Students see how calculus can explain the structure of a rainbow, guide a robot arm, or analyze the spread of AIDS. Each module starts with a concrete problem and moves on to provide a solution. The discussions are detailed, realistic, and pay careful attention to the process of mathematical modeling. Exercises, solutions, and references are provided.
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'It is very hard to find good applications for students. This volume has successfully done it. The benefits to be won with this collection of applications are great.' UMAP Journal
Book Description
Students see how calculus can explain the structure of a rainbow, guide a robot arm, or analyze the spread of AIDS. Each module starts with a concrete problem and moves on to provide a solution. The discussions are detailed, realistic, and pay careful attention to the process of mathematical modeling. Exercises, solutions, and references are provided.
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1 of 1 people found the following review helpful:
5.0 out of 5 stars
An excellent set of modeling problems using calculus,
By Charles Ashbacher (Marion, Iowa United States) - See all my reviews (TOP 500 REVIEWER) (VINE VOICE) (HALL OF FAME REVIEWER)
This review is from: Applications of Calculus (Classroom Resource Materials) (Paperback)
While the teaching of calculus is largely composed of presenting and solving basic and illustrative problems, that approach can tend to leave the students with a limited impression of how valuable it is. At least once in the two course calculus series, the students should be given a more complex problem that is based on a scenario that appears in the world. This book is a collection of outstanding elements of that class of problem.
The problems are: *) Arbitrating disputes - maximizing quadratic polynomials finds a fair solution to a labor dispute *) Fitting lines to data - minimizing quadratic polynomials finds the regression line to a data set *) Somewhere within the rainbow - minimizing trigonometric functions explains the properties of a rainbow *) Three optimization problems in computing - maximizing functions shows how to store and transmit data most efficiently *) Newton's method and fractal patterns - Newton's method generates fractal patterns in the complex plane *) How old is the Earth? - the exponential decay of rubidium is used to date very old rocks *) Falling raindrops - four differential equation models describe how a raindrop falls *) Measuring voting power - integrals of polynomials give a measure of voting power *) How to tune a radio - trigonometric integrals explain tuning a radio *) Volumes and hypercubes - integrals calculate the volumes of objects in three and higher dimensions *) Reliability and the cost of guarantees - probability integrals predict how long equipment will last *) Queueing systems - differential equations and limits analyze waiting lines *) Designer curves - parametric curves are used in computer aided design of automobiles *) Modeling the AIDS epidemic - differential equations model the spread of AIDS *) Speedy sorting - integrals, limits and L'Hopital's rule compare the speed of sorting algorithms *) Hydro-turbine optimization - Lagrange multipliers allocate water to hydroelectric turbines *) Portfolio theory - Lagrange multipliers choose a best stock-market portfolio This set of modules would also be suitable for a special topics course in mathematical modeling using calculus. They are all well written, well explained and solutions to the exercises are included.
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Inside This Book
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First Sentence:
Management and Labor are negotiating over a new contract. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
payoff polygon, slicing principle, weighted voting body, isochron diagram, arbitration problem, tire lifetimes, rainbow angle, local basin, innermost track, three turbines, comparison tree, same melt, power indices, voting bodies, end effector, unstable isotope, minimum deflection, insertion sort, kinematic equations, singular configurations, arbitration scheme, increasing failure rate, power polynomials, entire fall Key Phrases - Capitalized Phrases (CAPs): (learn more)
Selection Sort, Applications of Calculus, Burger King, Beloit College, British Columbia, New York, Law of Refraction, Philip Straffin, United States, Academic Press, Cambridge University Press, Colorado College, Colorado Springs, Scientific American, Steven Janke, Addison Wesley, Isaac Newton, Knox College, Law of Reflection, Northern Light Lake New!
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Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Management and Labor are negotiating over a new contract. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
payoff polygon, slicing principle, weighted voting body, isochron diagram, arbitration problem, tire lifetimes, rainbow angle, local basin, innermost track, three turbines, comparison tree, same melt, power indices, voting bodies, end effector, unstable isotope, minimum deflection, insertion sort, kinematic equations, singular configurations, arbitration scheme, increasing failure rate, power polynomials, entire fall Key Phrases - Capitalized Phrases (CAPs): (learn more)
Selection Sort, Applications of Calculus, Burger King, Beloit College, British Columbia, New York, Law of Refraction, Philip Straffin, United States, Academic Press, Cambridge University Press, Colorado College, Colorado Springs, Scientific American, Steven Janke, Addison Wesley, Isaac Newton, Knox College, Law of Reflection, Northern Light Lake New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
Citations (learn more)
This book cites 68
books:
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36
books
cite this book:
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- Probability and Statistical Inference (7th Edition) by Robert V Hogg on page 159, page 172, and page 65
- Introduction to Probability Theory by Paul G. Hoel on page 159, and page 172
- Chaos: Making a New Science by James Gleick on page 75, and page 76
- Introduction to Mathematical Statistics and Its Applications, An (4th Edition) by Richard J. Larsen on page 31, and page 59
- Differential Equations by HABERMAN on page 128
See all 68 books this book cites
- Calculus Problems for a New Century: Resources for Calculus Collection : A Project of the Associated Colleges of the Midwest and the Great Lakes Col (M a a Notes) by Robert Fraga in Front Matter, and page 3
- Learning by Discovery: A Lab Manual for Calculus (Classroom Resource Materials) (Volume 1) by Anita E. Solow in Front Matter (1), and Front Matter (2)
- Assessment Practices in Undergraduate Mathematics (M a a Notes) by Bonnie Gold in Front Matter
- Innovations in Teaching Abstract Algebra (Maa Notes, #60) by Ellen Maycock in Front Matter
- Geometry at Work (Mathematical Association of America Notes) by Catherine A. Gorini in Front Matter
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