The Laplacian of a function (image) ??(??, ??) of two variables, is defined as：
Show that the Laplacian operation is isotropic (invariant to rotation). You will need the following equations relating coordinates after axis rotation by an angle ??:
where (??, ??) are the unrotated and (??′, ??′) are the rotated
coordinates.
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The Laplacian of a function (image) ??(??, ??) of two variables,
is defined as：
Show that...
(1 point) Consider the function defined by ?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2 except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0. Then we have...
(1 point) Consider the function defined by
?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2
except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0.
Then we have
∂∂?∂?∂?(0,0)=∂∂y∂F∂x(0,0)=
∂∂?∂?∂?(0,0)=∂∂x∂F∂y(0,0)=
Note that the answers are different. The existence and continuity
of all second partials in a region around a point guarantees the
equality of the two mixed second derivatives at the point. In the
above case, continuity fails at (0,0)(0,0).
(1 point) Consider the function defined by F(x, y) = xy(9x2 + 5y2) x2 + y2 except at (x, y) = (0,0)...
17. X A function u of two variables is defined implicitly by u(х, 1) — /(г — tu(x, t)), where fis a given bounded, diff...
17. X A function u of two variables is defined implicitly by u(х, 1) — /(г — tu(x, t)), where fis a given bounded, differentiable function of one variable, f : R - R. 2019 School of Mathematics and Statistics, UNSW Sydney CHAPTER 1. FUNCTIONS OF SEVERAL VARIABLES 24 ди ди and Эх a) Calculate ди ди + u дt b) Show that = 0. дх ди c) Given that f(s) = 1 - tanh s, find the smallest positive...
Please use matlab cars. Answer: Function file; Command Window: 5.4 Write a user-defined function that plots...
Please use matlab
cars. Answer: Function file; Command Window: 5.4 Write a user-defined function that plots a circle given the coordinates of the center and the radius. For the function name and arguments use circleplot(x,y,R). The input arguments are the and y coordinates of the center and the radius. Use linspace to generte the angle from 0 to π with 100 points. (Hint: the circle equation: x+Rcos and yy-yRsin 0.) This function has no output arguments. Plot the circle using...
MATLAB, please provide code script Objective: Create a function file that animates projectile motion defined by...
MATLAB,
please provide code script
Objective: Create a function file that animates projectile motion defined by the following equations in a subplot. Your function should accept user inputs of launch speed and launch angle. The output of your function will be a top subplot that displays height (y) as a function of x. The bottom subplot should display the vertical velocity while the projectile is in motion. A video of what your animation should look like is posted with this...
the function of two real variables defined below: 1 –9x + 2y“ (x, y) + (0,0),...
the function of two real variables defined below: 1 –9x + 2y“ (x, y) + (0,0), f(x, y) = { 6x + 3y 10 (x, y) = (0,0). Use the limit definition of partial derivatives to compute the following partial derivatives. Enter "DNE" if the derivative does not exist. fx(0,0) = DNE fy(0,0) = 0
Assume the coordinate frame assignments shown in the figure for the Rhino robot used in the...
Assume the coordinate frame assignments shown in the figure for the Rhino robot used in the lab and the transformation matrix from the base frame to the end effector frame Ts is as given below Suppose we want to use the Rhino for a painting application where the end-effector should point at 4j degrees from the horizontal. In this case, we would need to align the end-effector frame Z axis (Z4) at 135 degrees to Z axis Given the desired...
3c and 3d 3. Given the function defined by fx)-2x3x-12x+ 20. a) By using Rational Root...
3c and 3d
3. Given the function defined by fx)-2x3x-12x+ 20. a) By using Rational Root Theorem and Synthetic Division, write flk) as a product of its factors dentily the zeros. b) The slope function can be found by using the formula: (lnxWrite the equation of the line tangent to the graph offat x 0. c) A tangent line drawn to the graph of f is said to be a horizontal tangent or parallel to x-axis if the slope is...
1. in Matlab, write a user-defined function, with two input (r,theta) , θ expressed in degrees)...
1. in Matlab, write a user-defined function, with two input (r,theta) , θ expressed in degrees) and two output arguments (X,Y). The inputs are a location on a polar coordinates corresponding to Cartesian plane expressed in rectangular coordinates. The picture below describes the problem. X, Y rcos θ Some formula that you may need: x = r * cos (theta * pi/180); y r * sin(theta * pi/180); Test your code for r=7, theta=55° and present your results.
Learning Goal: To be able to identify the initial stresses and the angle of rotation, including t...
Learning Goal: To be able to identify the initial stresses and
the angle of rotation, including the correct signs, and use these
in the stress-transformation equations to find the stress on a
plane or element at a different angle than the original. The method
of calculating the state of stress on an inclined plane is tedious,
prone to error, and incomplete—if we calculate σx′ and τx′y′, we
have to do a separate calculation to determine σy′. Consider the
stress element...
Equations: An equation with two variables, X and Y, is a simple way to show a...
Equations: An equation with two variables, X and Y, is a simple way to show a relationship given information about X, we can calculate the value (numerical amount) of Y. And every time calculate how much Y changes. For example, the equation Y 3(x) tells us that value of X. It means that every time X increases by 1, Y increases by 3. (substitute) the different values of X in the left-hand column of the table into the equation. of...
(1 point) Consider the function defined by
?(?,?)=??(9?2+5?2)?2+?2F(x,y)=xy(9x2+5y2)x2+y2
except at (?,?)=(0,0)(x,y)=(0,0) where ?(0,0)=0F(0,0)=0.
Then we have
∂∂?∂?∂?(0,0)=∂∂y∂F∂x(0,0)=
∂∂?∂?∂?(0,0)=∂∂x∂F∂y(0,0)=
Note that the answers are different. The existence and continuity
of all second partials in a region around a point guarantees the
equality of the two mixed second derivatives at the point. In the
above case, continuity fails at (0,0)(0,0).
(1 point) Consider the function defined by F(x, y) = xy(9x2 + 5y2) x2 + y2 except at (x, y) = (0,0)...
17. X A function u of two variables is defined implicitly by u(х, 1) — /(г — tu(x, t)), where fis a given bounded, differentiable function of one variable, f : R - R. 2019 School of Mathematics and Statistics, UNSW Sydney CHAPTER 1. FUNCTIONS OF SEVERAL VARIABLES 24 ди ди and Эх a) Calculate ди ди + u дt b) Show that = 0. дх ди c) Given that f(s) = 1 - tanh s, find the smallest positive...
Please use matlab
cars. Answer: Function file; Command Window: 5.4 Write a user-defined function that plots a circle given the coordinates of the center and the radius. For the function name and arguments use circleplot(x,y,R). The input arguments are the and y coordinates of the center and the radius. Use linspace to generte the angle from 0 to π with 100 points. (Hint: the circle equation: x+Rcos and yy-yRsin 0.) This function has no output arguments. Plot the circle using...
MATLAB,
please provide code script
Objective: Create a function file that animates projectile motion defined by the following equations in a subplot. Your function should accept user inputs of launch speed and launch angle. The output of your function will be a top subplot that displays height (y) as a function of x. The bottom subplot should display the vertical velocity while the projectile is in motion. A video of what your animation should look like is posted with this...
the function of two real variables defined below: 1 –9x + 2y“ (x, y) + (0,0), f(x, y) = { 6x + 3y 10 (x, y) = (0,0). Use the limit definition of partial derivatives to compute the following partial derivatives. Enter "DNE" if the derivative does not exist. fx(0,0) = DNE fy(0,0) = 0
Assume the coordinate frame assignments shown in the figure for the Rhino robot used in the lab and the transformation matrix from the base frame to the end effector frame Ts is as given below Suppose we want to use the Rhino for a painting application where the end-effector should point at 4j degrees from the horizontal. In this case, we would need to align the end-effector frame Z axis (Z4) at 135 degrees to Z axis Given the desired...
3c and 3d
3. Given the function defined by fx)-2x3x-12x+ 20. a) By using Rational Root Theorem and Synthetic Division, write flk) as a product of its factors dentily the zeros. b) The slope function can be found by using the formula: (lnxWrite the equation of the line tangent to the graph offat x 0. c) A tangent line drawn to the graph of f is said to be a horizontal tangent or parallel to x-axis if the slope is...
1. in Matlab, write a user-defined function, with two input (r,theta) , θ expressed in degrees) and two output arguments (X,Y). The inputs are a location on a polar coordinates corresponding to Cartesian plane expressed in rectangular coordinates. The picture below describes the problem. X, Y rcos θ Some formula that you may need: x = r * cos (theta * pi/180); y r * sin(theta * pi/180); Test your code for r=7, theta=55° and present your results.
Learning Goal: To be able to identify the initial stresses and
the angle of rotation, including the correct signs, and use these
in the stress-transformation equations to find the stress on a
plane or element at a different angle than the original. The method
of calculating the state of stress on an inclined plane is tedious,
prone to error, and incomplete—if we calculate σx′ and τx′y′, we
have to do a separate calculation to determine σy′. Consider the
stress element...
Equations: An equation with two variables, X and Y, is a simple way to show a relationship given information about X, we can calculate the value (numerical amount) of Y. And every time calculate how much Y changes. For example, the equation Y 3(x) tells us that value of X. It means that every time X increases by 1, Y increases by 3. (substitute) the different values of X in the left-hand column of the table into the equation. of...
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