Exercises
Ex. 1 → Compute the value of the sum:
Ex. 2 → Create a generator that computes the sequence defined by the relation:
Ex. 3 → Generate all the even numbers.
Ex. 4 → Let . In calculus, it is shown that . Determine experimentally the smallest number n such that . Use a generator for this task.
Ex. 5 → Generate all prime numbers less than a given integer. Use the algorithm called Sieve of Eratosthenes.
Ex. 6 → Solving the differential equation by applying the explicit Euler method results in the recursion:
Write a generator that computes the solution values un for a given initial value u0 and for a given value of the time step h.
Ex. 7 → Compute π using the formula:
The integral can be approximated using the composite trapezoidal rule, that is, by this formula:
where .
Program a generator for the values yi = f(xi) and evaluate the formula by summing one term after the other. Compare your results with the quad
function of SciPy.
Ex. 8 → Let x = [1, 2, 3] and y = [-1, -2, -3...