Week 8

Python Review... Victor Miclovich November 4, 2009

Noise • What’s happening? • I expect lots of questions by now... including working programs which non of you has ever sent me

Select Exercises • functions... we are all going to design functions – A recursive function of your choice; check http://wikipedia.org if you don’t know any... The aim of this exercise is to see you design functions from observing math! f (x) = x(x − 1)!, 0! = 1 ∀x ⊂ Z • Classful programming: but first, a re-discussion of procedural programming

Introduction to Scientific computing with Python C = 21 F = ( 9 / 5 ) ∗C + 32 print F 1

If you have done some C programming... we could have written: #include <s t d i o . h> int main ( ) { int C = 2 1 ; int F = ( 9 / 5 ) ∗ C + 3 2 ; 1

This is integer division... for practice, force it to be true division

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p r i n t f ( ”F i s %f ” ,F ) ; return 0 ; } I will show you guys two examples (C and Python)... I guess it is because I want you guys to get used to multi-language programming. Later, you might have to extend the power of a program by writing using a faster language.

Problems Using the squareroot function2 . Consider the vertical motion of a ball. How much time does it take for the ball to reach the height yc ? The answer is straightforward. When y = yc we have 1 yc = v0 t − gt2 2 That equation is a quadratic function... which we solve with respect to t. Rearranging we have: 1 2 gt − v0 t + yc = 0 2 And using the well-known formula3 for the two solutions of a quadratic equation, we find     p p v0 + v02 − 2gyc v0 − vo2 − 2gyc , t2 = t1 = g g There are two solutions because the ball reaches the height yc on its way up (t = t1 ) and on its way down (t = t2 > t1 ). The Python program??? We can use functions found in the math library v0 = 5 g = 9.81 yc = 0 . 2 import math t 1 = ( v0 − math . s q r t ( v0 ∗∗2 − 2∗ g∗ yc ) ) / g t 2 = ( v0 + math . s q r t ( v0 ∗∗2 − 2∗ g∗ yc ) ) / g p r i n t ’ At t=%g s and %g s , t h e h e i g h t i s %g m’ % ( t1 , t2 , yc ) The output from this program is At t=0.0417064 s and 0.977662 s, the height is 0.2 m. 2

>>>import math >>>math.sqrt(4) 3 buffalo method

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Importing modules in Python Modules are just collections of functions and hence also known as libraries; We can import like sos... import math and then access individual functions in the module with the module name as prefix as in x = math . s q r t ( y ) The other alternative is to import only the functions that you want... from math import s q r t # you can a l s o import e v e r y t h i n g from math import ∗ 4

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When you import everything, you may just write function names including the arguments/values everything function takes as input

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