Module-4

 

1. Bounded sets,

2. infinum,

3. supremum,

4. order completeness,

5. neighbourhood,

6. interior,

7. open sets,

8. closed sets,

9. limit points,

10. Bolzano Weierstrass Theorem,

11. closed sets,

12. dense sets,

13. countable sets,

14. uncountable sets.

15. Sequences –

16. convergence and divergence of sequences,

17. monotonic sequences,

18. subsequences.

19. Series –

20. Convergence and divergence of series,

21. absolute convergence,

22. Canchy’s general principle of convergence of series.

23. The series ∑1/n p .

24. Tests for convergence of series –

25. comparison test,

26. root test,

27. ratio test.

28. Continuity and uniform

29. continuity,

30. Riemann integrals,

31. properties,

32. integrability.

33. Complex numbers,

34. modulus,

35. conjugates,

36. polar form,

37. n th roots of complex numbers.

38. Functions of complex variables –

39. Elementary functions of complex variables,

40. Analytic functions.

41. Taylor series,

42. Laurent’s Series.