Exam 1, Lecture 5

The position of a as a function of time r t t 1 05 cos

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Unformatted text preview: position (t) 2 ar dr dt 2 (r ) 0.5 0.2 sin(2 d dt t) 2 A a (r ) d2 dt 2 2 dr d dt dt Constant = 0 First and second derivatives dr/dt = velocity ES 2 Computing in Engineering 21 Numerical Methods The solution of math problems through the use of iterative techniques. A.k.a… Roots of Equations: Quadratic equation: f(x) = ax2 + bx + c Quadratic formula: Direct approach for solving the roots f(x) = x 2 ax b b 2 4ac 2a + bx + c = 0 Graphical Perspective f(x) THE ROOTS Where the function equals zero x ES 2 Computing in Engineering Numerical Method -Bracketing Methods INITIAL GUESSES f(x) xl xu x The “Bisection” Method Repeated process Keep getting smaller and smaller with sections Calculate 2 positions and find midpoint Then mid point and Xu or Xl Again...again... Open Methods “Newton-Raphson” Derivative of curve f ' ( x) f(x) x1 x0 dy dx f ( x0 ) ( x0 x1 ) f ( x0 ) dy dx Goal is to make this zero X1 f (x ) x0 Use similar triangles x Numerical Methods Looking for exact number The use of an iterative procedure to calculate a numerical solution to a single equation or set...
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