Difference between revisions of "Taylor Series Pi and e"
From WLCS
| (9 intermediate revisions by the same user not shown) | |||
| Line 2: | Line 2: | ||
* You will use loops to determine the approximations of mathematical constants | * You will use loops to determine the approximations of mathematical constants | ||
* You will implement the Taylor series approximation of Pi (~3.1415...) | * You will implement the Taylor series approximation of Pi (~3.1415...) | ||
| − | * You will implement the Taylor series approximation of e (~2. | + | * You will implement the Taylor series approximation of e (~2.718...) |
'''Resources:''' | '''Resources:''' | ||
* [[Media:PythonWhileLoops.pptx]] | * [[Media:PythonWhileLoops.pptx]] | ||
* [https://en.wikipedia.org/wiki/Taylor_series Wikipedia: Taylor series] | * [https://en.wikipedia.org/wiki/Taylor_series Wikipedia: Taylor series] | ||
| + | * [[Media:CommonTaylorSeriesFunctions.pdf]] | ||
'''Directions:''' | '''Directions:''' | ||
# Prompt the user for a number N (this will be how many terms you will sum in your approximation) | # Prompt the user for a number N (this will be how many terms you will sum in your approximation) | ||
# Use a while loop to iterate N times (you will need a loop counter -- N is '''not''' your loop counter) | # Use a while loop to iterate N times (you will need a loop counter -- N is '''not''' your loop counter) | ||
| − | # Use several variables to create the | + | # Use several variables to create the summation for Pi |
| − | # Print out Pi | + | # Print out Pi |
| + | # Repeat the above steps for approximating '''e''' | ||
'''Taylor Series Approximation for Pi:''' | '''Taylor Series Approximation for Pi:''' | ||
| + | |||
[[File:TaylorSeriesPi.png]] | [[File:TaylorSeriesPi.png]] | ||
| + | |||
(Wikipedia) | (Wikipedia) | ||
| + | |||
'''Taylor Series Approximation for e:''' | '''Taylor Series Approximation for e:''' | ||
| + | |||
[[File:TaylorSeriesE.png]] | [[File:TaylorSeriesE.png]] | ||
| + | |||
(Wikipedia) | (Wikipedia) | ||
| + | |||
| + | |||
| + | '''Challenge:''' | ||
| + | * Implement the Taylor series calculations for sin(x) and cos(x) | ||
| + | * [https://en.wikipedia.org/wiki/Taylor_series#List_of_Maclaurin_series_of_some_common_functions Taylor/Maclaurin series of common functions] | ||
| + | * [[Media:CommonTaylorSeriesFunctions.pdf]] | ||
Latest revision as of 10:15, 11 January 2017
Objective:
- You will use loops to determine the approximations of mathematical constants
- You will implement the Taylor series approximation of Pi (~3.1415...)
- You will implement the Taylor series approximation of e (~2.718...)
Resources:
Directions:
- Prompt the user for a number N (this will be how many terms you will sum in your approximation)
- Use a while loop to iterate N times (you will need a loop counter -- N is not your loop counter)
- Use several variables to create the summation for Pi
- Print out Pi
- Repeat the above steps for approximating e
Taylor Series Approximation for Pi:
(Wikipedia)
Taylor Series Approximation for e:
(Wikipedia)
Challenge:
- Implement the Taylor series calculations for sin(x) and cos(x)
- Taylor/Maclaurin series of common functions
- Media:CommonTaylorSeriesFunctions.pdf
