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Section 4.2 Contour Integrals

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1 Section 4.2 Contour Integrals
MAT 3730 Complex Variables Section 4.2 Contour Integrals

2 Preview Introduce the line and contour integrals
Two type of integrals:

3 How should we define …

4 Recall

5 Integral Along a Direct Smooth Curve

6 Time Constraints Because of the time constraints, we have to skip some details. In particular, we are not going to define every term rigorously.

7 Properties

8 Special Case

9 Antiderivative

10 Theorem

11 Example 1

12 Formula We may as well use the formula

13 Example 1

14 Example 1

15 Theorem

16 Remark The formula is independent of the parametrization.

17 Contour Integrals

18 Properties

19 Example 2

20 Example 3

21 Standard Formula

22 Remarks The formula is independent of the center and the radius of the circle.

23 Example 3

24 Theorem

25 Next Class Read Section 4.3?

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