Informatics2-2021/Lab13
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| 14. sor: | 14. sor: | ||
Generate 500000 random points in the rectangle <math>[0,2]\times[0,4]</math>. Count how many of the points <math>(x,y)</math> have the property that <math>x^2>y</math>. Use this to approximate the integral <math>\int_0^2x^2 d x</math> Like in the end of the lecture. | Generate 500000 random points in the rectangle <math>[0,2]\times[0,4]</math>. Count how many of the points <math>(x,y)</math> have the property that <math>x^2>y</math>. Use this to approximate the integral <math>\int_0^2x^2 d x</math> Like in the end of the lecture. | ||
| − | ==Sorting | + | ==Sorting Lambda== |
Write a Python program to sort a list of tuples using Lambda. | Write a Python program to sort a list of tuples using Lambda. | ||
A lap 2021. május 11., 12:34-kori változata
Tartalomjegyzék |
Exercises
Introduction
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!
Monte-Carlo
Generate 500000 random points in the rectangle ![[0,2]\times[0,4]](/upload/math/d/1/f/d1f4d6baafac79655f4052ed2930bf35.png)
. 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.
Sorting Lambda
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)]
Homework 9
Each problem counts for 2 points
Numeric integral
Estimate the integral of 
on the interval [ − 2,5] with the left Riemann sum!
Numeric derivative
Plot the function sin(x) and its derivative on the interval [ − π,π]. Calculate the derivative with finite difference method!
