 Welcome back MechanicalEI, did you know that in cartography the property distortion of shapes to make them as small as desired is achieved using conformal mapping? This makes us wonder, what is conformal mapping? Before we jump in, check the previous part of this series to learn about what harmonic functions are. Now consider an analytic mapping F which maps the set D into the set E and is given by W equals F of Z where Z equals X plus IY and Z belongs to capital D. If two curves C1 and C2 in a Z plane intersect at Z0 then the angle from curves F of C1 to F of C2 in a W plane intersect at F of Z0 is the same as the angle from C1 and C2. If the derivative of the function is non-zero then there exists a conformal map for the analytic function that is the analytic function F of Z is conformal at any point say Z0 where it has a non-zero derivative. A complex mapping of the form W equals F of Z which again equals to AZ plus B where A and B are complex constants is called a linear mapping. The bilinear or Mobius transformation is given by W equals F of Z and is equal to AZ plus B upon CZ upon D where A, B, C and D all belong to the set capital C and AD minus BC is not equal to zero. They are so called because both Z and W in the above equation are linear hence bilinear. Cross ratio is the term which remains invariant under bilinear transformation and is defined for W equals F of Z which maps from distinct points Z1, Z2 and Z3 on two distinct points W1, W2 and W3 as follows. One last term of significant importance is fixed points of bilinear transformation and are defined as the points that satisfy the equation F of Z equals AZ plus B upon CZ plus D equals to Z. Since we first saw what conformal and linear mapping are and then went on to see what bilinear mapping is so like, subscribe and comment with your feedback to help us make better videos. Thanks for watching. Also, thanks a lot for those constructive comments. You helped the channel grow. So here are the top mechanical EIs of our last videos. In the next episode of Mechanical EI, find out what standard transformations are.