CHEM%20140L%20Session%2009

CHEM%20140L%20Session%2009 - Session 09 Symbolic Math in...

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9-1 Session 09 Symbolic Math in Mathcad Topics In this session the following spreadsheet concepts will be explored: 1. Using Symbolic Math 2. Manipulating Equations Expand Factor Substitute Simplify Collect Partial-Fraction Expansion •F l o a t 3. Symbolic Matrix Math Symbolic Matrix Transpose Symbolic Matrix Inverse Symbolic Matrix Determinant 4. Symbolic Integration 5. Symbolic Differentiation 6. Solving a System of Equations Symbolically
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CHEM 140L Session 9 - Symbolic Math in Mathcad 9-2 Using Symbolic Math To this point in the course, we have seen how Mathcad can perform numerical evaluations of mathematical problems. One of Mathcad’s unique functions is its ability to do symbolic math . Symbolic math is when a mathematical problem is solved in terms of the symbols themselves, rather than the numerical values. Symbolic math is often useful when you want to know how Mathcad obtained a numerical result by seeing the equation solved symbolically. This is a useful tool when debugging a Mathcad worksheet. Symbolic math is also used for generating a general expression that can be used in other numerical calculations. Mathcad can also aid in the simplification of complicated expressions. Mathcad’s symbolic math functions are located in the Symbolics menu and the Symbolic Keyboard toolbar. The Symbolic toolbar functions uses the live symbolic operator ( 6 ). The live symbolic operator automatically recalculates the value of an expression whenever information to the left of or above the operator changes. Symbolic math computed using the Symbolics menu are not live and do not automatically update the results, even if the input data has changed. A symbolic calculation must be updated manually. Let’s consider a simple example to illustrate how symbolic math works. ( ) ( ) xx − ⋅ − = 45 0 Considering the above expression, we see that it has two solutions; x = 4 and x = 5. Let’s see how Mathcad can evaluate this expression symbolically. Since we want to find the values of x that satisfy the equation, click on the equation and select either one of the x variables. Note that the symbolic equality [ Ctrl = ] was used in the equation. To solve for the variable x , use the Solve option from the Variable submenu found under the Symbolics menus.
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CHEM 140L Session 9 - Symbolic Math in Mathcad 9-3 The solutions to the expression are presented in a two element vector. As we can see, Mathcad computed the correct expected final result. The Symbolic Keyboard toolbar can be accessed by clicking on the Symbolic Keyboard button, . Using the proceeding example, we will attempt to find the solutions using the Symbolic Keyboard toolbar. If we enter an incomplete equation, such that we do not use the symbolic equality, Mathcad will set the expression equal to zero. We start by entering the expression and clicking on the [solve] button on the Symbolic Keyboard toolbar.
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CHEM 140L Session 9 - Symbolic Math in Mathcad 9-4 The word “solve” appears after the expression, with an empty placeholder. The placeholder is the place at which the user inputs which variable to solve for.
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This note was uploaded on 04/11/2010 for the course CHEM 1101 taught by Professor Leroy during the Spring '10 term at University of Toronto.

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CHEM%20140L%20Session%2009 - Session 09 Symbolic Math in...

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