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Learning By Discovery contains 26 laboratory modules that can be used as lab components in your course, or assigned as independent projects. The labs are written without specific computer commands, so students read mathematics, not text. Suggestions are provided for implementing these labs on Derive, Maple and Mathematica. Many can be done on graphing calculators.
Introduction: Resources for Calculus Collection
The Five Volumes of the Resources for Calculus
Acknowledgements
Preface
A Note to Students
Graphing Functions
Introduction to Limits of Functions
Zooming In
Discovering the Derivative
Investigating the Intermediate Value Theorem
Relationship between a Function and Its Derivative
Linking Up with the Chain Rule
Sensitivity Analysis
Newton’s Method
Indeterminate Limits and l’Hopital’s Rule
Riemann Sums and the Definite Integral
Area Functions
Average Value of a Function
Arc Length
A Mystery Function
Exploring Exponentials
Patterns of Integrals
Numerical Integration
Becoming Secure with Sequences
Getting Serious about Series
Limit Comparison Test
Approximating Functions by Polynomials
Radius of Convergence for Power Series
Polar Equations
Differential Equations and Euler’s Method
Shapes of Surfaces
Syllabi for Calculus I&ampII