Sets and Functions: – Mathematical Induction – Finite and Infinite Sets – The Algebraic and Order Properties of – Absolute Value and Real Line – The Completeness Property of – Applications of the Supremum Property – Applications of the Supremum Property, Intervals.
Sequence: Sequence and Series: Sequences and their Limits – Limits Theorems – Monotone sequences – Subsequences and Balzano – Weierstrass Theorem. The Cauchy criterion – Properly divergence sequences.
Series: Introduction to series – Absolute Convergence – Tests for Absolute Convergence – Limit Comparison Test, Root Test, Ratio test, Integral Test, Raabe’s Test – Tests for Non absolute Convergence – Alternating Series Test, Dirichlet and Abel Test.
Limits of Functions: – Limit Theorem – Some Extensions of the Limit Concept.
Continuous Functions: – Continuous Functions – Combinations of Continuous Functions –Continuous Functions on Intervals – Uniform Continuity – Continuity and Gauges – Monotone and Inverse Functions.