NTU Course
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Real Analysis (Ⅱ)

Offered in 112-2Updated

  • Serial Number

    73601

  • Course Number

    MATH7202

  • Course Identifier

    221 U2880

  • No Class

  • 3 Credits

  • Compulsory / Elective

    GRADUATE INSTITUTE OF MATHEMATICS / Institute of Applied Mathematical Sciences

      Compulsory

    • GRADUATE INSTITUTE OF MATHEMATICS

      • Elective

    • Institute of Applied Mathematical Sciences

  • I-Kun Chen

  • Mon 3, 4 / Wed 3, 4

  • 天數302

  • Type 3

  • 40 Student Quota

    NTU 30 + non-NTU 10

  • No Specialization Program

  • Chinese
  • NTU COOL
  • Core Capabilities and Curriculum Planning
  • Notes

  • NTU Enrollment Status

    Enrolled
    0/30
    Other Depts
    0/0
    Remaining
    0
    Registered
    0
  • Course Description
    1. Differentiation : Hardy-Littlewood maximal function, Lebesgue differentiation theorem, functions of bounded variation, absolutely continuous functions, differentiability of functions 2.Elements of Functional Analysis: Baire Category Theorem and its consequences, open mapping theorem and closed graph theorem, separation principles and Hahn-Banach theorem, Hilbert spaces, Banach spaces, dual spaces 3. L^p spaces 4. Signed Measures: absolute continuity, Radon-Nikodym Theorem 5. Fourier Transform 6. Hausdorff Measure and Fractals
  • Course Objective
    This course aims at introducing basic theory and techniques of modern analysis.
  • Course Requirement
    Course prerequisite: Introduction to Mathematical Analysis I, II; Real Analysis I
  • Expected weekly study hours after class
  • Office Hour
  • Designated Reading
  • References
    [1] Elias M. Stein and Rami Shakarchi, Real Analysis [2] Richard Wheeden and Antoni Zygmund, Measure and Integral: An Introduction to Real Analysis [3] Elliott H. Leib and Michael Loss, Analysis
  • Grading
  • Adjustment methods for students
  • Course Schedule