MA1MSP留学生辅导、讲解Mathematica、MATLAB编程语言辅导、讲解MATLAB
辅导Python编程|讲解SPSS
MA1MSP: Mathematical and Statistical Programming
Assignment 4
This assignment counts to 35% of the total marks of this module. Full marks of this
assignment can be gained from complete answers to ALL questions and submitting the
MATLAB files to me by email (john.evans.18@nuist.edu.cn) before 12pm (noon) 5th
June, 2019 (Wednesday).
Note:
For Questions 1, 2, you need to write a function named ‘MSP Asgn4 Qx StudentID.m’, where
’x’ should be the question number (namely one out of 1, 2) and ’StudentID’ should be your
Student ID number.
For Questions 3, 4 and 5, you will need to develop two codes, i.e. one function named
‘MSP Asgn4 Qxa StudentID.m’ and one script named ‘MSP Asgn4 Qxb StudentID.m’, respectively,
where ‘x’ should be the question number (namely one out of 3, 4 and 5) and ‘StudentID’
should be your Student ID number.
At the beginning of each file, add a comment line to state ‘This is the script/function for Q.x
of Assignment 4’ where ’x’ is the question number.
For each script (not function), add two command lines “clear all” and “close all” right below
the first comment line.
If no script or function file is uploaded then a mark of zero will be recorded for that part of the
question.
Your code should not output anything to the command window unless explicitly stated, except for
error messages. If your code does output anything that is not asked for, marks will be deducted.
By submitting your work you are confirming that the code is your own, independent work.
1. Consider a bank deposit where the interest is added to the deposit at the end of each year. The
amount collected after n years can be computed as
P = D(1 + I/100)n
,
where P is the future value, D is the initial deposit amount and I is the interest rate in percent.
We consider three different banks A, B and C.
Bank A pays the client an interest rate of 1.5%;
Bank B pays the client as follows:
1% rate if the initial amount D is less than or equal to ￡20,000,
1.5% rate if D is more than ￡20,000, but less than or equal to ￡40,000,
2.ab% rate for D greater than ￡40,000, where ab are the last two digits of your student
number.
Bank C pays the client an interest rate of 2% for the first three years, and then the interest
rate decreases to 1%. Note that the interest is always computed from the full balance,
which includes the interest accumulated over the previous years.
1Write a function ’MSP Asgn4 Q1 StudentID.m’ that requires three inputs: the initial amount
deposited D, the number of years n, and a single character that identifies which bank is being
considered, and returns one output as the future value of the deposit P.
[7.5 marks]
2. If A is an n × m matrix and B is an m × p matrix, the matrix product C = AB is the n × p
matrix defined by the equation
Write a function named ’MSP Asgn4 Q2 StudentID.m’ that takes two matrices, A of dimensions
n × m and B of dimension m × p, as inputs and returns their product matrix C, which
should fulfill the following tasks:
(a) Before performing the multiplication, the function should test if the number of columns in
A equals to the number of rows in B, and display an error message if this condition is not
satisfied;
(b) The calculation of C must be accomplished by using triple nested for loops, but NOT
using any built-in MATLAB matrix multiplication function or operator;
(c) After the calculation, the function should check if the generated matrix C is of dimensions
n × p. If yes, it displays a message ‘The dimensions of C are correct!’; Otherwise, outputs
an error message ‘The dimensions of C are wrong!’.
[7.5 marks]
3. (a) Write a function named ’MSP Asgn4 Q3a StudentID.m’ that takes as input a vector x
(including scalar) and returns the vector (including scalar)
y = aex/b cos(2x)
where the constants a, b are given by the last two digits of your student number ab. If any
of these digits are equal to zero, then replace them with 2.
[3 marks]
(b) Write a script named ’MSP Asgn4 Q3b StudentID.m’ that
i. plots the function y coded in Part (a) in the interval x ∈ [0, 5π] using a solid blue line
with linewidth 2.
ii. uses function handles to calculate the zeros of the function coded in Part (a) that are
close to the values nπ/2 with n = 0, 1, . . . , 10 and save them to a vector. Plot the
points corresponding to the zeros you have saved as red diamond symbols in the same
plot of Part (b)i.
iii. Add approximate title, legends and axis labels to the above plot.
[4.5 marks]
4. Let f(x) be defined on the interval [a, b] and let the interval be divided into n+ 1 equally spaced
points x0, x1, . . . , xn, where x0 = a and xn = b. Then the Trapezoidal rule for approximating
2the definite integral of f over the interval is as follows:
[f(x0) + 2f(x1) + 2f(x2) + . . . + 2f(xn?1) + f(xn)] .
(a) Write a function named ’MSP Asgn4 Q4a StudentID.m’ which takes three inputs: the
lower limit a, the upper limit b and the number of sub-intervals n, and uses the Trapezoidal
rule to approximate the integral
where p is the last digit of your student number, and outputs the calculated approximate
integration value.
(Note that you must NOT use any of the MATLAB built-in functions for calculating integrals
or applying the Trapezoidal rule.)
[3 marks]
(b) Write a script ’MSP Asgn4 Q4b StudentID.m’ that uses the function coded in Part (a) to
approximate the integral values of y for a fixed interval [π/2, π] but different numbers of
sub-intervals n = 100, 200, 300, . . . , 1600. Plot the approximate results of y (y-axis) vs n
(x-axis) as cross symbols linked by dashed blue line. Add appropriate title and axis labels
to the plot.
[2 marks]
5. (a) We say two matrices A, B are similar if there exists an invertible matrix X such that
AX = XB. Write a function named ‘MSP Asgn4 Q5a StudentID.m’ which will take three
inputs: a matrix X and two matrices A, B. The function will then
– first test if X is invertible. If X is not invertible, the function will return the error
message, ‘Error: matrix must be invertible.’
– If X is invertible the function will test if A, B are similar using the given matrix X.
If A, B are similar, the function outputs the single number 1. If A, B are not similar,
it outputs the single number 0.
You must also include some help documentation for the user.
[5 marks]
(b) Write a script named ‘MSP Asgn4 Q5b StudentID.m’ which will test the function from
part (a) for the following matrices: