MATH 412: Real Analysis II


  • MATH 412. Real Analysis II

    Contents:

    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).

    Textbook:

    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.

    HW 7: Do problems 1-5 on p. 396.

    There will be a quiz on Thursday, March 1.

    Midterm Exam on Tuesday, March 4.

    HW 8: Do problems 1-5 on pp. 400-401.

    HW 9: Do problems 1-5 on p. 413.

    There will be a quiz on Thursday, April 5.

    HW 10: Do problems 1-5 on p. 420.

    HW 11: Do problems 1-6 on p. 454 and 1-6 on pp. 456-457.

    HW 12: Do problems 1-4 on p. 459.

    HW 13: Do problems 1-5 on p. 466.

    There will be a quiz on Thursday, April 19.

    HW 14: Do problems 1-5 on p. 508.

    HW 15: Do problems 1-5 on p. 551.


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    Last updated April 19, 2018.