Definition of simply-connected and multiply-connected region. Cauchy's theorem for a simply-connected region, and its consequence theorem....

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Definition of simply-connected and multiply-connected region. Cauchy's theorem for a simply-connected region, and its consequence theorem. Cauchy's integral formula (theorem, its consequence, application ). z' dz (z + 5)(z-2i) I ask: Evaluate the contour integral where C: C:2-3, using the Cauchy's integral formula. 2. Represent the complex number z=-3/3+3i graphically in the complex plane, find its principle value of argument and modulus. Calculate Vz. %3D 3. Find a flux of the vector field a=(3-y)i+xj+(x+2z)k through a part of the surface S: 2x +3y-z-12 0 created as a result of intersection of the plane S with coordinate planes. 4. Find a circulation of the vector field a=-xy' i+ xj+z k on shifting a uni x=2 cost, y = 2 sint %3D mass along the contour L: , te[0,27]. z =3 4x 5. Find the angle between the gradients of the scalar fields u(x,y,z)= v(x, y, z) = ye*- –3/z+2x at the point M(1, 1, 2). p+2 (p-1)(p +2p+5 5. Find the original of Laplace transform: F(p) =- %3D Definition of simply-connected and multiply-connected region. Cauchy's theorem for a simply-connected region, and its consequence theorem. Cauchy's integral formula (theorem, its consequence, application ). z' dz (z + 5)(z-2i) I ask: Evaluate the contour integral where C: C:2-3, using the Cauchy's integral formula. 2. Represent the complex number z=-3/3+3i graphically in the complex plane, find its principle value of argument and modulus. Calculate Vz. %3D 3. Find a flux of the vector field a=(3-y)i+xj+(x+2z)k through a part of the surface S: 2x +3y-z-12 0 created as a result of intersection of the plane S with coordinate planes. 4. Find a circulation of the vector field a=-xy' i+ xj+z k on shifting a uni x=2 cost, y = 2 sint %3D mass along the contour L: , te[0,27]. z =3 4x 5. Find the angle between the gradients of the scalar fields u(x,y,z)= v(x, y, z) = ye*- –3/z+2x at the point M(1, 1, 2). p+2 (p-1)(p +2p+5 5. Find the original of Laplace transform: F(p) =- %3D