11925910(PQKBTitleCode)TC0000540647(PQKBWorkID)10586140(PQKB)11126434(MiAaPQ)EBC697633(EXLCZ)99255000000005291520110311d2011 uy 0engur|n|---|||||txtccrReal analysis[electronic resource] a historical approach /Saul Stahl2nd ed.Hoboken, N.J. Wiley20111 online resource (316 p.)Pure and applied mathematicsDescription based upon print version of record.0-470-87890-8 Includes bibliographical references and index.Real Analysis: A Historical Approach; Contents; Preface to the Second Edition; Acknowledgments; 1 Archimedes and the Parabola; 1.1 The Area of the Parabolic Segment; 1.2 The Geometry of the Parabola; 2 Fermat, Differentiation, and Integration; 2.1 Fermat's Calculus; 3 Newton's Calculus (Part 1); 3.1 The Fractional Binomial Theorem; 3.2 Areas and Infinite Series; 3.3 Newton's Proofs; 4 Newton's Calculus (Part 2); 4.1 The Solution of Differential Equations; 4.2 The Solution of Algebraic Equations; Chapter Appendix: Mathematica Implementations of Newton's Algorithm; 5 Euler5.1 Trigonometric Series6 The Real Numbers; 6.1 An Informal Introduction; 6.2 Ordered Fields; 6.3 Completeness and Irrational Numbers; 6.4 The Euclidean Process; 6.5 Functions; 7 Sequences and Their Limits; 7.1 The Definitions; 7.2 Limit Theorems; 8 The Cauchy Property; 8.1 Limits of Monotone Sequences; 8.2 The Cauchy Property; 9 The Convergence of Infinite Series; 9.1 Stock Series; 9.2 Series of Positive Terms; 9.3 Series of Arbitrary Terms; 9.4 The Most Celebrated Problem; 10 Series of Functions; 10.1 Power Series; 10.2 Trigonometric Series; 11 Continuity; 11.1 An Informal Introduction11.2 The Limit of a Function11.3 Continuity; 11.4 Properties of Continuous Functions; 12 Differentiability; 12.1 An Informal Introduction to Differentiation; 12.2 The Derivative; 12.3 The Consequences of Differentiability; 12.4 Integrability; 13 Uniform Convergence; 13.1 Uniform and Nonuniform, Convergence; 13.2 Consequences of Uniform Convergence; 14 The Vindication; 14.1 Trigonometric Series; 14.2 Power Series; 15 The Riemann Integral; 15.1 Continuity Revisited; 15.2 Lower and Upper Sums; 15.3 Integrability; Appendix A: Excerpts from ""Quadrature of the Parabola"" by ArchimedesAppendix B: On a Method for the Evaluation of Maxima and Minima by Pierre de FermatAppendix C: From a Letter to Henry Oldenburg on the Binomial Series (June 13, 1676) by Isaac Newton; Appendix D: From a Letter to Henry Oldenburg on the Binomial Series (October 24, 1676) by Isaac Newton; Appendix E: Excerpts from ""Of Analysis by Equations of an Infinite Number of Terms"" by Isaac Newton; Appendix F: Excerpts from ""Subsiduum Calculi Sinuum"" by Leonhard Euler; Solutions to Selected Exercises; Bibliography; Index"Combining historical coverage with key introductory fundamentals, Real Analysis: A Historical Approach, Second Edition helps readers easily make the transition from concrete to abstract ideas when conducting analysis. Based on reviewer and user feedback, this edition features a new chapter on the Riemann integral including the subject of uniform continuity, as well as a discussion of epsilon-delta convergence and a section that details the modern preference for convergence of sequences over convergence of series. Both mathematics and secondary education majors will appreciate the focus on mathematicians who developed key concepts and the difficulties they faced"--Provided by publisher.Pure and applied mathematics (John Wiley & Sons : Unnumbered)Mathematical analysisFunctions of real variablesElectronic books.Mathematical analysis.Functions of real variables.515.8515/.8MAT005000bisacshStahl Saul141807MiAaPQMiAaPQMiAaPQBOOK9910139574403321Real analysis2126825UNINA03802nam 22006855 450 991048447620332120251116233155.09783030620455303062045X10.1007/978-3-030-62045-5(CKB)4100000011715662(DE-He213)978-3-030-62045-5(MiAaPQ)EBC6454884(PPN)25885619X(PPN)253253462(iGPub)SPNA0072405(EXLCZ)99410000001171566220210111d2021 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrier17th International Conference on Biomedical Engineering Selected Contributions to ICBME-2019, December 9–12, 2019, Singapore /edited by Chwee Teck Lim, Hwa Liang Leo, Raye Yeow1st ed. 2021.Cham :Springer International Publishing :Imprint: Springer,2021.1 online resource (XVI, 186 p. 123 illus., 109 illus. in color.) IFMBE Proceedings,1433-9277 ;799783030620448 3030620441 Includes bibliographical references and index.Pilot Study – Portable Evaporative Cooling System for Exercise-Induced Hyperthermia -- Meshless Method for Numerical Solution Fractional Pennes Bioheat Equation -- A Dynamic Finite Element Simulation of the Mitral Heart Valve Closure -- Choroid Segmentation in Optical Coherence Tomography Images Using Deep Learning -- Design Concept for an Automated Lower Extremity Dressing Aid for Monoplegic and Elderly People -- Obstacle Detector and Qibla Finder for Visually Impaired Muslim Community -- Rejecting Artifacts Based on Identification of Optimal Independent Components in an Electroencephalogram during Cognitive Tasks -- HydroGEV: Extracellular Vesicle-Laden Hydrogel for Wound Healing Applications.This book gathers contributions presented at the 17th International Conference on Biomedical Engineering, held on December 9-12, 2019, in Singapore. It continues the tradition of the previous conference proceedings, thus reporting on both fundamental and applied research. It includes a set of carefully selected chapters reporting on new models and algorithms and their applications in medical diagnosis or therapy. It also discusses advances in tele-health and assistive technologies, as well as applications of nanotechnologies. Organized jointly by the Department of Biomedical Engineering of the National University of Singapore and the Biomedical Engineering Society (Singapore), this book offers a timely snapshot of innovative research and technologies and a source of inspiration for future developments and collaborations in the field of biomedical engineering.IFMBE Proceedings,1433-9277 ;79Biomedical engineeringNanotechnologyBiomechanicsBiomedical Devices and InstrumentationNanoengineeringBiomechanical Analysis and ModelingMedical and Health TechnologiesBiomedical engineering.Nanotechnology.Biomechanics.Biomedical Devices and Instrumentation.Nanoengineering.Biomechanical Analysis and Modeling.Medical and Health Technologies.345.04610.28Lim C. T.Leo Hwa LiangYeow RayeMiAaPQMiAaPQMiAaPQBOOK991048447620332117th International Conference on Biomedical Engineering2821287UNINA