Calculus I Review

A series of calculus lectures.

Calculus I in 20 Minutes
The Two Questions of Calculus:

1. How do you find instantaneous rates of change (velocities)?
   
2. How do you find the areas (or volumes) of exotic shapes?

Understand Calculus in 35 Minutes
This video makes an attempt to teach the fundamentals of calculus 1 such as limits, derivatives, and integration. It explains how to evaluate a function using limits, how to find the slope of the tangent line using derivatives and the limit definition of a derivative as well as to perform basic integration techniques to calculate the area under the curve.
Example:

1. Consider the function A(t) = 0.01t² + 0.5t + 100 whuch represents the amount of water (gallons) in a tank at any time t (minutes).
   (a) Calculate the amount of water at t = 0.9, 10, 11 and 20 min.
   (b) How fast is the amount of water changing in the tank at t = 10 min?
2. The rate of water flowing in a tank can be represented by the function R(t) = 0,5t + 20 where R(t) represents the number of gallons of water flowing per minute and t is the time in minutes. How much water will accumulate in the tank from t = 20 to t = 100 min?

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