Single Variable Calculus
Derivatives
There are not all the units of the course which means I only pick up some simple concepts support to design the algorithms.
- Geometric interpretation
- Physical interpretation
- Important for any measurement(economics, political, science, finance, physics, etc)
What is a derivatives?
The derivative is the slope of the lin tangent to the graph of f(x).
what is a tangent line, exactly?
- It is NOT just a line that meets the graph at one point.
- It is the
limitof the secant line(a line drawn between two points on the graph) as the distance between the two points goes to zero.
Notations
Calculus, rather like English or any other language, was developed by several people. As a result, just as there are many ways to express the same thing, there are many notations for the derivative.
Limits, Continuity, and Trigonometric Limits
Easy Limits
- It only needs to plug in the limiting value to get a meaningful answer.
- Jump Discontinuity
- Infinite Discontinuity
- Other discontinuities