MATH 6360 - Fall 2018
Applied Analysis

    Course Info. View syllabus.
      Week 1. Review of metric spaces, completeness, characterization of compactness, extreme value theorem. Contraction mappings and fixed points.
        Homework Set 1 (Solutions), due Friday, August 31.
          Week 2. Applications of contractions mappings: integral equations, solutions to initial value problems. Local existence and uniqueness of solutions, stability.
            Homework Set 2 (Solutions), due Friday, September 7.
              Week 3. The contraction mapping theorem in multivariate calculus.
                Homework Set 3 (Solutions), due Friday, September 14.
                  Week 4. The inverse and implicit function theorems.
                    Homework Set 4 (Solutions), due Friday, September 21.
                      Week 5. Towards Lp spaces. Exam 1, Sep. 28. To see whether you are prepared, take a practice run (Solutions).
                        Week 6. Extending the Riemann integral to Lp spaces. Banach spaces.
                          Homework Set 5 (Solutions), due Friday, October 5.
                            Week 6. Dual spaces. Uniform boundedness
                              Homework Set 6 (Solutions), due Friday, October 19.
                                Week 6. Consequences of uniform boundedness for Fourier series and polynomial interpolation.
                                  Homework Set 7 (Solutions), due Friday, October 26.
                                    Weeks 7 and 8. Uniform convexity, best approximation propert and duality for Lp-spaces. Bounded inverse, closed graph theorem.
                                      Homework Set 8 (Solutions), due Friday, November 9.
                                        Week 9. Hilbert spaces. Exam 2, Nov 16. To see whether you are prepared, take a practice run (Solutions).