Exercise 5.27 Find the Green functions on the following regions in R a) the semi-ball B(0, R) n {{z,y, 2) | z > 0}; b) the part of the ball in the first octant B(0, R) n {(z, y, z)| 1,y, z > 0}. Give hint and both solve a b

Q: The plane a+ y-0 intersects the surface 7+ 2:21 along a curve C. Use Lagrange multipliers to find…

A: We have 2 surfaces intersects to form a curve. We need to find the maximum and minimum of a function…

Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: Let She a regular surface parametrized by X (4₁6) denote the coefficient functions of the first…

A:

Q: Sdve the folosing Dfferenthal equations by using the method of Laplace Transforms: caly'+4y =4x…

A:

Q: Let the contour : [0,3] → C be given by 7(t) = { 11 (1) = 2eint, 0<t≤1 Y2(t) = 2(t − 2), 1<t≤3. i.…

A:

Q: Evaluate ff, (F n) dS in the following cases: (a) F = (2y+z, x+z, y − x) and S is the portion of the…

A: (a)

Q: Integrate h(x, y) = yi-xj over the triangle with vertices (-2, 0), (1, 0), and (0, 1) traversed…

A:

Q: Polynomial kernel given: k( xx, x;) = (1 + X;• Xj dot product of Xi and Xj Find the function 0 : R"…

A: As per the question we have to find the function φ(x) from Rn to Rm such that the kernel  k(xi , xj)…

Q: Let P and Q be points in R2. Show that a linear map G(u, v) = (Au+ Cv, Bu+ Dv) maps the segment…

A: Let P and Q be two points in R2. We have to show that a linear map G(u, v) = (Au + Cv, Bu + Dv) maps…

Q: Solve the Divichlet BUP Per an annulus Satisfying Pde: urr +t ur tte Yoo=0 Acr<2, ニo ノ acOc2た

A:

Q: Match each function with the description of its f(x, y, z) = 0 level surface. e f(x, y, z) = -2² -…

A: f(x,y,z)=-x2-y2-2z2=0 This is satisfied only by the points (0,0,0). Therefore, it corresponds to (d)…

Q: 4) Let B be a sphere with radius a and center 0 and r be the radial dis- tance. Applying Green's…

A: Consider the provided question, Let B be a sphere with radius a and center 0 and r be the radial…

Q: 9. Let E be the tetrahedron with vertices: (0,0,0), (3,2,0), (0,3,0), (0, 0, 2). E is bounded by…

A:

Q: 9. Show that the function (-, -) : IR² × R² → IR defined by setting = #1#2 + 2x12 + 2y1*2 + 8y1Y2 /2…

A:

Q: Determine where D is the region enclosed (5, 0, 0), (0,3,0), (0, 0, 3), by the tetrahedron with…

A:

Q: x 6) Find the average value of f(x) = √x²+16 on [0,3]. a) 1 b) WIT 3 WIN c) 3/3 d) 3

A:

Q: The coordinates of the AB part of the homogeneous wire in the x, y and z axes

A: In this question, we find the coordinate of the center of the gravity for the homogeneous wire with…

Q: Let p =1 Find a hyperplane [f:d] that strictly sepa- rates B(0, 3) and B(p, 1). [Hint: After finding…

A:

Q: Use Divergence Theorem to evaluate .(v²z²i +z²x²j+x²y²k).ds, where S is the upper part of the sphere…

A: Gauss Divergence Theorem : ∫∫SF·ndS=∫∫∫VdivF dV From ∫∫Sy2z2i+z2x2j+x2y2k·dS, F=y2z2i+z2x2j+x2y2k

Q: 10. Let w =f(e) = (3 + 4) z – 2 + i. (a) Find the image of the disk | z - 1| 1.

A:

Q: 2. Solve x². dy + 2xy = 4x³ using an + 2xy = 4x³ using an Integrating Factor. dx

A:

Q: [] and p = 3 Let q = Find a hyperplane [f: d]O that strictly separates B(q. 3) and B(p, 1)

A:

Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), (3, 2,0), (0,3,0), (0, 0,2). E is bounded by…

A: The tetrahedron bounded by the planes              from the plane…

Q: 3 dx a) 3- x

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: c) Show that the image of the annulus {z: 1 -1 | W - 1²/31 | > /// } W = Z-1

A: To Show: The image of the annulus z : 1&lt;z&lt;2 under w=2z-1 is the domain w : Re w&gt;-1,…

Q: can you answer  e) f)  g)

A:

Q: Use Divergence Theorem to evaluate [0²z?i+z?x²j+x*y²k).ds, where S is the upper part of the sphere…

A: To evaluate the below integral using the divergence theorem. ∫∫Sy2z2i+z2x2j+x2y2kds Here S is the…

Q: Let T be the tetrahedron with vertices (2,0,0), (0, 5, 0), (0, 0, 4) and the origin. Write f(x, y,…

A: The equation of the plane through (2,0,0),(0,5,0),(0,0,4) is x2+y5+z4=1 i.e.,10x+4y+5z=20 For y…

Q: Q6: Find the residues of a) f(z) = Z² 2Z and (ZH)²(Z²+4)

A: Since you added two questions, find the solution of the first one.

Q: Determine whether these statement forms are logically equivalent. In each case, construct a truth…

A: Boolean algebra is a branch of mathematics that is concerned with binary variables and operations on…

Q: 9.) Let E be the tetrahedron with vertices: (0,0,0), E is bounded by four planes: z = 0, x=0, 2 3…

A: Volume of tetrahedron

Q: Find the maximum value of f(z)| = |z²+ 3z - 1| on the unit disk |z| < 1.

A:

Q: The roots of the characterictic polynomial of o linear, homogeneous,constant coefficient equation as…

A: It is given that the roots of the characteristic polynomial are 3, 3, 2+4i. But as we know that the…