You must complete the project in a group of two students. Normally, all members of the group will receive the same grade; however, the instructor reserves the right to conduct individual interviews over the content of the project and to assign different grades to different members of the group.
There are several algebra concepts that are extremely important for successfully completing calculus I. In this project, you will learn some basic mathematica functions, you will use these mathematica functions to answer some algebra questions, and you will make some conclusions from your work on this project. You will be graded on the quality and clarity of your written presentation as well as the mathematical accuracy of your paper.
To label your work, use comments. For example, use the following to start your project (after every line, use SHIFT-ENTER to execute):
(* Your Name *)
(* Partner's Name *)
(* Math2431-100 *)
(* Summer 2012 *)
(* Project 1 *)
There are several methods to evaluate functions. The method here is probably the most useful (after every line, use SHIFT-ENTER to execute). Example:
Evaluate f(x) = 3x2 – 2x + 1
at x = 2:
f[x_] := 3x^2 – 2x + 1
f[2]
What is useful about this approach, we can quickly evaluate at several values for x. Evaluate f(x) = 3x2 – 2x + 1
at x = –2, 0, 1/2, 5 (after every line, use SHIFT-ENTER to execute):
x = {-2,0,1/2,5}
f[x]
There are several methods to graph functions. The method here is probably the most useful (after every line, use SHIFT-ENTER to execute). Example:
Graph g(x) = 2x3 + 4:
g[x_] := 2x^3 + 4
Plot[g[x],{x,-10,10}]
Look at the graph. It is difficult to see the y-intercept of the function on the graph. We can add an argument to the Plot
function to change the range of y-values on the graph:
Plot[g[x],{x,-10,10},PlotRange->{-8,8}]
What is useful about this approach, we can quickly graph several functions simultaneously. Example: Plot f(x) and
g(x) on the same set of axes (NOTE the use of { } around the two functions):
Plot[{f[x],g[x]},{x,-10,10}, PlotRange -> {-8, 8}]
Example: Factor 3x2 – 27:
Factor[3x^2-27]
Example: Solve x2 – x = 2:
Solve[x^2-x==-2,x]
However, Solve
gives real AND complex solutions. We only need real roots in calculus I, so use Reduce
(the output false
means there are no real solutions):
Reduce[x^2-x==-2,x]
Lastly, to find decimal approximations to roots, use NSolve. Example:
NSolve[x^2-x==5,x]
Once you are finished solving, use Clear[x]
to remove any stored values.
Complete the following using mathematica:
Solve
function and, if needed, the NSolve
functionPlot
both functions on the same set of axes.Plot
functionFactor
functionEvaluate
functionPlease follow these guidelines when preparing your report: