Math 302, Spring 2000

Course Information:

• Instructor: Rhonda Hughes
  
• Text: Kenneth A. Ross, Elementary Analysis: The Theory of Calculus; additional references will be on reserve in Collier.

  Topics:

  1. Review of Series: Chapter II, Sections 14 and 15. Convergence, Comparison Test, Cauchy criterion, absolutely convergent series, p-series, Ratio, Root, Alternating Series and Integral Tests.
  2. Sequences and Series of Functions: Chapter IV, Sections 23 - 27. Power Series, uniform convergence, Weierstrass M-test, differentiation and integration of series, Weierstrass Approximation Theorem.
  3. Differentiation and Integration: Chapter V, Sections 28, 29, 31 and Chapter VI, Sections 32-34. The Mean Value Theorem, Taylor Series, the Riemann Integral and its properties.
  4. Additional Topics selected from the following: Fourier Analysis, Inner product and Hilbert spaces, Cauchy-Schwarz inequality, orthonormal bases, Fourier series, mean square convergence, applications to PDE's, wavelets.