• Functional Analysis
    • Department of Mathematics
    • Credit. 4
    • MA308
    • Enroll
    • Spring , 2015
    • 4134
    • Course Description:
    • ( Exchange Programme )
    • Functional Analysis is the core course for the modern analysis. It is about the analysis on infinitely dimensional linear spaces. It is natural continuation for both mathematical analysis and linear algebra. Functional analysis plays an important role in the study for the partial differential equations and mathematical foundation for quantum mechanics.
    • Course Syllabus:
    • After completing the course, students should:
      1.Understand the basic concepts of functional analysis
      2.Learn how to illustrate the abstract notions in functional analysis via examples
      3.Learn how to solve the problems appear in PDEs via the powerful tools from functional analysis
      4.get a solid training for advanced courses on modern analysis
    • Schedule:
    • Topics/ Credit hours / Teaching methodology / Tasks / Intended learning outcomes / Assessment methods

      1.Metric spaces/6 Credit hours /
      2.Linear Spaces/2 Credit hours /
      3.Linear Maps/4 Credit hours /
      4.Hahn-Banach Theorem/4 Credit hours /
      5.Applications of Hahn-Banach Theorem/2 Credit hours /
      6.Normed Linear Spaces/4 Credit hours /
      7.Hilbert Spaces/4 Credit hours /
      8.Applications of Hilbert Spaces/2 Credit hours /
      9.Duals of Normed Linear Spaces/4 Credit hours /
      10.Weak convergence/4 Credit hours /
      11.Weak and weak* topology/2 Credit hours /
      12.Bounded Linear Maps/4 Credit hours /
      13.Examples of Bounded Linear Maps/4 Credit hours /
      14.Elementary Spectral theory/4 Credit hours /
      15.Examples of operators and their spectra/2 Credit hours /
      16.Compact maps/4 Credit hours /
      Two midterms, one review class, one final exam, one homework for every two weeks
  • Reading list
  • Other Materials
  • Discussion
  • Homework download/submit
    • Li Congming
    • Read more
    • Male
    • E-mail:
    • congming.li@sjtu.edu.cn
    • Profile
  • Prerequisite Course:

    Mathematical Analysis, Linear Algebra

  • Textbooks:

    Functional Analysis, Peter Lax, Higher Education Press; Notes on Functional Analysis by John Hunter
  • Grading:

    20%/Homework 20%
    30%/two midterm exams
    50%/final exam
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