Newton-Raphson method

Hi, its my first time posting on here so please be nice. I'm studying Aeronautical Engineering and have a course in MATLAB to do this semester. One of my assignments is to use the Newton-Raphson method to answer something and I'm completely stuck on how to proceed with the second part of the question:

CT = ((σ*(lambda^2)CL)/2) * (((1-a)/lambda)-θT)

where a is:

a = (((σ*lambda*CL)/2)+0.5) - sqrt((((σ*lambda*CL)/2)+0.5))^2-((σ*lambda*CL)*((1-lambda*θT)/8))

QUESTION 1

You are requested to plot the thrust coefficient CT against the tip-speed-ratio lamda for 5 different values of the pitch angle θT , namely θT = [10 degrees 5 degrees − 0.1 degrees − 2 degrees −5 degrees]. The objective of this exercise is that your MATLAB code reproduces figure 1. Note that for θT < 0, there exists
a maximum value of lambda above which CT becomes complex. You should take this into account when solving the required exercise.

QUESTION 2

You are requested to write a MATLAB program that, for given values of the parameters σ, CL, and θT , determines the value of the tip-speed-ratio, lamad, corresponding to a user-requested
value of the thrust coefficient CT . After writing the code, assume σ = 0.05, CL, = 2pi and θT = −2degrees, and use it to determine within machine accuracy the values of lambda associated with CT = 0.9143 and CT = 0.8564. Your program must solve equation (1) by means of Netwon’s method, that will have to be implemented by you. It is suggested that finite-differencing be used to calculate function derivatives. Please note that the use of any MATLAB solver, such as the function fsolve in alternative to the direct implementation of Newton’s method will not be accepted.

I've done the first one, it was quite hard for me but as I said I'm really stuck with the second. If anyone could give me some guidance or even start me off that would be great. Thank you.

-Jonathan

[Andrew Newell]

We don't generally answer homework problems unless you can show us evidence of some effort. Please have a look at http://www.mathworks.com/matlabcentral/answers/6200-tutorial-how-to-ask-a-question-on-answers-and-get-a-fast-answer.

[Walter Roberson]

http://www.mathworks.com/matlabcentral/answers/?term=tag%3A%22newton%27s+method%22