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.

Last updated April 19, 2018.