Worksheet 1, PHY301 - Fall 2003
Due Sept. 12 - two weeks

One way to begin learning C++ programming would be to study a bunch of simple working programs. If you choose that route, a suitable collection can be found at MSU CSE231

PROBLEMS

1. Write a C++ code that prints out your name.

2. Write a C++ code that calculates and prints out the following sum (where i is in radians)

$$(\sum_{i=0}^{100} Sin(i))^2$$ (1)

Check your result by doing the same calculation in Mathematica.

3. Write a C++ code that finds the integral of a function f(x) over the interval (a,b) using the simplest equally spaced Trapezoid rule. As an example use

$$\int_0^1 e^{-x^2} dx.$$ (2)

Plot the value of this integral(using xmgrace) as a function of the number of ``mesh points'' that you used on the interval (0,1). Also calculate the integral above using Mathematica to check that you got it right.

4. Do the same, but use the integration method in which the interval is again divided into equal intervals, but the integrand is evaluated only at the centers of those intervals. Use equal weights. Again check the answer with Mathematica.

5. Repeat problem 4, but this time make the integrand more challenging by including a singular factor 1/sqrt(x) in it. (You could instead include a factor 1/sqrt(x-0.5) in it; that will challenge your ability to use Mathematica.)

Info on xmgrace: http://plasma-gate.weizmann.ac.il/Grace/

How to compile and run a C++ code in 1240 BPS

To compile:

g++ -o file.exe file.c

To execute:

./file.exe