Section 8.2  Power Series and Analytic Functions

 

Try the Web Lecture for a Test of Your Understanding

• to be able to determine the convergence set of power series
• to be able to perform arithmetic operations of power series
• to be able to find power series expansions for f'(x) and the integral of f(t)dt evaluated from 0 to x, given f(x)
• to be able to change the index variables in summations
• to be able to determine Taylor series of a given function from other similar series

• power series
  
  
• converges/diverges
  
  
• converges absolutely
  
  
• radius of convergence
  
  
• Ratio test
  
  
• harmonic series
  
  
• alternating series
  
  
• Cauchy product
  
  
• differentiation and integration of power series
  
  
• analytic function

solved problems - using key ideas

• finding the convergence set of a power series, #5

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• arithmetic operations with power series, #9,11

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• finding power series expression for f'(x), given f(x), #19,21

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• change of index variables, #23

 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

• determining the Taylor series about the point x₀