Lecturer

Prof. Boris Tsirelson (School of Mathematical Sciences).

Instructor

Daniel Rosen.

Prerequisites

Analysis 3.

Grading policy

The final exam (24.01; 18.03).

LECTURE NOTES

0. Preliminaries.
1. From path functions to differential forms.
2. Manifolds in Rⁿ.
3. Integral of derivative.
4. Divergence theorem and its consequences.
5. Pushforward, pullback and change of variables.
6. Stokes' theorem.

Summary

• Sections 1-6.

TEXTBOOKS

• Jerry SHURMAN, "Multivariable calculus". (Online only, not printed.)
• Reyer SJAMAAR, "Manifolds and differential forms lecture notes". (Online only, not printed.)

ADDITIONAL LITERATURE

• Theodore SHIFRIN, "Multivariable mathematics" (2005 Wiley).
• John H. HUBBARD, Barbara Burke HUBBARD, "Vector calculus, linear algebra, and differential forms" (2002 Prentice).
• Vladimir A. ZORICH, "Mathematical analysis II" (2004 Springer). (Our library has 8 copies.)
• Wendell FLEMING, "Functions of several variables" (1977 Springer). (Our library has 3 copies.)
• (History, if you like) Hans Samelson, "Differential Forms, the Early Days; or the Stories of Deahna's Theorem and of Volterra's Theorem", The American Mathematical Monthly, Vol. 108, No. 6 (Jun. - Jul., 2001), pp. 522-530.

Solutions to selected exercises

• 2b24, 2c33.

EXAMS (in Hebrew)

• 2016, sample
• 24.01.2016; see also typical errors, comments etc.
• 18.03.2016; see also typical errors, comments etc.