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General Information
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For Students
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For Instructors
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Miscellaneous
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Functions
- Least Squares Approximation
- Applet 1 (Least Squares Approximation) : This applet explores fitting a polynomial p(x) of degree n to a given set of data points. It computes the best least squares approximation to the data, "best" in the sense that SUM (p(xi) - yi)^2 is minimized.
Limits
- Limit Laws
- Continuity
- Self Test 2 (Quiz I on Continuous Functions) : Use the definition of continuity to determine if a function is continuous or not. Comes with instant checking.
- Self Test 3 (Quiz on Properties of Continuous Functions)
Derivatives
- Definition of Derivatives
- Trigonometric Derivatives
- Velocity
- Applet 3 (Average Velocity) : Galileo experimented with falling objects. By meas-uring the distance fallen as a function of time he was able to conclude that the velocity is a linear function and that the acceleration is constant. This applet mir-rors his experiments.
- Curve Sketching
- Applet 4 (Behaviour of f, f' and f'' at given points) : Viewing a graph, determine information about a function and its first and second derivative.
- Self Test 7 (Quiz I on the behaviour of f, f' and f'' at given points) : This is a quiz to test your ability to use concepts of differentiablity to infer information about the graph of a function. Comes with instant checking.
- Self Test 8 (Quiz II on the behaviour of f, f' and f'' at given points) : You are given the graphs of f, f' and f'' and you have to determine which is which. Comes with instant checking.
Applications of Derivatives
- Tangent and Secant Lines
- Mean Value Theorem
- Linear Approximations
- Applet 7 (Linear Approximation using the First Derivative)
- Newtons Method
Integration
- Riemann Sums
- The Definite Integral
- Area Between Curves
Applications of Integration
- Applet 12 (Graph and Calculation of the Area between two curves)
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