Highlights of Calculus
Highlights of Calculus (Res.18-005, MIT OCW). Instructor: Professor Gilbert Strang. Highlights of Calculus is a series of short videos that introduces the basics of calculus - how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections: 1) Introduction - Why Professor Gilbert Strang created these videos, 2) Highlights of Calculus - Five videos reviewing the key topics and ideas of calculus, Applications to real-life situations and problems, and 3) Derivatives - Twelve videos focused on differential calculus, More applications to real-life situations and problems. (from ocw.mit.edu)
|Lecture 10 - Inverse Functions f-1(y) and the Logarithm x = ln y|
For the usual y = f(x), the input is x and the output is y. For the INVERSE function x = f-1(y), the input is y and the output is x. If y equals x cubed, then x is the cube root of y: that is the inverse.
If y is the great function ex, then x is the NATURAL LOGARITHM ln y. Start at y, go to x = ln y, then back to y = e(ln y). So the LOGARITHM is the EXPONENT that produces y.
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