CHEM%20140L%20Session%2008

CHEM%20140L%20Session%2008 - Session 08 Solving Equations...

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8-1 Session 08 Solving Equations in Mathcad Topics In this session the following spreadsheet concepts will be explored: 1. Iterative Solutions The root() function The polyroots() function 2. Solving Simultaneous Linear Equations Solving Linear Equations by Matrices Solving Linear Equations using lsolve() 3. Given-Find Method for Solving Equations 4. What To Do When Mathcad's Solver Fails 5. X-Y Trace The theory behind solving equations in Mathcad is similar to that of the procedures employed in Excel. Students are encouraged to review Session 04 of this manual.
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CHEM 140L Session 8 - Solving Equations in Mathcad 8-2 Iterative Methods Scientific calculations often involve equations or a system of equations that cannot be solved directly. Mathcad provides an iterative solver to solve equations of this type. = The root() Function The root() function is a Mathcad function that is used to find a single solution to a single equation. The root() is an iterative solver, so an initial guess is required. Let’s try to find the solution to the equation fx x e x () =− 3 We will only be concerned with determining the real roots, and not the complex roots, of this equation, that is, we shall seek those values of x which satisfy the condition f ( x ) = 0. Because this is a cubic equation, we may assume there will be more than one root. It is not immediately clear how many roots are real and how many are imaginary. In general, before finding the roots of any equation, we should get an idea what the function “looks like”, by plotting the function.
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CHEM 140L Session 8 - Solving Equations in Mathcad 8-3 From the plot, we see there are at least 2 real roots, x - 1.5 and x - 4.5. To determine the first root, we would define an initial guess close to the anticipated value. The Mathcad worksheet would be setup as follows: We find the first root has a value of x = 1.857. To find the second root, let’s try an initial guess value of x = 4. As we can see, the second root is located at x = 4.536. If you want to confirm these are the only two real roots to the equation, try using initial guesses further from the solutions obtained. For example, let’s try using the initial guesses x = -10 and x = 10. Using the alternative initial guess, we see that we obtain the same values for the roots of the equation. If we substitute the computed solution back into the original function, we find the result is not exactly zero, but it is very close to zero.
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CHEM 140L Session 8 - Solving Equations in Mathcad 8-4 = The polyroots() Function For finding the roots of a polynomial function, the Mathcad function polyroots() is a function that will find all the roots simultaneously. To use the polyroot() function, the polynomial coefficients must be written as a column vector, starting with the constant.
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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- Toronto.

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CHEM%20140L%20Session%2008 - Session 08 Solving Equations...

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