1. MTH 324
Lecture # 18
Complex Integration

2. Previous Lecture’s Review
Definite Integrals
Line Integrals

3. Lecture’s Outline
Contours
Complex integrals
ML-inequality 3

4. Parametrization of a curve
Remark

6. Contours:
Smooth curve:
Piecewise smooth curve:

7. Simple curve:
Simple closed curve:
Contour: 7

9. Orientation on a curve:9

11. Remark:

12. Complex integral:
Remark: 12

14. Evaluation of contour integral:
Example: 14

15. Solution:

17. Example:
Solution:

19. Example:
Solution:

21. 21

22. Properties of contour integral:

23. Theorem:
Proof: 23

25. Example:
Solution: 25

27. Example:
Solution: 27

28. References
A First Course in Complex Analysis with Applications by Dennis G. Zill and Patrick D. Shanahan.
Complex variables and applications by James Brown and Ruel Churchill