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lec18_roots

# lec18_roots - Applications of root finding Graphical and...

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University of Mississippi Dept. of Physics and Astronomy Phys 503, Dr. Gladden Applications of root finding Graphical and brute force methods Bisection method Newton-Ralphson Method Projects and HW07 due today! Reading for root finding on handout.

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University of Mississippi Dept. of Physics and Astronomy Phys 503, Dr. Gladden Finding a root of an equation means determining a value for the independent variable for which the function is 0. Simple example: quadratic equation (2 roots) In general, for an Nth order polynomial, there will be N roots. f ( x n ) = 0 where x n is the nth root of f ( x ) x n = b ± b 2 4 ac 2 a f ( x ) = ax 2 + bx + c
University of Mississippi Dept. of Physics and Astronomy Phys 503, Dr. Gladden Roots are the solutions to the polynomial equation Solving optimization problems – taking derivatives of functions and setting them equal to 0. Questions like: Given the forces on a rocket, at what point in space does the drag force equal the thrust.

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