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Students will learn how to use calculus to solve real problems, how to use the library to find mathematical sources, how to read and write mathematical material, and how to cooperate with their peers in solving difficult problems.
Introduction: Resources for Calculus Collection.
The Five Volumes of the Resources for Calculus Collection Acknowledgments
Preface
Suggestions for Using This Volume
Note to Students
Syllabus for Calculus I
Derivatives
Optimal Design of a Steel Drum
John Ramsay, College of Wooster
Finding the Most Economical Speed for Trucks
John Ramsay, College of Wooster
Designer Polynomials
Charles Jones, Grinnell College
Cruise Control
Eric Robinson, John Maceli, Diane Schwartz, Stan Seltzer and Steve Hilbert, Ithaca College
Security System Design
Steve Hilbert, John Maceli, Eric Robinson, Diane Schwartz and Stan Seltzer, Ithaca College
Designing a Pipeline With Minimum Cost
John Ramsay, College of Wooster
Crankshaft Design
Steve Boyce, Berea College
Valve Cover Design
Steve Boyce, Berea College
The Tape Deck Problem
Matt Richey, St. Olaf College
Antiderivatives and definite integrals
(Pre-fundamental theorem)
Population Growth
Wayne Roberts, Macalester College
Drug Dosage
Diane Schwartz, John Maceli, Eric Robinson, Stan Seltzer and Steve Hilbert, Ithaca College
Logarithms: You Figure It Out
Matt Richey, St. Olaf College
Numerical Integration and Error Estimation
Steve Boyce, Berea College
An Integral Existence Theorem
Steve Boyce, Berea College
A Fundamental Project
Charles Jones, Grinnell College
Applications of integration
Inventory Decisions
Steve Boyce, Berea College
Tile Design
Minimizing the Area Between a Graph and Its Tangent Lines
Steve Boyce, Berea College (problem suggested by R.C. Buck)
Riemann Sums, Integrals, and Average Values
Eugene Herman and Charles Jones, Grinnell College
The Ice Cream Cone Problem
Matt Richey, St. Olaf College
Multivariate calculus
Waste Container Construction
John Ramsay, College of Wooster
Own Your Own Function of Two Variables
Eugene Herman and Anita Solow, Grinnell College
Three Cylinder Intersection Problem
John Ramsay, College of Wooster
Gradient Method O ptimization
John Ramsay, College of Wooster V.
Historical projects
Archimedes' Determination of the Area of a Circle
Mic Jackson and Sarah Angley, Earlham College
Archimedes' Approximation of 7t
Mic Jackson and David May, Earlham College
Zeno's Paradoxes
Charles Jones, Grinnell College Mic Jackson and Will Carter, Earlham College
Archimedes' Determination of the Surface Area of a Sphere
Mic Jackson and Krista Briese, Earlham College
Newton's Investigation of Cubic Curves
Jeffrey Nunemacher, Ohio Wesleyan University
Cavalieri's Integration Method