- In this video Kent Murdick introduces a car traveling at a constant speed of 50 Miles per hour. He uses this to motivate the rate of change of a function.
- The video below is a sequel. In this distance is no longer a linear function of time, but in the example it is quadratic. Kent demonstrates that the rate of change of the function depends upon the time.
These two videos together summarize a great deal of calculus. After you get into the depth of the course, we suggest that you review this introductory material.
- Now the video below might be considered a bit silly (but not nearly as silly as this ); however, a careful listen will show that it describes the fundamental rules for computing limits, and it is a list of the standard rules for differentiation. You won’t learn calculus simply by singing, but at least the lyrics contain lists of the fundamental rules.
- This video was made for the sake of precalculus, but it also applied to calculus. Notation for various number systems are introduced: those for the natural numbers, the integers , the rational numbers, and the real numbers. Ultimately calculus is the study of the real number system. However, the study occurs from an arcane point of view: we study the real number line and its underlying differentiable structure by looking at functions that preserve this structure.
On several occasions you will wish to review a topic from Precalculus. The precalculus video pages are arranged in much the same way that these are.
- This video introduces interval notation.