Continuity: Functions, continuity and compactness
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Course Material
- Number Systems: Ordered fields, rational, real and complex numbers
- Archimedean property, supremum, infimum and completeness
- Topology of real numbers: Convergence, completeness, open sets, Closed sets, compact sets
- Heine Borel theorem, connected sets
- Sequences and Series of Real Numbers, Limits of sequences, algebra of limits
- 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
- Uniform continuity, continuity and connectedness
- Monotone functions and discontinuities
- Differentiation: Definition examples
- Intermediate mean value theorem and Applications
- Existence of minimizers and maximizers
- Mean value theorem and Applications
- L’Hopital’s Rule, Taylor’s theorem
- Chapters 16
- Department Mathematics
- Teacher
Dr. Muhammad Samraiz
