Question

what is nonlinear analysis

Answer 1

n our daily life,we usually encounter with non-linear play ground(a play ground having bunch of resistors,voltage sources,transistors,billions of logic gates etc) as it is much difficult,being an engineer we take things from non-linear play ground and put them into linear play ground after applying abstraction techniques on it and then apply linear formulas(KVL,KCL,nortoN equivalent,thevnin equivalent etc) and get the required result
So transition of non-linearity into linearity by applying abstraction techniques and then apply linearity formulas on it and then get answer is the "HEIGHT OF EE"

Answer 2

Non-linear circuit elements are those which do not follow a linear voltage-current relationship. Therefore they do not follow Superposition Principle and also other Linear Network Theorems like Thévenin's and Norton's Theorems. Non-linear circuits are required to be solved either analytically using basic KVL, KCL, Node Method, Loop Method etc (but it is too troublesome in most cases) or by using smart techniques like graphical analysis (plotting V-I curves and studying them), piecewise linear approximations (approximating the non-linear element to behave as different linear elements at different regions of operation) and small-signal incremental analysis (using Taylor's Theorem approximation to linearize a non-linear circuit over a small signal variation).
For details you may watch
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-6/
http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-002-circuits-and-electronics-spring-2007/video-lectures/lecture-7/