CS201
Lab 7 - Function Parameters

Objectives:

• Calculate the area under a curve using a C program.
• Practice use of nested for-type loops, switch statements, enumerated types and passing function as parameter.

Readings:

• Read Chapter 7 in the Hanly/Koffman text. Read "Case Study: Bisection Method for Finding Roots" in page 348-356 for ideas and better understanding.

Deliverables: (DUE AFTER THE END OF YOUR LAB IN THE WEEK STARTING AT 9TH APRIL)

• Submittal of the following files:
  • Makefile
  • Proto.h
  • Lab7.c
  • Trap.c
  • XSquaredSinX.c
  • HalfCircle.c
  • TestFunction.c

TO DO

• Design and Write a program to solve Programming Project #6 on page 363-364 of the Hanly/Koffman text.
• Your program should find the area under a curve y = f(x) between the lines x=a and x=b. Approximate this area by summing trapezoids (Formed by a line from x0 vertical up to the function, to y0 = f(x0), then straight line to y1 = f(x1), back down to the x-axis, and left to original.)
  

• We assume that function is positive over the interval [a,b].
• For n subintervals of length h, whereh=(b-a)/n, Trapezoidal rule is:
  
  
  
• Write a function Trap with input parameters a,b,n and f that implements the trapezoidal rule.
• Call Trap with values for n of 2,4,8,16,32,64, and 128 on functions
  
  

• Carefully choose which parameters need to be passed by reference, and when passing by value is enough. 
• Make sure to use nested (i.e. double)  for-type loop to calculate and print out your results.
• Define enumerated type to reflect your three functions (i.e. xsquaredsinx, halfcircle, testfunction), and use it in the nested loop. Switch-type statement may also be helpful.
• Make sure that your Makefile is going to properly rebuild the executable.
• You will need to build four separate source files, one include file for prototypes, and a stub for my TestFunction that will be supplied after submittal.
• TestFunction Stub
• Type of function is double.
• Name of function is TestFunction.
• Number of parameters is one.
• Type of parameter is double.
• Your stub will need to be called properly in your main program. The value it returns (can be anything) should be properly formatted as an output statement (see below).
• When we grade your program, we will overwrite your TestFunction.c with our version of TestFunction.c and your program will then produce an expected output that we will check for.
• Inputs: none, the program just runs.
• Outputs: (#'s represents your calculated data):
  CS201 - Lab 7 - Area Under The Curve
g(x) = XSquaredSinX
a = 0.00000, b = 3.14159
n =   2, h = #.#####, area = ######.#####
n =   4, h = #.#####, area = ######.#####
n =   8, h = #.#####, area = ######.#####
n =  16, h = #.#####, area = ######.#####
n =  32, h = #.#####, area = ######.#####
n =  64, h = #.#####, area = ######.#####
n = 128, h = #.#####, area = ######.#####

h(x) = HalfCircle
a =-2.00000, b = 2.00000
n =   2, h = #.#####, area = ######.#####
n =   4, h = #.#####, area = ######.#####
n =   8, h = #.#####, area = ######.#####
n =  16, h = #.#####, area = ######.#####
n =  32, h = #.#####, area = ######.#####
n =  64, h = #.#####, area = ######.#####
n = 128, h = #.#####, area = ######.#####

f(x) = TestFunction
a = 0.00000, b = 12.00000
n =   2, h = #.#####, area = ######.#####
n =   4, h = #.#####, area = ######.#####
n =   8, h = #.#####, area = ######.#####
n =  16, h = #.#####, area = ######.#####
n =  32, h = #.#####, area = ######.#####
n =  64, h = #.#####, area = ######.#####
n = 128, h = #.#####, area = ######.#####

Grading Scheme

Program compile and execute 20%
Program meets all specifications 60% (e.g. makefile, pass by value/reference, proto.h, enumerated types, nested for loop, function parameter etc. Also ask your TA specifically about what preciously he is looking for)
Program follow code conventions and contain proper documentation. 20%