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MATH328

MATH 328 - Real Analysis II

Suggested Syllabus

Course description and prerequisite informationsee UW General Catalog
Text: Varies by instructor.

Limits and continuity of functions, sequences, series tests, absolute convergence, uniform convergence.  Power series, improper integrals, uniform continuity, fundamental theorems on continuous functions, theory of Riemann integrals.

  • Functions
    • review of limits, continuity
    • extreme and intermediate value theorems
    • uniform continuity
    • sequences of functions, uniform convergence
  • Derivatives
    • definition of the derivative and derivative rules
    • mean value theorem
    •  L'Hopital's rule
  • Integrals
    • Riemann integrals
    • basic properties (linearity, order preservation, interval additivity)
    • fundamental theorem
    • definition of ln \$ x\$, the exponential function
    • improper integrals
  • Power Series
    • series of functions, uniform convergence
    • radius and interval of convergence
    • differentiation and integration
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