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• 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