MA1CANU Python Programming

CALCULUS (MA1CANU) 
Python Programming Assignment 
This assignment counts for 20% of the total marks of this module. Full marks for this 
assignment can be gained from complete answers to ALL questions and submitting the 
Python script .py for each questions on Blackboard system before 14:00, 20th 
December 2024 (Friday). 
Submission Instructions 
For each of the following questions 
 Put your Python script file into an individual script with the file name
PS_Assgn_Q(n)_StudentID.py using the Save As option under the File menu on
the editor window.
Where `n' should be the question number (i.e. one of 1, 2, 3, 4) together with any
subpart (e.g. 3a), and `StudentID' is your 8-digit Student ID number.
 At the beginning of each Python script, add a comment line to state `This is the
script for Q (n) of Assignment' where 'n' is the question number.
 For each question involving a graph plot, save each graph as a .png file
PS_Assgn_Q(n)_StudentID.png using the Save option on the plot window.
 All graphs must 代写MA1CANU Python Programming  include your student number in the title of the graph.
 All scripts and .png/.jpg files must be uploaded together as one submission to
Blackboard under Assessment. If multiple submissions are received only your final
submission will be marked. N.B. resubmission deletes all previous submissions so
ALL files must be re-uploaded.
 Scripts submitted in any form other than a .py file will not be
marked.
Exercises 
When answering the following questions use the principle of top-down design to design 
your algorithm before encoding it. (You do not need to submit proof of this on this occasion 
but in using it you should make your scripts both accurate and efficient, as well as saving 
yourself time.) You might also find it useful to review lectures and practical examples. 
Note that you should only use Python commands and built-in functions covered in lectures 
and practicals to answer these exercises unless you are directed otherwise. 1. Write a Python script that can print the following actions for a matrix 
2. Write a Python script of the matrix 
to print the transpose, inverse, determinant, trace, singular values and   3
4. Write a Python script file to print the solution of the equation 
6. Consider the series for the function is given by 
a. Write a function my_   _(  ) that takes values over the interval    = 0 to 5 as input and 
returns the approximate value of   (  ). [4 marks] 
b. Use a script to apply the function my_   _(  ) developed in (a) to plot the sum   (  ) versus 
   using a for loop for    = 0 to 5. Label the axes appropriately and use your UoR student 
Id number as the title for the plot and submit .png/.jpeg file of output. [4 marks] 
c. Print a column vector    by extracting the elements from the third column of array   . 
 [2 marks] 
Print the cross-product function    =    ×   . [2 marks] 
e. Print the vector   =    +   . [2 marks] 
Print a row vector B by extracting the elements from the second row of array   . 
 [2 marks] 
a. Print a matrix A . [2 marks] 
5. Define the variables    = 0.4,    =0.8 and then use them to create a Python script file 
and print a row vector (assign it to a variable named e) that has the elements:[12 marks] 
3. Consider 
i. Write a function my_ that takes values of as input and returns the approximate 
value of   . [2 marks]
ii . Use a script of the function my_ developed in (i) to use for loop to calculate and 
print the solution. [4 marks] 
 7. Use for loops to calculate and print the sum of the following quantities [10 marks] 
Hint: Consider (−1)
. (answer: 0.71432) 
Also, plot the catacaustic of the asteroid on the same plot over the same range for  : 
 
 Make sure to use enough points to create smooth curves. Provide a plot title, labels 
 for the axes, and a legend for the two curves and submit a .png/.jpeg file output. 
 
9. Create a Python script file to generate a surface mesh plot of the following function: 
Make the step sizes for the    and    directions the following: . Use your 
student ID number as a plot title and labels the axes appropriately [8 marks] 
10. A system of linear equations is given by: 
Create a Python script file to solve this system by implementing the following steps: 
 Use the elimination method to solve it and use the error command to report the error 
if it occurs. 
 Display the solution if a unique solution exists. 
If the unique solution exists, plot the lines representing the equations on the same 
graph and mark the intersection point as the solution. 
 If a unique solution doesn't exist, provide an appropriate message indicating the 
case (e.g., parallel lines, co-incident lines). 
Apply your Python script to the system 
If the solution exists and is plotted use your UoR Student ID number as the title for 
the plot and also submit a .png/.jpeg file along with your script. [6 marks] 
 11. Use odeint to create a Python script file to generate a general solution of the following first 
order linear differential equation: 
a. Write a the system of equations system_of_equation(t,a) that takes values of , as 
input and returns . [2 marks] 
b. Use a script the function developed in (a) to plot , on the same axes 
together in the same figure. Label the axes appropriately and use your UoR student Id 
number as the title for the plot and submit .png/.jpeg file of output. [4 marks] 
12. Write a user-defined Python script for the following math function: [6 marks] 
The input to the function is    (in radians) and the output is. Write the function such that can be 
 vector. Use the function to plot and submit a .png/.jpeg file as output for (polar plot) . 
using enough points to create smooth curves. Label the axes appropriately and use your 
UoR student Id number as the title for the plot and submit .png/.jpeg file of output. [ 4 m a r k s ] 
takes values of    ,   ,    as input and returns    ,   . [2 marks]
 c. Use a script the function developed in (a) and (b) to plot    ,    on the same axes together 
values of    ,    as input and returns    ,   . [2 marks]
a. Write a the parametric equations for Cayley's Sectic function cayley_sectic(t,a) that takes 
 b. Write a the parametric equations for Doppler Spiral function Doppler_spiral(t,b,k) that