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class_notes18 - Engineering 3 Class 18 Today: solving...

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Engineering 3 – Class 18 Today: • solving transcendental equations • finding areas under curves Final: Sept. 13 (Wednesday), in class
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Transcendental Equations Transcendental equations: Equations which cannot be solved exactly, require a numerical solution. –E x am p l e s : Solutions to these equations are not exact 2 cos( ) e tan( ) 2 sin( ) 4 3 x x xx x x ⎛⎞ ⎜⎟ ⎝⎠ = =− +
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Procedure for determining numerical solutions for x : 1. Plot the left-hand side vs. x and the right-hand side vs. x . This will help you determine approximately where your solution(s) will be and how many solutions you have. Alternatively, you could bring all terms over to one side, plot that side vs. x , and see where the plot crosses the origin. 2. If you haven’t already done so, bring all terms over to one side so that your equation is of the form f ( x ) = 0. 3. Determine the number of solutions for x , the range(s) of values you want to try for x ( xmin and xmax ), and the interval intv for x . The interval determines how accurate an answer you should expect (minimum accuracy of answer is approximately intv /2). 4. Write a for loop for each solution to try out all values of x in your range and determine the value xfin such that | f ( xfin ) | is closest to zero. 5. Print xfin – this is your answer.
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Solve for x in the following equation: 21 2 xx += −
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• First, plot left-hand side (LHS) and right-hand side (RHS) versus x.
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This note was uploaded on 08/06/2010 for the course ENGR 3 taught by Professor Ben-yaakov during the Summer '08 term at UCSB.

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class_notes18 - Engineering 3 Class 18 Today: solving...

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