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Solutions to the take-home and in-class parts of a mat420 final exam, focusing on integration, residues, complex analysis, and laurent series. Students can use this document to check their answers and understand the concepts covered in the exam.
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MAT420 Final: Take Home Part Due December 11, 2007 Prof. Thistleton
Please write all answers in the space provided.
∫ (^2) π
0
5 cos^2 (θ) + 4
dθ
∫ (^2) π
0
cos(2θ) 13 − 12 cos(θ)
dθ
∫
C+ 2 (0)
sin(z) z^2 + 1
dz
∫
C+ 1 (0)
z sin^2 (z)
dz
Res
[ sin(z) z^2 + 1
, i
]
Res
[ 1 z sin(z)
]
MAT420 Final: In Class Part December 11, 2007, 3:00-5:00 p.m. Prof. Thistleton
Please write all answers in the space provided.
C
z^3 dz
∫
C
z
dz
∫
C
z
dz