# Computing With Python: An Introduction to Python for Science by Claus Fuher By Claus Fuher

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5. (a) Create a list u. Store in its first three elements e0, e'"' and e2'"'. These represent the starting values Wq, "i, and 112 in the above formula. Build up the complete list from the recursion formula. (b) Construct a second list td in which you store the values nh, with n = 0,1000. Plot td versus u, see § VII. 1. , \eat"—un\, where f„ represents the values inside the vector td. Set axis labels and a title. The recursion is a multistep formula to solve the differential equation w' = an with the initial value w(0) — wq = 1.

Of particular use in scientific computing are the formatting options for the float type. 5 Exercises In this example the name of the object which gets its value inserted is given as argument to the format method. The first {} pair is replaced by the first argument, the following pairs by the subsequent arguments. 5" Here, two values are processed, a string name without a format specifier and a float value which is printed in fixed point notation with one digit after the decimal point. Remark: Braces in the string Sometimes a string might contain a pair of curly braces, which should not be considered as placeholders for a format method.

L4 = [k**2 for k in L3] (d) Concatenate L3 and L4 to a new list L5. 8 Exercises Exercise 2. Use the command range and a list comprehension to generate a list with 100 equidistantly spaced values between 0 and 1. Exercise 3. , without using your Python shell. Exercise 4. Consider the Python statements L = [n-m/2 for n in range(m)] ans = 1 + L + L[-1] and assume that the variable m has been previously assigned an integer value. What is the value of ans? Answer this question without executing the statements in Python.