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Winter term 2021/2022 for the course Computational Economics
发布时间:2022-01-28
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Winter term 2021/2022
for the course Computational Economics
Exercise 1: Visualization
a) Create a colored plot with contours of the function f(x,y) Both x- and y-dimension should range from −10 to 10.
b) Prepare a 3D plot of the function f(x,y)
Exercise 2: Dataframes
a) Load the csv fifile persons2.csv into a dataframe.
• Insert a column bmi which indicates the body mass index (BMI) of the person which is defifined as bmi
• A BMI between 19 and 24 is considered to be normal. Which person does not have a normal BMI?
• Create a histogram of the BMI with step size one. Choose reasonable scales and labels for x and y-axis.
Exercise 3: Control Flow
a) Write a for-loop that calculates the following sum
Test your loop with n = 10.
b) Write a function that tests if a positive integer n can be written as sum of two squared integers, i. e. Test your function for the integer n = 100.
Exercise 4: Linear Algebra
a) The solution of a linear system
is often rewritten as minimizing a function
We can calculate the gradient to
Write a matrix expression in R to compute ∇F(x) for
Exercise 5: Numerical Analysis
a) Convert the number 243 043 from base 10 into the hexadecmal. State the correspon-ding R code.
b) Visualize the function and its 5th-order Taylor approximation for
Use an x-axis ranging from −5 to 5 and y-axis from 0 to 20.
Exercise 6: Optimality Conditions
a) Verify that is a minimum of the function
State the corresponding R code.
Exercise 7: Optimization
a) Implement the one-dimensional Newton’s method to fifind a local extreme point of a function given a starting point
and a tolerance
Stop the algorithm, when
Complete the following R code.