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Lecture Notes - Application of First Order ODE

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Lecture Videos-Application of First Order ODE

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Lecture Videos-Application of First Order ODE

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Newton's Law of Cooling :
Part 1 : https://youtu.be/eA6E_xm5J_4
Part 2 : https://youtu.be/otftXllD7G4

Natural Growth and Decay : https://youtu.be/I7xu4a06Vy8

Electric Circuit : https://youtu.be/mUIsRD3HY0g

Newton's Second Law of Motion : https://youtu.be/C7KJOdQssOc

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Chap 1 Application of 1st Order ODE : Newton's Law of Cooling Part 1

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Lecture Notes - Application of Second Order ODE

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Lecture Videos - Applications of Second Order Linear ODE

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Lecture Videos - Applications of Second Order Linear ODE

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Part 1 : https://youtu.be/bXKyONibylc

Part 2 : https://youtu.be/ZuUlDgmNYPM

Part 3 : https://youtu.be/plfhBRNJ0Bk

Part 4 : https://youtu.be/VmlIwiJvXdM

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1.
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1. Form a group of maximum four members.
2. Find an application of any type of first order or second order ordinary differential equations. The application MUST NOT be

similar to the applications given in the lecture notes. You can refer to any sources such as books or internet, or you can also create your own situation or application based on your understanding on first order or second order ordinary differential equations.
3. Create a 3 - 5 minutes video or short movie about the application.  All group members must appear in the short video.

The contents of the video that will be assessed are :
i. Correctly chosen application of first order or second order ordinary differential equation.

ii. Correctly determine type of the differential equation (for first order : separable, homogenous, exact, linear or Bernoulli ; for second order : homogenous, non-homogenous.)

iii. Solution of the differential equation. (Note that you do not need to explain the whole calculation steps in the video. Just explain the idea. The calculation steps can be submitted separately in e-learning).
4. The due date for the submission of the video and solution in the is on 21 Jan 2023 (5pm)
5. You also need to attach proof of group discussion.

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Insert your chosen application/situation here.

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Please provide a photo during your discussion (can be physical or online).

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Upload your short video here.

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Give a reflection on what you get from the group assignment and explain whether it helps you to understand the topic.

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Group Members
1. Amirul Zikri Bin Ramli
2. Muhammad Aiman Syafiq Bin Sapri
3. Mohamad Syukri Bin Sharom

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Application/ Situation
A glass of hot tea initially at 80°C is to be cooled by leaving it on the table, where the room temperature is 25°C. Suppose that the temperature of the hot tea after 5 minutes has dropped to 55°C. When will it be at 30°C?

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Proof of Discussion

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Short Video

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Reflection
The group assignment that’ve been held shows that the application of Ordinary Differential Equation is used in daily life even in the simplest thing we do in our routine. This assignment also helps in understanding the topic of Ordinary Differential Equation since it can be describe in the situation of a daily life activities applied.

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1. Clement Chan Whye Kuang A21ET0037
2.Lee Chin Yong A21ET0079
3.Nicholas Tan Kian Siang A21ET0154
4.Sam Wai Keat A21ET0212

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Group Members:
1. HONG JUN JIAT
2. RESHMEN A/L JAYANATHAN
3. SURYAPRAKAZSH A/L SHUPPARA MANIAM
4. TANG JIA XUAN

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Application/Situation
The angular acceleration of the spinning top is defined by α = (3t2 + 12) 𝑟𝑎𝑑/s2, where t is in seconds. If the spinning top is originally rotating at 𝜔0 = 12 rad/s and  𝜃0 = 6 rad, determine the magnitude of the angular velocity, 𝜔 and angular displacement, 𝜃 when t = 2 s.

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Proof of Discussion

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Short Video

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Reflection
This group project let us gain more understanding about first order ordinary equations. We can apply it in our daily life. For example, we can apply it in the Newton's Law of Cooling, Newton's Second Law of Motion and others. Thus, we can calculate the result for the situation.

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We were able to have a better understanding about the applications of Ordinary Differential Equations while relating it to our daily life. The practicality of this assignment has given us an in-depth comprehension on how to apply Ordinary Differential Equations

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1. Lim Jia Sheng
2. Megan Cheong Kai En
3. Michelle Chua Pei Yi
4. Tay Jie Er A21ET0238

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When the roasted chicken was removed from the oven, it's temperature measured is 200°C. It was placed in a room with temperature of 25°C.
5 minutes later, the chicken was cooled to 160°C. The process satisfies the Newton’s Law of Cooling given by
dT/dt= -k(T-Ts)
Determine how long did it take for the roasted chicken to cool off to the temperature of 65°C to be served.

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https://youtu.be/VkRJurbwFE8

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🐣Short Video of First Order Differential Equations✨

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1. Eva Kan Kuan Yee
2. Evon Kan Kuan Lam
3. Ho Zi Qing
4. Khor Yayen

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In the second day of infection, the corona virus in a human body currently holds 1 million cells. Given that the viruses have a constant replication rate of 0.75%. When the cell mediated immune response is stimulated, the viruses are dead at the rate of 2%.

How many cells will be in the human body 2 days from now?

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https://youtu.be/gAcp5Z0mY6g

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This group assignment let us gain more knowledge on the topic of first order differential equation and how it is closely related to our daily life. Besides, this assignment also gives us a chance to relax ourselves because taking video is fun !!!

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Group Members

1. Bong Kah Hui A21ET0022
2. Felicia Tang Yan Zi A21ET0051
3. Lam Xue En A21ET0075
4. Lo Su Yin A21ET0084

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Application/ Situation
When we want to dissolve some solid in a solvent, it takes some time to dissolve most of the solute. In this video, we are using Milo powder as the solute and water as the solvent.

If 50% of Milo powder dissolves in 10s,

how long does it take to dissolve 99.99% of Milo powder in water?

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SSCE 1793 - Application of First Order Differential Equation

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From this group assignment, we get to know that there are some application of differential equation in our daily life that we did not realize before this. We have also enhance our understanding on this topic and on solving the differential equation.

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1. Priyanka Devi A/P Ganesan (B21ET0013)
2. Andi Suriana Binti Momang @ Zubair (B21ET0004)
3. Farrah Yasmeen Batrisyia Binti Mohd Fauzie (B21ET0005)
4. Intan Liyana Binti Mohd Hanapi (A21ET0065)

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1. Priyanka Devi A/P Ganesan (B21ET0013)
2. Andi Suriana Binti Momang @ Zubair (B21ET0004)
3. Farrah Yasmeen Batrisyia Binti Mohd Fauzie (B21ET0005)
4. Intan Liyana Binti Mohd Hanapi (A21ET0065)

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A cake was baked and after it was cooked, it was taken out from the oven to be cooled on a table at room temperature 24°C with an initial temperature of 170°C at 12pm. Suppose the temperature of the cake dropped to 90°C after 30 minutes. Temperature of the cake is governed by dT/dt=-k(T-Ts) where T(t) is the temperature of the cake at time t, Ts is the room temperature and k is cooling constant. Determine a suitable time to eat the cake if the ideal temperature to consume the cake is 40°C.

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1.  Yeoh Yu En (A21EE0036)
2. Liew Wen Xuan (A21EM0080)
3. Muhammad Zikri Adib bin Husin (A21EM0168)
4. Muhanned Mardy Hassan (A21EM4010)

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1. Crespo Lianlisut Tengang A21ET0038
2. Aizuddin Akmal Bin Mafaralo B21ET0002
3. Nur Alya Binti Rosli A21ET0168
4. Nur Adlin Syamilah Binti Harun A21ET0166

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A group of students bought some cold water then after some time during their discussion, the water was not cold anymore. The temperature became similar to the room temperature. They would want to know temperature of the water 15 minutes earlier.

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From this group assignment, we are now able to use differential equation to solve some questions that does not go through easy calculation such as addition, subtraction and etc. Through the learning of differential equation as well we are capable to solve harder and complex equations.

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1. NORHAZWANI BINTI OTHMAN
2. AIDATUL AFZAN FATIHA BINTI SAIFULIZAM
3. NOR SURIANI BT YAHAYA
4. CRYSTAL LIM ZHAN JING

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- First Order Linear Equation (two variable)
- The difference speed for upstream and downstream area with the same distance and person.

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17/01/2023 - Tuesday
Webex on 11.00 pm

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Link youtube https://youtu.be/-lsro-XfqdA

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There are many application of differential equation in our daily routine without doing any experiment we just can calculate it..

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https://www.canva.com/design/DAFXhteuuMI/VzWflEpAPXvvYZETYrXgng/edit

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An egg experiences free fall from a height of 3m measured from ground. What is the time taken for the  egg to fall to the ground?

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1. OMAR MOHAMED ELSAYED (A21EM3003)
2. ABDELRAHMAN TAHER (A21EM3006)
3. MUHAMMAD RAYHAN HADIYAT (A21EM4022)
4. TAYEB MAHMOOD SAMI (A21EM3007)

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A curious ice cream lover decided to put his curiosity to test by experimenting with Newton's cooling law. The person purchased an ice cream cone and measured its initial temperature. The initial temperature was -18 degrees Celsius. The ambient temperature was measured and was found to be 27 degrees Celsius. The temperature of the ice cream cone was then measured at regular intervals of time and the rate of change of temperature was calculated to be -0.5 degrees Celsius per minute.

Using the above information, the constant k was calculated using the formula k = dT/dt / (T(t) - T_a) . k = -0.5/(-45) = 1/90 per minute.

The temperature of the ice cream as a function of time was then calculated using the equation T(t) = e^(kt+ln(-18 - 27)) + 27 and this was compared with the measured temperature at each interval of time. The error, if any, was noted down.

This experiment helped the person to understand how temperature affects the rate of melting of ice cream and the accuracy of using Newton's cooling law in predicting the melting rate of ice cream.

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The experiment on testing Newton's cooling law on an ice cream cone provided insight into the relationship between temperature and the rate of melting. It showed the accuracy of using the law in predicting the melting rate and highlighted the other factors that can affect the cooling rate. Overall, it was a valuable learning experience on the application of physical laws in real-life situations.

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1. NOR AUJI SYAMIMI BINTI NORAZLAN (A21ET0160)
2. PUTRI SYAKILA BINTI IBRAHIM (A21ET0311)
3. TIARA ANAK RIPIN (A21ET0244)
4. AMIRA NAZURA BINTI EIWAN SAH(B21ET0003)

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A chicken is removed from an air fryer at temperature of 300F. Three minutes later, the temperature is 200F. How long will it take for the chicken to cool off to 70F, when the room temperature is 50F?

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Ordinary Differential Order Application- Newton Law

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From this group assignment, we can see how the ordinary differential equation can be applied and use to our daily life and how we can understand better about this topic since we can relate in our daily life.

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1. Chan Yan Min
2. Kam Yen Jiet

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1. siti nur syuhada binti mokhsen
2.Nor Hafizzah binti Nazri
3.Noor syafikah binti che mohamad yusoff
4.Nor Amira Nasha binti Nasif

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1. Ikhlasul Iman Islahul Umam
2. Raja Falih

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A psychopath wants to take revenge on her bullies. She bought poisonous liquid from a drug dealer and freeze it into the ice. The poisonous ice was put into a hot drink for her bullies. When the ice were melt in the hot drink, the poison dissolved into the water. Calculate the time for the ice to melt and the hot drink become cold.

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An RL circuit has an emf of 5 volts, a resistance of 50 ohms, an inductance of 1 henry, and no initial current. Find the current in the circuit at any time t.

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The first order ordinary differential equation is very important for engineering students to learn. because it is widely used in solving engineering problems. one example of using the first order ordinary differential equation is to find the formula for calculating the current in the RL circuit like the example we made. but not only that its use is still quite widespread, it can also be used in Newton's Law of Cooling, Natural Growth, Decay, and Vertical Motion - Newton's Second Law of Motion.

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A lousy car driver reverses without alert. In fact, the car crash into a furious bicycle. We want to determine the relations between speed, velocity and acceleration. Hence, we also want to know the force exerted in the bicycle rider.

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Through this assignment, we have gained knowledge and understanding on first or second order ordinary differential equations. We also know the application of first or second order ordinary differential equations that happening at our daily life.

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1. Muhammad Arslan Babur  A20EM3003
2. Mazen Omar Mahmoud  A20EM4015
3. MOHAMMED KHALIL SAIF MOHAMMED AL-ADEMI
4. OSAMA A. S. SHURRAB

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A gamer accidentally knocks a glass over and immediately realizes his mistake. Fortunately, as long as he can calculate how fast the glass falls, he can ultimately catch it and save it from breaking.

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Making a short video about differential equations was not exactly what we had expected as a group assignment for this course. However, it was undoubtedly an amazing opportunity to learn the real applications of our coursework. Usually, it is difficult to imagine how all the mathematical analysis and solutions interact in real time, however, by making this video all of us learned a lot as we understood the derivation and solution of the velocity differential equation for a falling body. It was definitely a memorable moment when we linked the derived expression to the equations we had learned about in class. Eventually, identifying and solving the differential equation obtained using the methods we learned from the course provided invaluable insights in applying mathematical analysis in our daily lives.

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1. Haamid Jamaldeen Mansoor - A21EM3001
2. Muhamad Arsyad bin Suhaimi A17KM0185
3. Mustafa Noman A20ET4008
4. Kawser Habib - A21EM4020

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Sodium-24 (Na-24) undergoes radioactive decay. Suppose Na-24 has a half-life of 15 hours. After 30 hours, only 50g has remained. What's the initial amount of Na-24?

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https://drive.google.com/drive/folders/1zTX1qFHU8_L4EIBrmvn3oIzHxKpeUm3n?usp=share_link

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Through this Group Assignment, we were able to demonstrate a real-world example of a first-order differential equation. As a team, we divided the steps of the differential equation between us. Once the first person was done with his work, he would show his work to the group and explain what he did allowing the next person to continue his step and so forth. We were able to get a good understanding of how Radioactive decay follows the pattern of Natural Growth and Decay.

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1. Ilhan Shah Bin Amran - A21ET0064
2. Amalia Marsya Binti Rosli - A21ET0010

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There has been a gunslinging action that happened earlier at noon. Law enforcement quickly came and discovered that there was a dead body with a bullet wound. The dead body was found bleeding at 3pm with the body temperature of 27c. After an hour, the temperature of the body has dropped by 3c. Assuming that he has an average human temperature which is 37c during the time of death, calculate the time of the killing?

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From this group assignment, we were able to understand more about first order differential equation and also able to relate it to our daily lives.