ch18sc1skeleton

# ch18sc1skeleton - 2 Evaluate where is defined by 3 2 2 2 C...

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1 Section 18.1 Contour Integrals Section _______________ ( ) ( ) Parametric Curve , x f t y g t = = Orientation of the curve Let’s go back to: Math 241 – Rimmer ( ) ( ) ( ) : parametric curve in the complex plane defined by , , real C x x t y y t a t b t = = ≤ ≤ ( ) ( ) ( ) Now let , define z t x t iy t a t b C = + ≤ ≤ If is piecewise smooth, we will now call it a ________. C ( ) An integral of on is called a ______________. f z C If is simple and closed we use C To reinforce the positive orientation we use The general symbol is ( ) To evaluate the countour integral In the formula for replace by then f z z dz = ( ) for continuous and smooth C f z dz f C = Math 241 – Rimmer 18.1 Contour Integrals

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Unformatted text preview: 2 Evaluate where is defined by 3 2 , 2 2 C z dz C z t t it t = +- ā¤ ā¤ ā« Math 241 ā Rimmer 18.1 Contour Integrals ( ) ( ) ( ) 2 so f z z f z t = = = = = ( ) 3 2 z t t it = + ā ( ) dz z t dt ā² = ā ( ) z t ā² = dz = ( ) ( ) ( ) 2 2 2 C z dz f z t z t dt-ā² = = ā« ā« = = = = = = Math 241 ā Rimmer 18.1 Contour Integrals 2 2 Evaluate where is left half of the ellipse 1 36 4 from 2 to 2 C x y dz C z i z i + = = = -ā« 2 2 We need to parametrize : 1 36 4 x y C + = x y = = t ā¤ ā¤ ( ) z t = ( ) z t ā² = ( ) dz z t dt ā² = = C dz = ā« = = = = Orientation:...
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ch18sc1skeleton - 2 Evaluate where is defined by 3 2 2 2 C...

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