How to Solve Equations and Create Graphs with Microsoft Mathematics?

Microsoft Mathematics provides a set of mathematical tools that help students get school work done quickly and easily. With Microsoft Mathematics, students can learn to solve equations step-by-step, while gaining a better understanding of fundamental concepts in pre-algebra, algebra, trigonometry, physics, chemistry, and calculus. Microsoft Mathematics includes a full-featured graphing calculator that’s designed to work just like a handheld calculator. Additional math tools help you evaluate triangles, convert from one system of units to another, and solve systems of equations.

Familiarize yourself with the interface

When you first open Microsoft Mathematics, you’ll see the following elements displayed:

1. The Calculator Pad which includes a number pad and the following button groups: Statistics, Trigonometry, Linear Algebra, Calculus, Standard, and Favorite Buttons.
2. The Worksheet tab is displayed by default, and is where you will do most of your numerical computing. This tab includes both an input and output pane. The input pane gives you the option of using the graphing calculator, keyboard or ink input. When you click buttons on the calculator pad, you construct a mathematical expression in the keyboard input pane. 
3. The Graphing tab can be used to create most mathematical graphs. This tab includes an input pane to enter the function equation, inequality, data sets, or parametric equations that you want to plot. 
4. Math Tools : On the Home tab, in the Tools group, you'll see buttons for additional math tools:

• Equation Solver to solve a single equation or a system of equations.
• Formulas and Equations to find frequently used equations from science and math, and explore them graphically or by solving for a particular variable. 
• Triangle Solver to find the measures of the remaining sides and angles of a triangle when some sides and angles are known. 
• Unit Conversion Tool to convert measurements in one system of units to another.

Microsoft Mathematics

Using the Graphing Calculator

The primary tool in Microsoft Mathematics is a full-featured scientific calculator with extensive graphing and equation-solving capabilities.  You can use it just like a handheld calculator by clicking buttons, or you can use your keyboard to type the mathematical expressions that you want the calculator to evaluate. 

Solve an equation:

Our sample problem is to find the area of a walkway that surrounds a rectangular swimming pool. The pool measures 9 meters by 15 meters, and the walkway is 2 meters wide. 

Using the buttons on the calculator

1. Calculate the area of the pool and walkway by clicking the following calculator buttons. Use parentheses to group calculations appropriately: 
   
2. Calculate the area of just the pool: 
   
3. Subtract the area of the pool from the area of the pool and walkway: gbr 5
   

Using the Inking Capabilities:

With Microsoft Mathematics users can input an equation or fraction using the improved ink input capabilities. Users can write mathematical expressions in the Ink input pane using the pen from a Tablet PC or an ultra mobile PC. You can also use a mouse.  Ink input is available on both the Worksheet and Graphing tabs.

1. On the Home tab, Select the Ink option in the Input tab gbr 6
   
2. In the Ink input area draw the following fraction using your pen from your Tablet PC, or your mouse if you have a laptop  gbr 7
   
3. Hit Enter

Solving Equations Step-by-Step

Microsoft Mathematics provides step-by-step solutions to many types of problems, from simplification of algebraic expressions to solving systems of equations. If a step-by-step solution is available for an expression, you will see the heading "Solution steps" between the input and output expressions in the output pane. 

1. Using the Equation from above- 2x/4=2
   
2. Hit Enter
3. You’ll see the equation is solved in the Output Pane
4. Click on Solution steps
   
5. You’ll see the completed Step-by-step solution for the equation in the Output pane

Note : If a step-by-step solution is available for an expression, you will see the heading "Solution steps" between the input and output expressions in the output pane regardless if you enter the expression using the calculator, keyboard, or ink input option

How to Create a Graph

To create most mathematical graphs, you use the Graphing tab. The Graphing tab includes an input pane that you use to enter the function, equation, inequality, data set, or parametric equation that you want to plot. To work with the graph after you plot it, the Graphing tab also includes a pane that describes what is plotted in the graph, and a graph pane that displays the graph. 

General steps for plotting a graph

1. Click the Graphing tab.
   
2. Expand the appropriate input pane: Equations & Functions, Equations, Data Sets, Parametric, or Inequalities. 
3. In the Dimensions list, click 2D or 3D.
   
4. In the Coordinates list, click Cartesian, Polar, Spherical, or Cylindrical. 
5. Enter the expression or data you want to plot. 
6. Click Graph

Plotting 2D Graphs

Plot a Line

You can plot any line by using Microsoft Mathematics. The simplest way is to put the equation of the line into slope-intercept form and plot the right side of the equation as a function of y. You can plot any form of the line as an equation, and you can also plot two data points and draw the resulting line. 

Sample Equation:

 

Plot a line as a function of y

1. Click the Graphing tab. 
2. Expand Equations & Functions. 
3. In the first input box, enter y=(2/3) x +3.
   
4. Click Enter
5. Click Graph and see results
   

Plot an equation or function in 2D Cartesian coordinates

To plot one equation or function

Sample Equation:

1. Click the Graphing tab. 
2. Expand Equations & Functions. 
3. In the Dimensions list, click 2D. 
4. Select Polar. 
   
5. Click in the first box. 
6. In the Input box that appears, type: sin(ntheta), and then click Enter. 
   
7. Click Graph. 
   

Note: To plot multiple equations or functions follow the same steps as above, but add another equation to the second box. If you want to add a third equation or function, click Add, and then enter the equation or function in the new box that appears. 

Animate a graph

When you create a graph that involves unknown parameters, such as the graph of y = sin(ax), Microsoft Mathematics initially picks an arbitrary value for the unknown parameter a and draws the graph using that value. After the graph is created, however, you can change the value of a and animate the graph by using a range of values for the unknown parameter. What you see during the animation is a series of graphs, each drawn with a slightly different value of the unknown parameter. If your graph involves multiple unknown parameters, you can choose which parameter to animate. You can also set the values of some parameters to specific values while you animate another. 

To animate a graph

1. On the Graphing tab, expand Graph Controls
   
2. In the Parameter list, parameter that you want to animate. 
3. In the Lower Bound box, enter a lower bound for the parameter. The default is 0. 
4. In the Upper Bound box, enter an upper bound for the parameter. The default is 2. (You can enter an upper bound that is smaller than the lower bound. In this case, Microsoft Mathematics animates from the larger value to the smaller.)
5. Click ►
   

About 3D Surface Graphs

A 3D surface graph is a way to represent three-dimensional data in two dimensions. In its simplest form, it shows a function of two variables x and y as a "carpet", with the height of the carpet at any point (x,y) equal to the value of the function at that point. You can create more complicated surfaces, such as spheres and tori, as the graphs of equations in three variables. 

You can create 3D surface graphs of a function of two variables: as graphs of equations in three variables, or as graphs of three parametric equations. 

You can display 3D surface graphs in two ways. 

1. The default is to show a colored surface, where the color is based on the angle each point of the surface makes with each of several differently colored light sources. 
2. You can also show the surface as a wireframe (also called a mesh or grid), which shows the surface as made up of lines). You have probably seen similar graphs in documentaries that show the making of a computer-animated film.

A color surface graph.

A wireframe graph.

Plot One Equation or Function

Sample Equation: 

1. Click the Graphing tab. 
2. Expand Equations & Functions. 
3. In the Dimensions list, click 3D
   
4. Click in the first box. 
5. In the Input box that appears, Type an equation or function definition,3theta-phi, and then click Enter
6. Click in the first box. 
7. In the Input box that appears, Type an equation or function definition,3theta-phi, and then click Enter
   
8. Click Graph. 
   

Rotate a 3D Graph  

When you view a 3D surface graph, as when you view a 3D object in real life, part of the graph is hidden from view. To see all of the features of the graph, you need to view the graph from different angles. 

To rotate a graph

1. On the Graphing Tools tab, in the Display group, click the axis around which you want to rotate the graph in the Rotate list. 
   
2. Click Counterclockwise or Clockwise. When you rotate a graph by using one of these buttons, the graph continues to rotate until you click the button again.2. Click Counterclockwise or Clockwise. When you rotate a graph by using one of these buttons, the graph continues to rotate until you click the button again.

Note: To rotate a graph in any direction, hold your left-mouse key down, and drag the graph in the direction you want the graph to rotate. To put the graph into motion, hold your left mouse key down, drag the graph and release