Math 424 - Fundamental Concepts of Analysis I

See UW General Catalog for course description and prerequisite information.


  • Advanced Calculus (Second Edition) by Patrick M. Fitzpatrick
  • Principles of Mathematical Analysis (Third Edition) by Walter Rudin

Suggested Syllabus


  • epsilon-delta definition and sequence definition of continuity
  • epsilon-delta and sequence definitions of a limit
  • pointwise convergence, uniform convergence, uniformly Cauchy sequences
  • uniform limits and continuity


  • definition of the derivative
  • tangent line approximation
  • algebra of derivatives and the chain rule
  • Rolle’s Theorem and the Mean Value Theorem
  • higher derivatives and Taylor’s Theorem
  • Intermediate Value Theorem for derivatives

The Riemann-Stieltjes Integral

  • definition of the Riemann-Stieltjes integral
  • integrability of continuous and monotone functions
  • properties of the integral
  • change of variables
  • Fundamental Theorem of Calculus
  • integration by parts
  • Mean Value Theorem for Riemann integrals

Uniform Convergence and Power Series

  • uniform convergence and integration
  • uniform convergence and differentiation
  • Weierstrass M-test
  • power series and radius of convergence
  • differentiation of power series
  • Weierstrass Approximation Theorem

Instructors Only