xuebaunion@vip.163.com

3551 Trousdale Rkwy, University Park, Los Angeles, CA

留学生论文指导和课程辅导

无忧GPA：https://www.essaygpa.com

工作时间：全年无休-早上8点到凌晨3点

微信客服：xiaoxionga100

微信客服：ITCS521

matlab代写-DEC 11 2019

时间：2020-12-15

Computational Methods ASSESSMENT DEC 11 2019

Prof. Catherine O’Sullivan

INSTRUCTIONS - READ CAREFULLY:

1. This is a coursework assessment however no collaboration between

students is allowed.

2. Access to the internet and email has been disabled on your computer

and cannot be used. Removable storage (e.g. usb keys) may not be

used. The network is being monitored and students violating these

conditions will be identified and disciplined. HOWEVER YOU

CAN ACCESS THE MATLAB HELP FACILITIES

3. All roughwork should be completed on the final two sheets of this

handout.

4. These guidelines with your name on them should be submitted at the

end of the assessment.

5. Follow the instructions provided for saving your files. Please save your

work continuously to the h: drive to avoid any loss of files.

6. Your name and student id number should be included in all MATLAB

files as a comment.

7. The assessment contains two compulsory questions. Each question is

worth 25 marks.

I have read and understand these instructions:

• Name (Print clearly):

• Signature:

1

Problem 1

Part A

Heyman (1998) proposed that the following equation can be used to plot

the shape of the dome of St. Paul’s Cathedral:

z = 0.7206

[

r3 + 0.3338r7 + 0.0496r11 + 0.0041r15 + 0.0002r19

]

(1)

where z is the elevation of the roof and r is the radial distance from the

centre of the dome.

Develop a function called stpaulsdome.m that takes as input two one

dimensional arrays x and y that each have the same number of entries. The

average value of the numbers stored in each array should be 0. The function

should calculate a 2D array of data points that correspond to surface of the

dome according to Heyman’s equation (Hint: take r =

√

x2 + y2).

The function you develop should for loops for all repeated calculations

(i.e. do not use implied loops).

Reference:

www.jstor.org/stable/532075

[13 marks]

Part B

Develop a MATLAB script called problem1.m that

1. Efficiently creates two, one-dimensional arrays, each having uniformly

spaced data between -1 and 1.

2. Uses the function stpaulsdome.m to calculate the elevation of the

surface of the dome at the defined grid points.

2

3. Visualizes the shape as a 3-D surface.

If you have implemented the equation correctly the surface will be upside

down relative to what we expect to see. Develop a second figure that uses an

efficient approach to plot the shape of the roof with the correct orientation.

[12 marks]

3

Problem 2

Part A

Develop a MATLAB function called forwarddiff that takes as input a two

one-dimensional array x and y and returns the the approximate derivative

dy

dx .

Use for loops for any calculations required, rather than using intrinsic

MATLAB functions or implied loops.

[8 marks]

Part B

You should find a datafile called“UKcensus.txt” on your S-drive. This

file contains the UK census data between 1971 and 2011 which are recorded

at 10 year intervals. The first column contains the year. The second column

gives the UK population.

Develop a MATLAB script file called Problem2.m that

1. Reads in the data stored in the file UKcensus.txt.

2. Uses linear interpolation to estimate the UK population for each year

from 1971 ro 2011.

3. Determines the best fit line to the data to estimate the rate of increase

in population over the past 10 years.

Does the slope of the best fit line to the data give an accurate estimate

of the rate of population growth in 2011? (Explain by adding a comment

in your m file) Make a better estimate using the available data and the

function you have developed.

How might you estimate the current rate of population growth? (Explain

by adding a comment in your m-file). [17 marks]

4

ROUGHWORK PAGE 1

5

ROUGHWORK PAGE 2

6

Prof. Catherine O’Sullivan

INSTRUCTIONS - READ CAREFULLY:

1. This is a coursework assessment however no collaboration between

students is allowed.

2. Access to the internet and email has been disabled on your computer

and cannot be used. Removable storage (e.g. usb keys) may not be

used. The network is being monitored and students violating these

conditions will be identified and disciplined. HOWEVER YOU

CAN ACCESS THE MATLAB HELP FACILITIES

3. All roughwork should be completed on the final two sheets of this

handout.

4. These guidelines with your name on them should be submitted at the

end of the assessment.

5. Follow the instructions provided for saving your files. Please save your

work continuously to the h: drive to avoid any loss of files.

6. Your name and student id number should be included in all MATLAB

files as a comment.

7. The assessment contains two compulsory questions. Each question is

worth 25 marks.

I have read and understand these instructions:

• Name (Print clearly):

• Signature:

1

Problem 1

Part A

Heyman (1998) proposed that the following equation can be used to plot

the shape of the dome of St. Paul’s Cathedral:

z = 0.7206

[

r3 + 0.3338r7 + 0.0496r11 + 0.0041r15 + 0.0002r19

]

(1)

where z is the elevation of the roof and r is the radial distance from the

centre of the dome.

Develop a function called stpaulsdome.m that takes as input two one

dimensional arrays x and y that each have the same number of entries. The

average value of the numbers stored in each array should be 0. The function

should calculate a 2D array of data points that correspond to surface of the

dome according to Heyman’s equation (Hint: take r =

√

x2 + y2).

The function you develop should for loops for all repeated calculations

(i.e. do not use implied loops).

Reference:

www.jstor.org/stable/532075

[13 marks]

Part B

Develop a MATLAB script called problem1.m that

1. Efficiently creates two, one-dimensional arrays, each having uniformly

spaced data between -1 and 1.

2. Uses the function stpaulsdome.m to calculate the elevation of the

surface of the dome at the defined grid points.

2

3. Visualizes the shape as a 3-D surface.

If you have implemented the equation correctly the surface will be upside

down relative to what we expect to see. Develop a second figure that uses an

efficient approach to plot the shape of the roof with the correct orientation.

[12 marks]

3

Problem 2

Part A

Develop a MATLAB function called forwarddiff that takes as input a two

one-dimensional array x and y and returns the the approximate derivative

dy

dx .

Use for loops for any calculations required, rather than using intrinsic

MATLAB functions or implied loops.

[8 marks]

Part B

You should find a datafile called“UKcensus.txt” on your S-drive. This

file contains the UK census data between 1971 and 2011 which are recorded

at 10 year intervals. The first column contains the year. The second column

gives the UK population.

Develop a MATLAB script file called Problem2.m that

1. Reads in the data stored in the file UKcensus.txt.

2. Uses linear interpolation to estimate the UK population for each year

from 1971 ro 2011.

3. Determines the best fit line to the data to estimate the rate of increase

in population over the past 10 years.

Does the slope of the best fit line to the data give an accurate estimate

of the rate of population growth in 2011? (Explain by adding a comment

in your m file) Make a better estimate using the available data and the

function you have developed.

How might you estimate the current rate of population growth? (Explain

by adding a comment in your m-file). [17 marks]

4

ROUGHWORK PAGE 1

5

ROUGHWORK PAGE 2

6