Please use *format compact* and *format short* before you begin, i.e., type these commands into the command window. *format compact *condenses the command window output and *format short *reduces the floating point numbers in MATLAB to 4 decimal places. If problems require answers with more decimal places, you may use *format long* to get 8 decimal places. If you have ANY doubt about the syntax you are using to invoke a particular elementary function such as exp, cos, sin, etc., then type *help elfun* into the command window. *elfun *stands for elementary functions and this command provides a list of elementary functions with their corresponding MATLAB syntax. Remember to use a semicolon “;” to suppress output when the output is not necessary.

Exercise 1: You need to use a period preceding any matrix operations. Remember that +,-,*, /, ^ are all considered matrix operations in MATLAB. Thus, if you declare a row vector *x* = 0:pi/4:5*pi/4, then cos(*x*) is a row vector as well with the same dimensions as *x*. So cos(*x*) *automatically* inherits the dimensions of *x. *This is a very important concept moving on. So if we try to multiply *x**cos(*x*), we will get an error because we are multiplying a row vector by a row vector. From Linear Algebra, we know we cannot do this. We can only multiply row vectors by column vectors and vice versa. Therefore, we need to input a period preceding the matrix operators * to indicate that we want to multiply each element of the row vectors *componentwise*, i.e., we type *x.**cos(*x*). We use the period (or dot) preceding matrix operators when we are dealing with functions.

Exercise 2: See page 3 of the protocol.

Exercise 3: Remember, if we wish to plot cos(*x*) vs *x*, we must first declare* *the row vector *x* prior to creating the row vector cos(*x*) since cos(*x*) depends on *x*. If we declare cos(*x*) first, then MATLAB will use the present value of *x* saved in the workspace. This may be some *x* that was declared in a previous problem and NOT the same *x* we want to use now.

Exercise 5: You NEED to create a *function + function *M-file. See page 5 of the protocol. Most the code is given to you, just copy and paste it into a new script file and replace all “??” with the appropriate code.

Exercise 6: Make sure you clear your function from the workspace as stated in part (b). I will mark off points for that. Also, make sure you invoke your function in the command window as stated in the question. For part (b), you need to write a function M-file (NOT in the command window) and invoke the function M-file in the command window.

Make sure that all the codes are not copied from anywhere.