MATH 412: Real Analysis II

  • MATH 412. Real Analysis II


    Differentiable Mappings, Taylor's Formula, Local Invertibility, Implicit Function Theorem, Morse's Lemma, Differentiable Manifolds, Lagrange Multipliers, Integration Theory, Fubini's Theorem, Change of Variables Formula, Elements of Fourier Analysis.

    Particulars: Primary emphasis will be placed on conceptual developments and proofs.

    Prerequisite: Math 411 (Real Analysis I).


    J. E. Marsden and M. J. Hoffmann, Elementary Classical Analysis (Second Edition), W. H. Freeman, San Francisco, 1993.

    Click here for the syllabus.

    HW 1: Do problems 2, 4, 5 on p. 330; 3, 4, 5 on p. 334.

    HW 2: Do problems 1-5 on p. 344.

    HW 3: Do problems 1-5 on pp. 348-349.

    There will be a quiz on Thursday, February 1st.

    HW 4: Do problems 1-4 on p. 352, and 4-5 p. 355.

    There will be a quiz on Tuesday, February 13.

    HW 5: Do problems 5-6 on p. 362.

    HW 6: Do problems 1-6 on p. 367.

    There will be a quiz on Thursday, February 22.

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    Last updated January 30, 2018.