Mathematica Command Sheet

**  To enter commands, simply type in the browser window, followed by the "enter" key  (not the "return" key) **

**  It may be helpful to use the Basic Input Pallete for your computations.  Palletes can be found under the File Menu. **

1.  Getting Help

•     ? CommandName gives a description of the command, commandName, along with syntax
•     ?? CommandName gives a description of the command, commandName, along with syntax anda list of all options that can be used with the command
•      Highlight a command, then pull down Help Menu and choose Find Selected Function - this gives a description of the command along with syntax

2.  Defining and Evaluating Functions

•     f[x_]:=  algebraic expression in x defines f as a function of x
• f[x_]:= 3x+5, enter
•     f[xValue] gives the value of the function, f, for x = xValue
• f[2], enter            (should provide 11 in return)
  
•     f'[x] gives an algebraic derivative of f[x]
• f'[x], enter
•     f'[xValue] gives the value of the derivative of f[x] for x = xValue
• f'[2], enter            (should provide 3 in return)

3.  Solving an Equation

•       Solve[ expression == value, variable ] solves the given equation for the indicated variable
• Solve[3x+5==0,x], enter                            
•       NSolve[ expression == value, variable ] solves numerically the given equation for the indicated variable

4.  Numerical Approximation

•         //N gives a numerical approximation of an expression
• f[2.2]//N, enter          (should give you a numerical/decimal solution)

5.  Plotting Functions

•         Plot[f[x] , {x, xmin, xmax}, options (seperated by a comma)] plots the function defined as f[x] on the interval for the variable x between xmin and xmax
•         AxesLabel->{"x-label","y-label"} labels ;the axes of the graph with x-label and y-label respectively
•         PlotLabel->"PlotTitle" places the title PlotTitle at the top of the graph
•         AxesOrigin->{xValue, yValue} specifies that the axes drawn should cross at the point (xValue, yValue)
•         GridLines->Automatic draws gridlines on the plot

6.  Displaying Several Plots

•         Name = Plot[f[x] , {x, xmin, xmax}, options (seperated by a comma)] provides a name for this particular graph
•         Show[ {list of named graphs seperated by commas} ] displays a collection of previously generated and named graphs on the same grid

7.  Integrating Functions

•         Integrate[f[x], x] finds an antiderivative for f[x]
• Integrate[x^2, x], enter            (should give you (1/3)x^3 + C as the solution)
•         Integrate[f[x], {x, xmin, xmax}] integrates a function symbolically
• Integrate[x^2, {x, 2, 4}], enter        (should give you 64/3 - 8/3 = 56/3 as the solution)
•         NIntegrate[f[x], {x, xmin, xmax}] finds a numerical approximation to an integral
• NIntegrate[x^2, {x, 2, 4}], enter      (should give you a numerical approximation to 56/3)

8.  Solving a Differential  Equation

•         DSolve[diffequation, y[x], x] solves a differential equation for the function y(x) with independent variable x