7. Find the Jacobian matrix of the following. a) x= (u+v),y = (u-v).= = 2uvw b) x=r cos 0, y =r sin 0,z = z

Q: Let x(t) be a Brownian motion with x(0). Mathematically prove or disprove that -4x(t)is a Brownian…

A:

Q: 7. In A ABC,X is the centroid. A A. If CW = 15, find CX and XW. W B B. If BX = 8, find BY and XY. C.…

A:

Q: 5) Consider four points A, B, C, and D whose geometrical locations correspond to the corners of a…

A: We have to find out the potential difference at various points.

Q: Consider f(t) = (cos t, sin t, t?) and g(x, y, z) = (x² + y² + z², 3x + 4y – 12z) and h = g(f(t)) =…

A:

Q: { Vo, æ L,

A:

Q: Transform the DE; (t-1)sin(t) y" + y'+y tan(t); y(2)=1, y'(2)3D3 into a system of two first order DE…

A: Given the second order differential equation           (t-1)sin(t)y''+y'+y=tan(t), y(2)=1, y'(2)=3…

Q: 3. Let f: R→ R³ and 9: R³ R be defined by f(t) = (t², sin(t), et) and g(x, y, z) = xy + z. Using…

A:

Q: Consider the simple lincar model Y, = Be + B,x, + C. where -N(0,0²); i= 1,2, --,n. 1. Show that a)…

A: Hello! As you have posted more than 3 sub parts, we are answering the first 3 sub-parts(a, b-i,…

Q: Solve the integral ſ. (cx – y)dx + (ax + cy)dy along the curves x = y³ from (0,0) to (1,1) a – The…

A: Consider the integral I=∫ccx-ydx+ax+cydy along the curve x=y3 from 0,0 to 1,1. Given a=2 and c=8.…

Q: az əz 1. ax' dy If z = In(e* + e"), show that %3D %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if ux = v, and u,…

A: Given u = x2-y2v = 2xy Then ux = 2xuy = -2yvx = 2yvy = 2x

Q: 5. Show that the function f(x,y,z) = 2z³ – 3z(x² + y²) satisfies the Laplace Equation, a²f + ду? əx²…

A: The given function is: f(x,y,z)=2z3-3zx2+y2f(x,y,z)=2z3-3x2z-3y2z

Q: (a) Applying the Kirchhoff's second law, show that the system of differential equa- tions is dle L-…

A:

Q: 4. Find the work done by the force field F = (x? sin(y),y) on a particle that moves along the cubic…

A: Given: The force field, F→=x2siny,y on a particle that moves along the cubic y=x3 from 1,1 to 2,8.

Q: Two functions u and r of x and y are said to satisfy the Cauchy- Riemann equations if u, = v, and -…

A: Given that the functions u and v are said to satisfy Cauchy Riemann equations if ux=vy   and uy=-vx…

Q: Determine the Jacobian matrix of the function f:R³ → R³ given by f(x,y,z) = (3x²y+ yx²,4x²yz², 6xz³…

A:

Q: Find the Jacobian of following functions f(x,y,z) = 3xy – yz + 2y³z² – 5xyz³ g(x,y, z) = xyz – x³yz…

A:

Q: Assuming that the voltage may be described by the sinusoid v = K sin(wt + p), determi values of K, w…

A: Consider the given oscilloscope recording as shown below: And the given voltage is: Objective is…

Q: 3 -1 Let and Y. 1 Find such that they non zero in IR rows OF linearly XY depend ent. are

A:

Q: 3. Let X and P be the position and linear momentum operators of a single particle, respectively. The…

A:

Q: Compute N(0) if r(t)= and prove that T(0) and N(0) are orthogonal

A: Given rt=<t sin t+cos t,2t2,sin t -t cos y> Then vector is given by r→t=t sin t+cos…

Q: 3. In many applications, the regions of interest are defined in spherical coordinates (e.g. lat,…

A:

Q: For this problem why did we integrated from -90degre to 90degree, instead of integrating from…

A: To discuss the suggested solution for the length of the given curve

Q: 8. Prove that the differential operator M: C² [a,b] → C[a,b] defined by d²u du Mu= 2+3u dx is a…

A:

Q: 3. Verify that the vector X is a solution of the given linear system. dx = -x – 2y dt cos 4t – sin…

A:

Q: Use Gauss's law to find the charge enclosed by the cube with vertices (±1,±1,±1) if the electric…

A:

Q: Show that the Euler-Cauchy Equation ry" + ary + by = 0, r+0 can be transformed into the constant…

A:

Q: If y and z are functions of u and v, then the Jacobian of the function transforming (x, Y, z) → (x,…

A:

Q: (a) express ux, u y, and uz as func-tions of x, y, and z both by using the Chain Rule and by…

A:

Q: 3. Use Green's Theorem to evaluate (y-6y) dr + y + 10y) dy where Cis shown below y (-11) (1-2)

A:

Q: Show that the matrix cos e sin e 01 A = =- sin e cos e 1 is invertible for all values of e; then…

A: To show that the matrix is invertible.

Q: 3. Let f R→ R³ and g: R³ → R be defined by f(t)= (t2, sin(t), et) and g(x, y, z) = xy + z. Using…

A:

Q: Let Uj, U2, Uz € R³ be an orthonormal system and let f : R³ → R be differentiable. Prove that af af…

A: Given that {u1,u2,u3} be an orthonormal system in ℝ3. Let us assume that {x,y,z} be the standard…

Q: 2. Find the matrix of chain rule given u = xy + xz + yz; x = cos t, y = sin t, z = t.

A: Given

Q: 2. Use the Fourier transform to solve this transport equation for u = u(x, t), defined on the whole…

A: Given that                       2ut-3ux = 0 and  u (x,0) = e-x2            We can write this as…

Q: 2.7 Given that the spacial components of motion, x = x(X, (), are: x₁ = X₁ + X₂ (e' - K), X₂X₁…

A: Solution : x1=X1+X2(et-K)      …(1) x2=X2+X1(e-t-K)   …(2) x3=X3    …(3) Solving above equations,…

Q: Find (x ,y, z) by using Jacobi or Gauss of Gauss Jordan method 5z — Зу + х%3 -1 2y – z = 2 z - 4x =…

A:

Q: 8. [M] Show that {1, cos t, cos? t,..., cos t} is a linearly inde- pendent set of functions defined…

A:

Q: Q2)A) If U (x,y)%3DXY-sin n is a function and x,y are function of r,9 defined as follow x =r cos 9 y…

A:

Q: (1) Determine the Jacobian ôx/ôq for the following system: x= [u, v, w], q = [x, y, AJ. u = x + 3y…

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Two functions u and v of x and y are said to satisfy the Cauchy- Riemann equations if ux = v, and u,…

A:

Q: Find u x v where 1) u = (4,3,6) and v = (2, 5, -3). u = (1,-1, 1) and v = 2) (2,1,0), 4) u = i+jcos…

A:

Q: 4. (a) Show that F (2xy + z³)i+x²j+3xz²k is conservative force field. Find the scalar potential of…

A: Please see the attachment

Q: 1 1 J(A) = ,T AX 2 i=1 j=1 =;(x1A11x1 + X1A12×2 + X2A21X1 + x2Az (A - yariable, X-parameter)

A: Given,      J(A)=12XTAx      =12∑i=12∑j=12xiAijxj      =12x1A11x1+x1A12x2+x2A21x1+x2A22x2where A…

Q: a L, Vo, V (x) = Vo, For the finite well defined by its potential E<VO, apply the relevant boundary…

A:

Q: x²y – x – 2 = 0 xy² – y – 6 = 0 - - with xo 0.9 and yo 2.9. W - -he determieent of the x2 noetriv of…

A:

Q: b) Suppose to i that and V х-у Calculate the x and and y by and Jacobian ð (u, v) 2 (x, y) hence…

A: Suppose that x and y are related to u and v by…

Q: Find the Jacobian of following functions f(x,y, z) = 3xy – yz + 2y z2 - 5xyz3 g(x,y, z) = xyz -…

A:

Q: a) Find the solution for u(x, y, z) yux − xuy + uz = u2 u(x, y, 0) = 1/y

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 5. Given that G(x, y) = (x² + 1, y²) and F(u, v) = (u + v, v²), compute the Jacobian derivative…

A: