Convergence, completeness, completion of real numbers
Course Material
- Number Systems: Ordered fields
- rational, real and complex numbers
- Archimedean property
- supremum, infimum and completeness
- Convergence, completeness, completion of real numbers
- open sets, closed sets, compact sets,
- Heine Borel theorem, connected sets.
- Sequences and Series of Real Numbers
- Limits of sequences, algebra of limits.
- Bolzano Weierstrass theorem, Cauchy sequences, liminf, limsup
- Limits of series, convergences tests, absolute and conditional convergence, power series
- Continuity: Functions, continuity and compactness, existence of minimizers and maximizers
- uniform continuity, continuity and connectedness, intermediate mean value theorem
- Monotone functions and discontinuities.
- Differentiation: Mean value theorem, L’Hopital’s Rule, Taylor’s theorem
- Chapters 15
- Department Mathematics
- Teacher
Dr. Muhammad Samraiz
