1. COMPLEX
ANALYSISS4 CE & EEE
B TECH
KERALA UNIVERSITY
PREPARED BY
ANOOP T
ASST PROFESSOR
DEPT OF MATHEMATICS
HEERA COLLEGE OF ENGINEERING AND TECHNOLOGY
THIRUVANANTHAPURAM

2. Complex Number


3. Representation


4. Complex function


5. Limit of a complex function


6. 

7. Continuity of a complex function


9. Differentiable complex function


10. C-R Equations


11. Analytic Function


12. Analytic Function
(Sufficient Condition)

13. Note


14. Note
Entire function:- analytic in the
entire complex plane
Singularity:- the point at which the
function fails to be analytic

15. Harmonic Function


16. Harmonic Conjugate


17. How to find Harmonic Conjugate


18. Milne-Thompson Method


19. Results

20. Results


21. Cauchy’s Theorem


22. Note:


23. Converse of Cauchy’s Theorem


24. Cauchy’s Integral Formulae


25. Cauchy’s Integral Formulae


26. Taylor’s Series & Laurent’s Series


27. Note:


28. Laurent’s Series


30. Maclaurin’s Series


31. Singularities
Singularity
Removable
Pole
Essential

32. Residue


33. Residue at a simple pole


34. Residue at a pole of order m


35. Residue


36. Residue theorem

37. Improper integrals


38. Improper integrals

-R
R
|z|=1

39. 
Improper integrals