1. Expressing functions as infinite series
Power Series
Expressing functions as infinite series

2. Basic Ideas…
Assume that a function f(x) can be expanded as a power series and that you know the value of f(x) and its derivatives at x = a
The coefficients will depend on the nature of the function

3. You can determine the coefficients by differentiating and letting x = a:

4. A fundamental result…
Any continuous, differentiable function can be “re-cast” as:
This is also known as the Taylor Series or Taylor Expansion

5. The Maclaurin Series (a = 0)
Examples:
sin(x) ex