Differential Equations, Partial Derivatives, and Matlab for Engineers

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Homework Assignment
AI Summary
This coursework assignment focuses on applying differential equations and partial differentiation to solve engineering problems, and demonstrates the knowledge of mathematical modeling of physical systems and simulation using MATLAB and Simulink. The assignment is divided into two main tasks. Task 01 requires students to solve various differential equations using Matlab and plot graphs with specific requirements, including subplots, axis labeling, and titles. Task 02 involves modeling the rate of change of a bacterial population using a differential equation, solving it with Matlab, plotting the solution using 'ezplot', and analyzing the bacterial population's state. Additionally, students are expected to conduct literature searches to explain the applications of mathematical modeling in Electrical and Electronic Engineering, Mechanical Engineering, and Civil Engineering. The assignment emphasizes the application of mathematical concepts in engineering contexts and the use of computational tools for problem-solving and analysis.
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Coursework Title: Differential equations, partial derivatives,
its applications and solving physical systems using Matlab
Module Name: Engineering Mathematics
Module Code: 4500ICBTEG
Level: 4
Credit Rating: 15
Weighting: 30% of the module mark
Maximum mark
available: 100%
Lecturer: Ms. Irushi Ediriweera
Contact: Email: irushiE@icbtcampus.edu.lk
Issue Date: TBC
Hand-in Date: TBC
Hand-in Method: Through Canvas and ICBT SIS (electronic)
Feedback: Your work will be marked and returned within two weeks using a
Feedback sheet. A copy of this is available on Blackboard which provides
the mark allocation
Programmes: HD in Electrical and Electronic Engineering
HD in Biomedical Engineering
HD in Mechatronics Engineering
HD in Mechanical Engineering
HD in Automotive Engineering
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You are advised that the School of Engineering, Technology and Maritime
Operations operates a zero tolerance approach to late submission of coursework. Any
coursework submitted late will be awarded a zero mark unless there
are valid mitigating circumstances supported with evidence of the mitigation claimed.
Be advised that loss of computer data will not be accepted in mitigation; it is
entirely your responsibility to ensure the secure backup of all electronic data.
In this assessment, the student will demonstrate the ability to:
1. Apply the principles of differential equations and partial differentiation to solve
Problems in Engineering.
2. Demonstrate the knowledge of differential equations and mathematical modelling
of physical systems and simulation using MATLAB and Simulink.
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Engineering Mathematics - Coursework
TASK 01
Part A
1.A.1) Solve the following differential equations using Matlab.
a)p
x + 8p = 9, p(0) = −1
b)2y
x2 2y
x+ 3y = 4x2
c) y
t = 6y − 5,y(0) = π
d)3y
x3 + 82y
x2 2y
x = y
(5x4= 20 marks)
Part B
1.B.1) Using the given specifications, plot the following graph using Matlab.
X range= 0 to 100 with increments of 0.001
Plot the below graphs on the same figure
Y= 3sin(2x)+ 4cos(x)
G= 6cos2(x)- 3sin(2x)
(8 mark
s)
Plot the above graphs as a subplot so that graph of ‘y’ is on the left hand side and graph ‘g’
is on the right hand side of the subplot. (8 marks)
Label the x and y axis accordingly (2 marks)
Provide a title for the graph (2 marks)
(20 marks)
(Total marks for Task 01= 40 marks)
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TASK 02
Part A
The rate of change of a population of bacteria in a petri-dish can be described as the difference between the
birth rate and the death rate. If the birth rate = bx, where b is a constant and x is the number of bacteria, and
if death rate= px2, where p is a constant, answer the following questions based on the description provided.
2.A.1) Provide the differential equation related to the rate of change of bacterial population with
time based on the above given information. (5 marks)
2.A.2) If b=1, and p=0.8, solve the differential equation stated in 2.1 using Matlab assuming there
were 1500 bacteria present in the dish initially. (Provide a clear screen shot of the code and
solution obtained in the answer script).
(15 marks)
2.A.3) ezplot” command is useful to obtain a quick visualization of a function. Plot a graph of
the solution using the ‘ezplot’ command to show the population of bacteria present after 2
hours. (5 marks)
2.A.4) Comment on the state of the population of bacteria after 2 hours using the graph plotted
above. (5 marks)
(Total for Part A= 30 marks)
Part B
2.B.1)
Through a literature search explain in detail 3 applications if mathematical modelling in any of
the below mentioned fields.
Electrical and Electronic Engineering
Mechanical Engineering
Civil Engineering (3x10= 30 marks)
(Total for Part B= 30 marks)
***END OF COURSEWORK***
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