Page - 125 - in Programming for Computations – Python - A Gentle Introduction to Numerical Simulations with Python 3.6, Volume Second Edition

5.7 Exercises 125 So,using the functionadd tofill thearray, takes50%longer time! 5.7 Exercises Exercise5.1:NestedforLoopsand Lists The code below has for loops that traverse lists of different kinds. One is with integers, one with real numbers and one with strings. Read the code and write down the printout you would have got if the program had been run (i.e., you are not supposed toactually run theprogram, just read it!). for i in [1, 2]: # First indentation level (4 spaces) print(’i: {:d}’.format(i)) for j in [3.0, 4.0]: # Second indentation level (4+4 spaces) print(’ j: {:.1f}’.format(j)) for w in [’yes’, ’no’]: # Third indentation level (4+4+4 spaces) print(’ w: {:s}’.format(w)) # First indentation level for k in [5.0, 6.0]: # Second indentation level (4+4 spaces) print(’ k: {:.1f}’.format(k)) Filename:read_nested_for_loops.py. Exercise5.2:ExceptionHandling:Divisions in aLoop Write a program that N times will ask the user for two real numbers a and b and print the result of a/b. Any exceptions should be handled properly (for example, just give an informative printout and let the program proceed with the next division, if any). The user should also be allowed to stop execution with Ctrl-c. SetN = 4 in the code (for simplicity) and demonstrate that it handles different types of user input (i.e., floats, integers, text, just pressing enter, etc.) in a sensible way. Filename:compute_division.py. Exercise5.3:TaylorSeries,sympyand Documentation In this exercise, you are supposed to develop a Python function that approximates sin(x)whenxisnearzero.Todothis,writeaprogramthatutilizessympy todevelop a Taylor series for sin(x) aroundx = 0, keeping only 5 terms from the resulting expression.Then,usesympy to turn theexpression intoa function.Let theprogram alsoplot sin(x)and thedevelopedfunction together forx in [−π,π]. Filename:symbolic_Taylor.py. Remarks Part of your task here, is to find andunderstand the requireddocumenta- tion. Most likely, this means that you have to seek more information than found in ourbook.Youmighthaveto readabout theTaylorseries (perhapsuseWikipediaor