Preclass assignment due with problem set # 15

Reading : Stewart: 8.1 and 8.2
Key areas of focus :

In 8.1 understand the difference between the limit as x grows without bound of f(x) and the limit as n grows without bound of f(n). The Montotonic Sequence Theorem on p. 570 is of vital importance. In 8.2 focus on the meaning of convergence and divergence of a series the nth term test for divergence, and the important examples of geometric series and harmonic series.
Reading Question :
8.2 #1, 17

There is a reading question on the ILT.

A note about series:
Students often find this unit the most challenging. There is a tendency to confuse sequences with series, terms of a series with partial sums, and, when we used to teach straight by the book many students seemed to miss the whole story line. To address these issues we won't take the linear approach of the textbook. We've motivated the need to look at power series by considering how values of the trigonometric functions can be obtained with a high degree of accuracy. We'll look at Taylor series from the perspective of successive approximation of a function by polynomials -in keeping with the story line from differential and integral calculus of making better and better approximations of something and then using a limiting process. When this unit is over I don't want you to think "series, isn't that when you have the formulas with all the factorials and you have a bunch of tests you do to determine convergence." Instead, I'd like you to
think of approximating functions by Taylor polynomials and understand the significance of the `center'
be happily amazed that many familiar functions have representations as infinite polynomials (power series) whose coefficients are determined by derivatives evaluated at a single point and recognize that a power series can be used to define a function
have a clear notion of what it means for a series to converge
understand radius of convergence of a power series and be comfortable manipulating power series using substitution, integration, and differentiation.
be able to use convergence tests and understand the logic behind the use.