• A. Average Velocity
• B. Limits
• C. Derivatives
• D. Plotting
• E. Sums/Integrals

1. Average to instantaneous velocities through the study of vertical displacement and slopes of tangent lines. Average Velocity 1 html  mws   

2. Slopes of secant lines and tangent lines. Average Velocity 2 html  mws

B . Limits

1 . An exploration of the limit concept.  Included are graphical activities to support understaning of  the definition of a limit. Limits 1 html  mws

2. A single activity that ask students to find a for a given . Limits 2 html  mws

3. Several activities exploring the limit concept and continuity through studying piecewise defined functions.

Limits 3 html  mws

4. Construction of secant lines and tangent lines for the graphs of several functions using the difference quotient and its limit. Limits 4 html  mws

5. Activities exploring the notion of a limit at . Limits 5 html  mws

6. Jump discontinuities, infinite discontinuities and one-sided limits. Limits 6 html  mws

7. Activities illustrating the limitations of graphs and graphical software to determine the value of a limit. Limits 7 html mws

8. An activity illustrating the squeeze theorem. Limits 8 html mws

9. Several illustrations of L'Hopital's Rule. Limits 9 html mws

C. Derivatives

1. Estimating the derivative with the difference quotient. Derivatives 1 html  mws

2. Comparing the graph of a function to the graph of its derivative.  This is done for smooth functions and functions with discontinuous derivatives. Derivatives 2 html  mws

3. This worksheet is an introduction to Maple's diff and D procedures. Derivatives 3 html  mws

4. Applications of the derivative as a rate of change.   Derivatives 4 html  mws

5. An application requiring students to obtain estimates for instantaneous speed from position data. .A Falling Pillow html  mws

6. A rate of change application involving the human eye. Eye Sensitivity html  mws

7. Derivatives of trigonometric functions. Derivatives 5 html  mws

8. Several activities regarding the chain rule.  One activity explores the parametric formula for dy/dx.  Others explore applications of the chain rule.  Derivatives 6 html  mws

9. The quotient rule. Derivatives 7 html  mws

10. Applications of related rates and implicit differentiation. Derivatives 8 html  mws,   

11.  Implicit plots, implicit differentiation and related rates.  Devil's Curve html  mws

12. The second derivative. Derivatives 9 html  mws

13. An activity that explores Maple's notation for finding higher derivatives. Derivatives 10 html mws

14. Linear and Quadratic approximations. Derivatives 11 html  mws

15. An activity exploring an exponential functions and its derivative. Another activity explores orthogonal families of functions using exponential functions as examples. Derivatives 12 html  mws

16. This activity explores the relationship between the derivative of a function at a point ( a, b ), and the derivative

of the inverse function at the point ( b, a ). Derivatives 13 html  mws

17. Seven activities.  Two on the absolute extrema of continuous functions on closed intervals, two on the first derivative test, two applied problems and one with a focus on critical numbers. Derivatives 14 html  mws

18. Seven activities.  Three focus on concavity, one on the second derivative test and three on graphical connections between a function and its derivatives. Derivatives 15 html  mws

19. Applied optimization problems. Derivatives 16 html  mws

20. Rolle's Theorem and the Mean Value Theorem. Derivatives 17 html  mws

21. Four activities.  Three involve differential equations (using Maple to solve them, slope fields for autonomous d.e.'s and the logistic equation).  Derivatives 18 html  mws

1. A Maple tutorial on plotting including the use of the display command. Plotting1 html  mws

2. Using Maple to plot sets of ordered pairs. Plotting 2 html  mws

3. A short activity on domains of functions. Plotting 3 html  mws

4. Shapes of curves and applications. Plotting 4 html  mws

E. Sums/Integrals

1. Sigma notation. Sums/Integrals 1 html  mws

2. Leftsums, rightsums, middlesums and areas. Sums/Integrals 2 html  mws

3. The definite integral as a signed area. Sums/Integrals 3 html  mws

F. Projects

1. A project on rates of change and limits.  The function explored is a piecewise defined function relating the freezing point of a substance to the amount of a certain present chemical. project1.pdf

2. A project on derivatives and population models, specifically the population of Canadian Lynx.. project2.pdf  

A sample supporting webpage for project2. proj2.htm

3. A project on the definite integrals and its application to probability. project3.pdf 

A sample supporting webpage for project3. proj3.htm