Estimating change (PDE)

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In summary, the problem involves finding the rate of change of temperature experienced by a particle moving clockwise around a circle with a radius of 1m at a constant rate of 2 m/s. The temperature function is given by T(x,y) = xsin(2y) and the point P(1/2 , (sqrt[3])/2) is used to calculate the rate of change in degrees C per meter and per second. The solution involves finding the unit tangent vector in the direction of motion.
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Homework Statement


Suppose that the Celsius temperature at the point (x, y) in the xy plane is T(x,y) = xsin(2y)
and that the distance in the xy plane is measured in meters. A particle moving clockwise around the circle of radius 1m centered at the origin at the constant rate of 2 m/s

a. how fast is the temperature experienced by the particle changing in degrees C per meter at the point P(1/2 , (sqrt[3])/2) ?

b. how fast is the temperature expereinced by the particle changing in degrees C per second at P?


Homework Equations


T(x,y) = xsin(2y)

P(1/2 , (sqrt[3])/2)



The Attempt at a Solution



i can do all the other estimating change problems where it gives me a function, 2 points, and ds = some constant just fine. but when i look at this i get kind of lost. i see the solution starts out by finding u in the direction of motion but I am not really sure how to find what i need out of this problem. I would appreciate any insight or a nudge in the right direction.

Thanks so much!
 
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  • #2
can someone just point me in the direction of finding the unit tangent vector in the direction of motion please? i don't need a entire solution
 

What is "Estimating change (PDE)"?

"Estimating change (PDE)" stands for "Partial Differential Equations" and refers to a mathematical method used to model and analyze physical systems that change or evolve over time and space.

What are some examples of physical systems that can be modeled using "Estimating change (PDE)"?

Some examples include fluid flow, heat transfer, electromagnetic fields, and population dynamics.

What is the difference between "Estimating change (PDE)" and "Estimating change (ODE)"?

"Estimating change (PDE)" deals with systems that change over both time and space, while "Estimating change (ODE)" deals with systems that only change over time.

What are the main challenges in solving "Estimating change (PDE)" problems?

The main challenges include determining an appropriate mathematical model, choosing appropriate boundary and initial conditions, and finding an analytical or numerical solution.

What are some real-world applications of "Estimating change (PDE)"?

"Estimating change (PDE)" has many practical applications in fields such as engineering, physics, and biology. Some examples include predicting weather patterns, designing aircrafts and cars, and studying the spread of diseases.

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