May 14

section covered in text

8.2.  Power Series, Analytic Functions, and the Taylor Series Method
 

• to be able to dertermine whether a power series converges or diverges
• to be able to find the sum, differences, products, and quotients of power series
• to be able to differentiate and integrate power series
• to be able to change the summation index
• to be able to find the Taylor series of a function'
• to be able to use the Taylor series method to estimate the solution of an initial value problem

• power series about a point x₀
• convergence or divergence of series
• absolute convergence
• radius of convergence
• ratio test
• convergence set
• Cauchy product
• analytic functions
• Taylor, Maclaurin series
• Taylor series method

solved problems - using key ideas

• determining convergence set of a power series, #1,6
• sums of power series, #10
• Cauchy product, products of series, #12
• finding derivative of a power series, #18
• finding integral of a power series, #22
• shifting the summation index, #24,28
• determining a Taylor series of a given function, #30
• determining the first 3 terms of a series solution, #40,37