UID:
almahu_9947367122502882
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.
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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
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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
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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
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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
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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)
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PROJECT 24 Falling with Air Resistance: Data and a Linear Model
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English
Additional Edition:
ISBN 0-12-673031-8
Language:
English
