Extend the concept of limits from sequences to functions. Master the ε-δ definition, understand continuity in depth, and prove fundamental theorems that form the backbone of calculus and real analysis.
Master the precise ε-δ definition of function limits, Heine's theorem, one-sided limits, limits at infinity, and infinite limits
Prove uniqueness, local boundedness, sign preservation, and master arithmetic operations, squeeze theorem, and Cauchy criterion
Understand point and interval continuity, classify discontinuities, analyze elementary functions, and operations on continuous functions
Master the Intermediate Value Theorem, Extreme Value Theorem, Boundedness Theorem, and uniform continuity on closed intervals
Rigorous limit and continuity definitions
ε-δ formalization, uniform continuity
Sequential characterization of limits
Intermediate Value Theorem