CS101 - Lab Activity 3

Name: ____________________ NetID: ______________ Section#: ______

Objectives

In this lab, you will:

• Understand the difference between MATLAB functions and scripts.

• Learn to use function parameters and return values.

• Write a function to compute relativistic kinetic energy.

• Write a function to find the maximum distance to the origin

• Write a function that returns more than one value.

• Use the conditional Matlab if statement

References

• Lecture 2.

• MATLAB Help: Using MATLAB Programming and Data Types M-File Programming.

• MATLAB Help: Using MATLAB Mathematics Matrices and Linear Algebra.

• MATLAB by Gilat: Sections 6.1, 6.2, 6.7.

Part 1: Standard MATLAB Functions

Section I. Random numbers

1. Complete the MATLAB command to create a row vector of 10,000 random integers with either the value 0 or 1 (like flipping a coin heads-1, tails-0). You must use the rand function.
   
   
   

   x = floor ( .5 + ___________________________________ );
   
   
   

2. Write a single MATLAB command to compute the arithmetic average of 10,000 random integers generated by the 'rand' function in question #1 above. Use the MATLAB mean function and the vector x to compute the arithmetic average. Write the MATLAB command and not the answer (approx. .5) that your command returns. Use the MATLAB help facility if you have a question about using the mean function. If your mean isn't between .48 and .52 then probably your answer to #1 is probably incorrect.

   _________________________________________________
   
   
   

3. Fill in the three blanks below to complete a MATLAB command to create a column vector of 500 random real numbers with a value between -2*pi and 2*pi.
   
   
   y = ______________ + _____________ * rand(_________________________________) ;
   
   (You can test your code by typing min(y) and max(y). These values should lie close to -2pi and 2pi respectively.)

   Section II. Polynomials

4. To find the roots of the polynomial 2x³ + 15x² + 6x - 1, we type the following into the command window,

   >> roots([2 15 6 -1])

   Write the result.
   
   
   
   
   
   ____________________________________________________________________________

5. Write the single MATLAB command to find all the roots of -x + x¹⁰⁰ . (Don't write the roots, just write the MATLAB command that gives the roots.)

   >> p = __________________________________________________
   >> roots(p)

   Hint: x¹⁰⁰ - x = x¹⁰⁰ + 0*x^{99 +} 0*x⁹⁸+ ... + 0*x³ + 0*x² - 1*x + 0. Create a vector [ 1 (followed by 98 0's) -1 0]. Use linspace or zeros function to create the 98 0's.

6. Use the polyval function to compute the value of x³ + 2x² + 3 at x=3 . Don't write the solution, just write the MATLAB command that gives the solution.)

   
   _________________________________________________________

   Section III. Miscellaneous functions

7. Fill in the blank with the result that MATLAB gives when you type the following commands.
   >> x = [ 5.9 5.1 -1 0 4.99 -3.99 ];
   >> floor(x)
   ans =
   
   _____________________________________________________
   
   >> ceil(x)
   ans =
   
   
   _____________________________________________________
   
   >> z = [1 3 5 7 9];
   >> cumsum(z) % note how this differs from the sum function
   ans =
   
   _____________________________________________________
   
   
   >> w = 1:2:9;
   >> cumprod(w) % note how this differs from the prod function
   ans =
   
   _____________________________________________________

Part 2: Scripts and Functions

1. ______________________________________________________________________________________
   
   
   
   

2. ______________________________________________________________________________________
   
   
   
   

3. Y / N

4. Y / N

5. ___________________________________________
   
   
   

6. ___________________________________________
   
   
   

7. ___________________________________________
   
   
   

8. _________________________________________________________________
   
   
   _________________________________________________________________
   
   
   _________________________________________________________________
   
   
   
   

9. ______________________________________________________________________________________
   
   
   
   
   

10. ______________________________________________________________________________________
    
    
    

Part 3: Kinetic Energy of a particle

11. ____________________________________________________________________________________
    
    
    

12. ____________________________________________________________________________________
    
    
    
    

13. ____________________________________________________________________________________
    
    
    
    

14. ____________________________________________________________________________________
    
    
    

15. ____________________________________________________________________________________
    
    
    
    _____________________________________________________________________________________
    
    
    
    ______________________________________________________________________________________
    
    
    
    ______________________________________________________________________________________
    
    
    
    
    ______________________________________________________________________________________

Part 4: Writing your own function

16. _________________________________________________________________________________
    
    
    
    

17.  z = _____________________________________________________________________________________________________________
    
    
    
    
    

18. _____________________________________________________________________________________________________________
    
    
    
    
    
    

Part 5: Multi-valued functions, if statement

19. Write the result MATLAB returns when you type the following:
>> t = [ 3, 7, 1, 9];
>> max(t)
>> min(t)

ans =
____________________________________________________________

20. Write the result MATLAB returns when you type the following:
>> m = 6;
>> mod(m, 2)
>> n = 7;
>> mod(n,2)

ans =

_________________________________________________________




21. What values do you get for numbers, num, maxNum, minNum = __________________________ ?


22. What values do you get for numbers, num, maxNum, minNum = __________________________ ?