After watching this ppt you will get answers of the questions like...
1) What does it mean?
2) What we study in calculus?
3) Who invented it?
4) What was the need to invent it?
and many more...
You will also learn about the basic difference between discrete and continuous.
And many real life and cool applications of calculus....
Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts.
After watching this ppt you will get answers of the questions like...
1) What does it mean?
2) What we study in calculus?
3) Who invented it?
4) What was the need to invent it?
and many more...
You will also learn about the basic difference between discrete and continuous.
And many real life and cool applications of calculus....
Among the disciplines that utilize calculus include physics, engineering, economics, statistics, and medicine. It is used to create mathematical models in order to arrive into an optimal solution. For example, in physics, calculus is used in a lot of its concepts.
Differential Equation is a very important topic of Mathematics. We tried our best to describes applications of differential equation in this presentation.
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Differential Equation is a very important topic of Mathematics. We tried our best to describes applications of differential equation in this presentation.
this is the ppt on application of integrals, which includes-area between the two curves , volume by slicing , disk method , washer method, and volume by cylindrical shells,.
this is made by dhrumil patel and harshid panchal.
Divergence and Curl is the important chapter in Vector Calculus. Vector Calculus is the most important subject for engineering. There are solved examples, definition, method and description in this PowerPoint presentation.
Solution Manual for Heat Convection second edition by Latif M. Jijiphysicsbook
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https://unihelp.xyz/solution-manual-for-heat-convection-by-latif-jiji/
****
Solution Manual for Heat Conduction
https://unihelp.xyz/solution-manual-heat-conduction-latif-jiji/
Solution Manual for Heat Convection second edition by Latif M. Jiji
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Edhole School provides best Information about Schools in India, Delhi, Noida, Gurgaon. Here you will get about the school, contact, career, etc. Edhole Provides best study material for school students."
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https://alandix.com/academic/papers/synergy2024-epistemic/
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https://arxiv.org/abs/2306.08302
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Watch this recorded webinar about real-time monitoring of application performance. See how to integrate Apache JMeter, the open-source leader in performance testing, with InfluxDB, the open-source time-series database, and Grafana, the open-source analytics and visualization application.
In this webinar, we will review the benefits of leveraging InfluxDB and Grafana when executing load tests and demonstrate how these tools are used to visualize performance metrics.
Length: 30 minutes
Session Overview
-------------------------------------------
During this webinar, we will cover the following topics while demonstrating the integrations of JMeter, InfluxDB and Grafana:
- What out-of-the-box solutions are available for real-time monitoring JMeter tests?
- What are the benefits of integrating InfluxDB and Grafana into the load testing stack?
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- Demonstration of InfluxDB and Grafana using a practice web application
To view the webinar recording, go to:
https://www.rttsweb.com/jmeter-integration-webinar
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2. What is the differential equation?
A differential equation is an equation involving derivatives of an unknown
function and possibly the function itself as well as the independent
variable.
Differential equations have many forms and its order is determined based on the
highest order of a derivative in it.
First order differential equations are such equations that have the unknown
derivative is the first derivative and its own function.
They are divided into separable and 1st order DFE linear.
3. First DFE
1st order DFE linear1st order DFE linear
𝑑𝑦
𝑑𝑥
= 𝐹(𝑥, 𝑦)
𝒅𝒚
𝒅𝒙
= 𝒇 𝒙 ∗ 𝒈 𝒚
So F(x, y) is simply f(x)*g(y)
4. How can we find the solution of the 1st ODE?
A first order linear differential equation is an equation of the form
( ) ( )
dy
P x y Q x
dx
( ) 0
dy
P x y
dx
Which can be solved by
separating the variables.
( )
dy
P x dx
y
ln ( )y P x dx c
( )P x dx c
y e
( )P x dx c
y e e
( )P x dx
y Ce
( )P x dxd
ye
dx
( ) ( )
( )
P x dx P x dxdy
e yP x e
dx
( )
( )
P x dxdy
P x y e
dx
5. ( ) ( )
dy
P x y Q x
dx
If we multiply both sides by
( )P x dx
e
( ) ( )
( )
P x dx P x dxd
ye Q x e
dx
Now integrate both sides.
( ) ( )
( )
P x dx P x dx
ye Q x e dx
Returning to equation 1,
6. The change in temperature
• An object’s temperature over time will approach the
temperature of its surroundings (the medium).
• The greater the difference between the object’s temperature
and the medium’s temperature, the greater the rate of change
of the object’s temperature.
• This change is a form of exponential decay.
T0
Tm
7. Newton’s Law of Cooling
It is a direct application for differential equations.
Formulated by Sir Isaac Newton.
Has many applications in our everyday life.
Sir Isaac Newton found this equation behaves like what is called in Math
(differential equations) so his used some techniques to find its general solution.
8. Derivation of Newton’s law of Cooling
Newton’s observations:
He observed that observed that the temperature of the body is proportional to the
difference between its own temperature and the temperature of the objects in
contact with it .
Formulating:
First order separable DE
Applying calculus:
𝑑𝑇
𝑑𝑡
= −𝑘(𝑇 − 𝑇𝑒)
Where k is the positive proportionality constant
9. Derivation of Newton’s law of Cooling (continued)
By separation of variables we get
𝑑𝑇
(𝑇−𝑇𝑒)
= −𝑘 𝑑𝑡
By integrating both sides we get
ln 𝑇 − 𝑇𝑒 + 𝐶 = −𝑘𝑡
At time (t=0) the temperature is T0
−ln 𝑇0 − 𝑇𝑒 = 𝐶
By substituting C with −ln 𝑇0 − 𝑇𝑒 we get
ln
(𝑇 − 𝑇𝑒)
(𝑇0 − 𝑇𝑒)
= −𝑘𝑡
𝑇 = 𝑇𝑒 + (𝑇0 − 𝑇𝑒)𝑒−𝑘𝑡
10. Applications on Newton’s Law of Cooling:
Investigations.
• It can be used to
determine the
time of death.
Computer
manufacturing.
• Processors.
• Cooling systems.
solar water
heater.
calculating the
surface area of
an object.
12. The police came to a house at 10:23 am were a murder had
taken place. The detective measured the temperature of the
victim’s body and found that it was 26.7℃. Then he used a
thermostat to measure the temperature of the room that
was found to be 20℃ through the last three days. After an
hour he measured the temperature of the body again and
found that the temperature was 25.8℃. Assuming that the
body temperature was normal (37℃), what is the time of
death?
13. Solution
T (t) = Te + (T0 − Te ) e – kt
Let the time at which the death took place be x hours before the arrival of the
police men.
Substitute by the given values
T ( x ) = 26.7 = 20 + (37 − 20) e-kx
T ( x+1) = 25.8 = 20 + (37 − 20) e - k ( x + 1)
Solve the 2 equations simultaneously
0.394= e-kx
0.341= e - k ( x + 1)
By taking the logarithmic function
ln (0.394)= -kx …(1)
ln (0.341)= -k(x+1) …(2)
14. Solution (continued)
By dividing (1) by (2)
ln(0.394)
ln 0.341
=
−𝑘𝑥
−𝑘 𝑥+1
0.8657 =
𝑥
𝑥+1
Thus x≃7 hours
Therefore the murder took place 7 hours before the arrival of the detective
which is at 3:23 pm
15. A global company such as Intel is willing to produce a new cooling system for their processors
that can cool the processors from a temperature of 50℃ to 27℃ in just half an hour when
the temperature outside is 20℃ but they don’t know what kind of materials they should use
or what the surface area and the geometry of the shape are. So what should they do ?
Simply they have to use the general formula of Newton’s law of cooling
T (t) = Te + (T0 − Te ) e – k
And by substituting the numbers they get
27 = 20 + (50 − 20) e-0.5k
Solving for k we get k =2.9
so they need a material with k=2.9 (k is a constant that is related to the heat capacity ,
thermodynamics of the material and also the shape and the geometry of the material)