Math 327 Uw |best| Access

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| Week | Topics | |------|--------| | 1 | – Quantifiers, negation, basic set operations, functions, injectivity/surjectivity. | | 2 | The Real Numbers – Axioms of an ordered field, completeness axiom, supremum/infimum, Archimedean property. | | 3 | Sequences I – Definition of convergence, epsilon-N proofs, uniqueness of limits, boundedness. | | 4 | Sequences II – Monotone Convergence Theorem, subsequences, Bolzano-Weierstrass Theorem. | | 5 | Cauchy Sequences – Definition, Cauchy Criterion for convergence, completeness of R. | | 6 | Limits of Functions – Epsilon-delta definition, sequential criterion for limits, limit laws. | | 7 | Continuity – Definition, combinations of continuous functions, continuity on intervals (Intermediate Value Theorem). | | 8 | More Continuity – Extreme Value Theorem, uniform continuity (introduction). | | 9 | Differentiation – Definition of derivative, derivative rules, Carathéodory’s formulation (sometimes). | | 10 | Mean Value Theorem & Applications – Rolle’s theorem, MVT, Cauchy MVT, L’Hôpital’s rule, Taylor’s theorem with remainder. | math 327 uw