EGR 103/Fall 2017/Lab 7

Basic Root-Finding Problems

• Main thing is to look at MATLAB:Fzero and the different ways of calling it.
• The sign plots are really helpful.
• The last equation has three sign changes but only two roots

Basic Min/Max Finding Problems

• Main thing is to look at MATLAB:Fminbnd and the different ways of calling it.

Chapra Problem 6.16

• This is a one-parameter search problem. There is an examples for a one-parameter searches at MATLAB:Fzero#One_Parameter

Chapra 6.20

• Be sure to run fzero in a loop - see MATLAB:Fzero#One_Parameter for help.

Chapra 6.21

• This simply requires using fzero twice - just be careful on how you initialize fzero and also be careful about units for the angles.

Chapra 7.23, 7.24, and 7.25(b/c)

• These problems will require fminsearch to find the extremes, as well as meshgrid and surfc to make the plots; more on that at Plotting Surfaces

General Notes - Code from Lab

First, you need to think about what it is you are being asked to do:

• Find a single value of a single variable that sets a function equal to zero (or sets a function equal to a particular value, such that the difference between the function and the particular value is zero):
  • Use fzero
  • First argument is an anonymous function calculating the function you want to be set to zero
  • Second argument is either a valid bracket surrounding the root of interest (preferred) or a single initial guess from which MATLAB will try to build a bracket.
• Find a single value of a single variable that minimizes a function within a particular bounded range:
  • Use fminbnd
  • First argument is an anonymous function calculating the function you want to minimize
  • Second argument is the left end of the bounded range
  • Third argument is the right end of the bounded range
  • The bounds are in two different argument!
  • If you want to maximize something, use the negative of the function ar the first argument (so you are minimizing the negative); note however that the function's value as given by fminbnd will have the wrong sign
• Find a single vector of values of a single variable that minimizes a function within a particular bounded range:
  • Use fminsearch
  • First argument is an anonymous function calculating the function you want to minimize; this function must be of a single variable but you may use different entries within that variable
  • Second argument is an initial guess which must have as many entries as the number of entries used in the function
  • If you want to maximize something, use the negative of the function ar the first argument (so you are minimizing the negative); note however that the function's value as given by fminbnd will have the wrong sign
  • Because you are giving an initial guess versus a boundary, you must be careful in picking the initial guess