Start Discovering Solved Questions and Your Course Assignments
TextBooks Included
Solved Assignments
Asked Questions
Answered Questions
spherical polar coordinates when a function fr is specified in polar coordinates it is usual to express grad f in terms
find constants a b and c such that the vector field defined byis irrotational with these values of a b and c determine
part 11 let a 1 2 3 4 5 and b ma nh nv tx ak meadefine a relation r from a to b that is a function and contains at
find the laurent series expansion of the functionabout a z 0 b z 1 and c z infin indicating the range of validity in
find partfparty and partfpartz in terms of the partial derivatives of f with respect to spherical polar coordinates r
consider the mapping w cosz determine the points where the mapping is not conformal by finding the images in the w
determine the constants a and b in order thatbe analytic for these values of a and b find the derivative of w and
determine whether the following functions are analytic and find the derivative where
consider the mapping w zn where n is an integer a generalization of the mapping w z2 use the polar representation of
find the images of the lines y x and y -x under the mapping w z2 also find the image of the general line through the
find the most general bilinear mapping that maps the unit circle z 1 in the z plane onto the unit circle w 1 in the w
part 1 refer to figure hw 7for problems 1-51 list all of the followingalevel-2 verticesbleavescsiblings of
for z x jy find the image region in the w plane corresponding to the semi-infinite strip x gt 0 0 y 2 in the z plane
the mapping w alphaz beta a beta both constant complex numbers maps the point z 1 j to the point w j and the point
show that the mapping w 1z maps the circle z - a a with a being a positive real constant onto a straight line in the
determine the image in the w plane of the circleunder the inversion mapping w
show that the bilinear mappingwhere theta0 is a real constant 0 le theta0 2pi z0 a fixed complex number and z0 its
given the complex mappingwhere w u jv and z x j y determine the image curve in the w plane corresponding to the
the two complex variables w and z are related through the inverse mappinga find the images of the points z 1 1 - j and
a cantilever beam of negligible weight and of length l is clamped at the end x 0 determine the deflection of the beam
1solve the following differential equationsad d 33 d2 9d2-2x-8y 0bym -4yn-9y36y 0cym -4y x 3 cos x e-2x hint use
a uniform cantilever beam of length l is subjected to a concentrated load w at a point distance b from the fixed end
the response xt of a system to a forcing function ut is determined by the differential equation modela determine the
using the convolution theorem determine the following inverse laplace transforms check your results by first expressing
use the initial- and final-value theorems to find the jump at t 0 and the limiting value as t rarr infin for the