Multiple variables,vector calculus,Complex va

ASSIGNMENT QUESTIONS 1. Find the area of the region bounded by the parabola y2=4ax and the line x+y=3a in the positive quadrant 2. Change the order of Integration in and then Evaluate it 3. By changing the order of integration evaluate 4. Evaluate by changing the order of integration 5. Evaluate 6. Evaluate , where V is the finite region of the space (tetrahedron) Formed by the planes x=0, y=0, z=0 and 2x+3y+4z=12 7. Find the volume of the ellipsoid 8. The temperature of points in space is given by . A mosquito located (1 ,1, 2)desires to fly in such a direction that it will get warm as soon as possible. In what direction should it move? 9. Prove that =(x2-y2+x) -(2xy+y) is a conservative field and find the scalar potential of . 10. Using Greens theorem, evaluate where C is the boundary of the triangle formed by the lines x=0,y=0, x+y=1 in the xy plane. 11. Verify Gauss divergence Theorem for = taken over the cube bounded by the planes x= 0, x = 1, y = 0, y = 1, z = 0, z = 1 12. Verify Gauss divergence theorem for and S is the surface of the rectangular parallelepiped bounded by . 13. Under the transformation ,find the image of 14. Find the bilinear transformation which maps ,i,0 onto 0,i, 15. Find the bilinear transformation which maps the points z=-1,0,1 into the points w=0,i,3i.