Some exercises to get used to numpy
- Make a vector of length 10 with elements all zero! Then modify its 4th element to 1 (zeros)
- Make a 3-by-3 matrix with elements ranging from 0 up to 8 (reshape)
- Make a random vector of length 30 containing random number between 0 to 1! Calculate its average and standard deviation! (rand, mean, std)
- Make a random vector of the same length with elements between -3 and 2!
- Make a random unit vector in 5 dimensions! First make a random vector in 5 dimensions and then normalize it to unit length!
Generate 500000 random points in the rectangle . Count how many of the points (x,y) have the property that x2 > y. Use this to approximate the integral Like in the end of the lecture.
Write a Python program to sort a list of tuples using Lambda. Original list of tuples:
[('English', 88), ('Science', 90), ('Maths', 97), ('Social sciences', 82)]
Sorting the List of Tuples:
[('Social sciences', 82), ('English', 88), ('Science', 90), ('Maths', 97)]
Write a Python program to filter a list of integers using Lambda. Original list of integers:
[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]
Even numbers from the said list:
[2, 4, 6, 8, 10]
Odd numbers from the said list:
[1, 3, 5, 7, 9]
Write a Python program to triple all numbers of a given list of integers. Use Python map.
Each problem counts for 3 points
Estimate the integral of on the interval [ − 2,5] with the left Riemann sum!
Plot the function sin(x) and its derivative on the interval [ − π,π]. Calculate the derivative with finite difference method!