Kooperativer Bibliotheksverbund

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Format: 1 Online-Ressource (xii, 326 p.) , ill , 24 cm

Edition: 2nd ed

Edition: Online-Ausgabe Elsevier e-book collection on ScienceDirect Sonstige Standardnummer des Gesamttitels: 041169-3

ISBN: 0126730318 , 9780126730319

Note: Designed to accompany: Calculus : the language of change / Keith D. Stroyan. 2nd ed. c1998. - Rev. ed. of: Calculus using Mathematica. c1993

Additional Edition: Reproduktion von Projects for calculus c1999

Language: English

URL: Volltext

UID:

Format: 1 Online-Ressource (xii, 478 p.) , 23 cm

Edition: Online-Ausgabe Elsevier e-book collection on ScienceDirect Sonstige Standardnummer des Gesamttitels: 041169-3

ISBN: 0444879277 , 9780444879271

Series Statement: Studies in logic and the foundations of mathematics v. 119

Note: Includes index

Additional Edition: Reproduktion von Foundations of infinitesimal stochastic analysis 1986

Language: English

Keywords: Nonstandard-Analysis ; Stochastik ; Stochastische Analysis ; Infinitesimalrechnung

URL: Volltext

UID:

Format: 1 online resource (339 p.)

Edition: 2nd ed.

ISBN: 1-281-03366-9 , 9786611033668 , 0-08-053994-7

Content: Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology.Subjects inc

Note: Rev. ed. of: Calculus using Mathematica. c1993. , Designed to accompany: Calculus : the language of change / Keith D. Stroyan. 2nd ed. c1998. , Front Cover; Projects for Calculus: the language of change; Copyright Page; CONTENTS; CHAPTER 1. INTRODUCTION TO THE SCIENTIFIC PROJECTS; 0.1 What Good Is It?; 0.2 How Much Work Are They?; 0.3 How to Write a Project; 0.4 Help on the World Wide Web; PROJECT 1. Linear Approximation of C02 Data; CHAPTER 2. EPIDEMIOLOGICAL APPLICATIONS; 1.1 Review of the S-I-R Model; 1.2 Basic Assumptions; 1.3 Derivation of the Equations of Change; PROJECT 2 The 1968-69 New York Hong Kong Flu Epidemic; PROJECT 3 Vaccination for Herd Immunity; 3.1. Herd Immunity; 3.2. The Contact Number Data; 3.3. Project Issues , 3.4. Vaccine FailuresPROJECT 4 S-I-S Diseases and the Endemic Limit; 4.1. Basic Assumptions; 4.2. The Continuous S-I-S Variables; 4.3. Parameters for the SIS Model; 4.4. The Importance of the Contact Ratio; 4.5. Conjectures; 4.6. Conclusions; PROJECT 5 Max-Min in S-I-R Epidemics; CHAPTER 3. THE ROLE OF RULES FOR DERIVATIVES; PROJECT 6. The Expanding Economy; PROJECT 7The Expanding House; 7.1. Volume Expansion Explained by Calculus; CHAPTER 4. APPLICATIONS OF THE INCREMENT APPROXIMATION; PROJECT 8A Derivation of Hubble's law; PROJECT 9Functional Linearity; PROJECT 10Functional Identities , 10.1. Additive FunctionsCHAPTER 5. DIFFERENTIAL EQUATIONS FROM INCREMENT GEOMETRY; PROJECT 11 The Tractrix; PROJECT 12 The Isochrone; 12.1. Conservation of Energy; PROJECT 13 The Catenary; 13.1. The Catenary Hypotheses; 13.2. Parameters; 13.3. Variables; 13.4. The Equation for Tension; 13.5. Optimizing Length and Strength; CHAPTER 6. LOG AND EXPONENTIAL FUNCTIONS; PROJECT 14 The Canary Resurrected; PROJECT 15 Drug Concentration and ""Biexponential"" Functions; 15.1. Primary Variables of the Model; 15.2. Parameters of the Model; 15.3. The Formulas for Concentration , 15.4. Comparison with Mythical Data15.5. Comparison with Real Data; PROJECT 16 Measurement of Kidney Function by Drug Concentration; 16.1. Variables and Parameters; 16.2. Overview of the Project; 16.3. Drug Data; PROJECT 17 Numerical Derivatives of Exponentials; PROJECT 18 Repeated Exponents; PROJECT 19 Solve dx = r[t]x[t] dt + f[t]; CHAPTER 7. THEORY OF DERIVATIVES; PROJECT 20 The Mean Value Math Police; 20.1. The Mean Value Theorem for Regular Derivatives; 20.2. The Theorem of Bolzano; 20.3. The Mean Value Theorem for Pointwise Derivatives; 20.4. Overall Speed IS an Average , PROJECT 21 Inverse Functions and Their Derivatives21.1. Graphical Representation of the Inverse; 21.2. The Derivative of the Inverse; 21.3. Nonelementary Inversion; PROJECT 22 Taylor's formula; 22.1. The Increment Equation and Increasing; 22.2. Taylor's formula and Bending; 22.3. Symmetric Differences and Taylor's formula; 22.4. Direct Computation of Second Derivatives; 22.5. Direct Interpretation of Higher Order Derivatives; CHAPTER 8. APPLICATIONS TO PHYSICS; PROJECT 23 The Falling Ladder (or Dad's Disaster); 23.1. Air Resistance on Dad (Optional) , PROJECT 24 Falling with Air Resistance: Data and a Linear Model , English

Additional Edition: ISBN 0-12-673031-8

Language: English

UID:

Format: 1 online resource (491 p.)

Series Statement: Studies in Logic and the Foundations of Mathematics ; Volume 119

Content: This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.

Note: Description based upon print version of record. , Front Cover; Foundations of Infinitesimal Stochastic Analysis; Copyright Page; CONTENTS; FOREWORD; CHAPTER 0. PRELIMINARY CONSTRUCTIONS; (0.0) Motivation with a Finite Probability Experiment; (0.1) Superstructures; (0.2) Results from Logic; (0.3) Basic Infinitesimals; (0.4) Saturation and Comprehension; CHAPTER 1. *FINITE AND HYPERFINITE MEASURES; (1.1) Limited Hyperfinite Measures; (1.2) Unlimited Hyperfinite Measures; (1.3) Measurable and Internal Functions; (1.4) Hyperfinite Integration; (1.5) Conditional Expectation; (1.6) Weak Compactness and SL1 , CHAPTER 2. MEASURES AND THE STANDARD PART MAP(2.1) Lebesgue Measure; (2.2) Borel and Loeb Sets; (2.3) Borel Measures; (2.4) Weak Standard Parts of Measures; CHAPTER 3. PRODUCTS OF HYPERFINITE MEASURES; (3.1) Anderson's Extension; (3.2) Hoover's Strict Inclusion; (3.3) Keisler's Fubini Theorem; CHAPTER 4. DISTRIBUTIONS; (4.1) One Dimensional Distributions; (4.2) Joint Distributions. Laws and Independence; (4.3) Some *Finite Independent Sums; CHAPTER 5. PATHS OF PROCESSES; (5.1) Metric Lifting and Projecting; (5.2) Continuous Path Processes; (5.3) Decent Path Processes , (5.4) Lebesgue and Bore1 Path Processes(5.5) Beyond [O, 1] and Scalar Values; CHAPTER 6. HYPERFINITE EVOLUTION; (6.1) Events Determined at Times and Instants; (6.2) Progressive and Previsible Measurability; (6.3) Nonanticipating Processes; (6.4) Measurable and Internal Stopping; (6.5) Martingales; (6.6) Predictable Processes; (6.7) Beyond [O.1] with Localization; CHAPTER 7. STOCHASTIC INTEGRATION; (7.1) Stieltjes Integrals and Variation; (7.2) Quadratic Variation; (7.3) Square Martingale Integrals; (7.4) Toward Local Martingale Integrals; (7.5) Notes on Continuous Martingales , (7.6) Stable Martingale Liftings(7.7) Semimartingale Integrals; AFTERWORD; REFERENCES; INDEX , English

Additional Edition: ISBN 0-444-87927-7

Language: English

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Format: 1 online resource (343 p.)

ISBN: 1-281-76761-1 , 9786611767617 , 0-08-087388-X

Series Statement: Pure and applied mathematics (Academic Press) ; 72

Content: Introduction to the Theory of infiniteseimals

Note: Description based upon print version of record. , Front Cover; INTRODUCTION TO THE THEORY OF INFINITESIMALS; Pure and Applied Mathematics; Copyright Page; CONTENTS; Preface; Acknowledgments; PART 1: CLASSICAL INFINITESIMALS; CHAPTER 1. INTRODUCTION: WHAT ARE INFINITESIMALS?; CHAPTER 2. A FIRST LOOK AT ULTRAPOWERS: A MODEL OF RATIONAL ANALYSIS; 2.1 A Free Ultrafilter u on a Countable Set J; 2.2 An Ultrapower of the Rational Numbers; 2.3 Some Calculus of Polynomials; 2.4 The Exponential Function; 2.5 Peano's Existence Theorem; 2.6 Summary; CHAPTER 3. SUPERSTRUCTURES AND THEIR NONSTANDARD MODELS; 3.1 Introduction , 3.2 Definition of a Superstructure3.3 Superstructures Are Big Enough; 3.4 Nonstandard Models of Superstructures; 3.5 The Formal Language; 3.6 Interpretations of the Formal Language; 3.7 Models of a Superstructure; 3.8 Nonstandard Ultrapower Models; 3.9 Bounded Formal Sentences; 3.10 Embedding xj in Set Theory; 3.11 *-Transforms of Categories; 3.12 Postscript to Chapter; CHAPTER 4. SOME BASIC FACTS ABOUT HYPERREAL NUMBERS; 4.1 Addition, Multiplication, and Order in 'R; 4.2 Some Simplifications of the Notation; 4.3 'R Is Non-Archimedean; 4.4 Infinite, Infinitesimal, and Finite Numbers , 4.5 Some External Entities4.6 Further Simplification of Notation and Classical Functions; 4.7 Hypercomplex Numbers; APPENDIX A. PRELIMINARY RESULTS ON ORDERED RINGS AND FIELDS; A.l Terminology; A.2 Ordered Rings and Fields; A.3 Archimedean Totally Ordered Fields; CHAPTER 5. FOUNDATIONS OF INFINITESIMAL CALCULUS; 5.1 Continuity and Limits; 5.2 Uniform Continuity; 5.3 Basic Definitions of Calculus; 5.4 The Mean Value Theorem; 5.5 The Fundamental Theorem of Calculus; 5.6 Landau's ""Oh-Calculus""; 5.7 Differential Vector Calculus; 5.8 Integral Vector Calculus; 5.9 Calculus on Manifolds , CHAPTER 6. TOPICS IN INFINITESIMAL CALCULUS6.1 Peano's Existence Theorem Revisited; 6.2 Interchanging Limits; 6.3 Euler's Product for the Sine Function; 6.4 Robinson's Lemma and Generalized Limits; 6.5 Dynamical Systems; 6.6 Geometry of the Unit Ball and Boundary Behavior; PART 2: INFINITESIMALS IN FUNCTIONAL ANALYSIS; CHAPTER 7. MORE TOOLS FROM MODEL THEORY; 7.1 Countable Ultrapowers; 7.2 Enlargements; 7.3 Comprehensive Models; 7.4 Saturated Models; 7.5 Ultralimits; 7.6 Properties of Polysaturated Models; 7.7 The Isomorphism Property of Ultralimits , CHAPTER 8. THE GENERAL THEORY OF MONADS AND INFINITESIMALS8.1 Monads with Respect to a Ring of Sets; 8.2 Chromatic Sets; 8.3 Topological Aspects of Monad Theory; 8.4 Uniform Infinitesimal Relations and Finite Points; 8.5 Topological lnfinitesimals at Remote Points; CHAPTER 9. COMPACTIFICATIONS; 9.1 Discrete Cech-Stone Compactification of N; 9.2 Measurable Infinitesimals; 9.3 The Samuel Compactification of the Hyperbolic Plane; 9.4 Normal Meromorphic Functions and Analytic Disks; 9.5 The Fatou-Lindelöf Boundary; 9.6 Bounded Holomorphic Functions and Gleason Parts , 9.7 Fixed Points of Analytic Maps on A M , English

Additional Edition: ISBN 0-12-674150-6

Language: English

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Format: Online Ressource (xii, 326 p.) , illustrations

Edition: 2. ed.

Edition: Online-Ausg. Amsterdam Elsevier Science & Technology Online-Ressource ScienceDirect

ISBN: 9780080539942 , 0080539947

Content: Introduction to the Scientific Projects. -- Epidemiological Applications. -- The Role of Rules for Derivatives. -- Applications of the Increment Approximation. -- Differential Equations from Increment Geometry. -- Log and Exponential Functions. -- Theory of Derivatives. -- Applications to Physics. -- Applications in Economics. -- Advanced Max-Min Problems. -- Applications of Linear Differential Equations. -- Forced Linear Equations. -- Applications in Ecology. -- Derivations with Vectors. -- Chemical Reactions. -- More Mathematical Projects. -- Additional Project References

Content: Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology. Subjects including: * Medicine * Engineering * Economics * Ecology * Physics * Biology

Note: Rev. ed. of: Calculus using Mathematica. c1993. - Designed to accompany: Calculus : the language of change / Keith D. Stroyan. 2nd ed. c1998. - Description based on print version record

Additional Edition: ISBN 0126730318

Additional Edition: Erscheint auch als Druck-Ausgabe Stroyan, Keith D. Projects for calculus San Diego [u.a.] : Academic Press, 1999 ISBN 0126730318

Language: English

Keywords: Electronic books ; Electronic books

DOI: 10.1016/B978-0-12-673031-9.X5000-X

URL: https://doi.org/10.1016/B978-0-12-673031-9.X5000-X

URL: Volltext

URL: Volltext  (Deutschlandweit zugänglich)

URL: lizenzpflichtig

URL: Inhaltstext

UID:

Format: Online-Ressource , xii, 478 p , 23 cm

Edition: Online-Ausg.] Elsevier e-book collection on ScienceDirect

ISBN: 0444879277 , 9780444879271

Series Statement: Studies in logic and the foundations of mathematics v. 119

Note: Includes index

Additional Edition: Erscheint auch als Druck-Ausgabe Stroyan, K. D. Foundations of infinitesimal stochastic analysis Amsterdam [u.a.] : North-Holland, 1986 ISBN 0444879277

Language: English

Subjects: Mathematics

Keywords: Stochastischer Prozess ; Nonstandard-Analysis ; Stochastische Analysis ; Nonstandard-Analysis

URL: Volltext  (Deutschlandweit zugänglich)

UID:

Format: XII, 478 S

ISBN: 0444879277

Series Statement: Studies in logic and the foundations of mathematics 119

Note: Literaturverz. S. 446 - 452

Additional Edition: Erscheint auch als Online-Ausgabe Stroyan, K. D. Foundations of infinitesimal stochastic analysis Amsterdam : North-Holland, 1986 ISBN 0444879277

Additional Edition: ISBN 9780444879271

Language: English

Subjects: Mathematics

Keywords: Stochastischer Prozess ; Nonstandard-Analysis ; Stochastische Analysis ; Nonstandard-Analysis

URL: Inhaltsverzeichnis

UID:

Format: XIII, 326 S , graph. Darst , 24 cm

ISBN: 0126741506

Series Statement: Pure and applied mathematics 72

Note: Includes index , Literaturverz. S. [316] - 321

Additional Edition: Erscheint auch als Online-Ausgabe Stroyan, K. D. Introduction to the theory of infinitesimals New York [u.a.] : Academic Press, 1976 ISBN 9780126741506

Additional Edition: ISBN 0126741506

Additional Edition: ISBN 9780080873886

Additional Edition: ISBN 008087388X

Language: English

Subjects: Mathematics

Keywords: Infinitesimalanalysis

URL: Inhaltsverzeichnis

Author information: Luxemburg, Wilhelmus A. J. 1929-2018