Math 3298 - Hampton - Lab 1 - Due 9/11

Lab reports should conform to the guidelines explained on the handout.  Collaboration during the lab is strongly encouraged, although the write-up of the lab report must be done individually.

Introduction to Mathematica: Basic commands and using the help system.

The Help system has an enormous amount of information.  The Help system is your friend.  Use the help system.

Do not use the Palettes, they are more trouble than they are worth (e.g. use Integrate[x^2,x] instead of ∫x^2dx).

Tips :
1. Shift-Enter is used to execute a command.
2. To interrupt a command, go to Kernel on the command bar at the top.
3. All function arguments are in square brackers, all lists are in curly brackets.
4. Built - in functions have capitalized first letters, and Mathematica is case - sensitive.
5. To get an approximate answer from an exact one, apply the function N (for numerical).
6. You can get information about a function by using ?Function or ?? Function for even more information.
7. Ctrl - K (or apple - K on a mac) auto - completes commands.  This is very useful for long commands like ParametricPlot3D.
8. Sometimes if you make a mistake (like using "=" instead of "==" for an equation) the only way to recover is to quit the kernel (Kernel -> Quit Kernel -> Local).

Introductory exercises

1. Compute the square root of 3 to 100 digits.

2. Given the function f[x_]:= x^3 + 3x +7:
	a. Compute the indefinite integral.
	b. Check to see that you got the right answer (ie. differentiate it).
	c. Plot the function (from x=-2 to x=2).
	d. Refine your plot to find an approximation (accurate to 2 decimal points) of one zero of the function by changing the plot domain.
	e. Make your plot prettier by labeling the x and f(x) axis (check out the further examples under the Plot information).
	f. Use the Solve and NSolve commands to find the roots of the function.
	g. Find the definite integral of the function on the interval [-2,2].  Check your graph from c. and see if this seems like a reasonable answer.
	
3.	Given the function g[x_] := Sin[x]:
	a. Plot the function (from x=-2 to x=2).
	b. Display this plot and the plot from 2.c. on the same graph.
	
4.	An example of the use of the Manipulate command is shown below.  Play around with the controls - how many kinds of conic curves can you generate (i.e. parabolas, ellipses, hyperbolas, lines...)?

5.	Save this file and put it into your account (on a mac, authenticate the "myfiles" directory and put stuff there) or on a flash drive.

Manipulate[ContourPlot[A x^2+B y^2 + C x y + D==0,{x,-PlotSize,PlotSize},{y,-PlotSize,PlotSize}],{{A,1},-1,1},{{B,1},-1,1},{{C,0},-1,1},{D,-10,10},{{PlotSize,10},1,100}]