Lecturer

Prof. Boris Tsirelson (School of Mathematical Sciences).

Instructor

Rafael Sherbu Cohen.

Prerequisites

Analysis 2; Linear algebra 2a.

Grading policy

The final exam (21.06; 05.08).

LECTURE NOTES

Preliminaries

1. Preliminaries.

Differentiation

2. Equations, from linear to nonlinear.
• What is the Implicit Function Theorem good for? (A discussion on Mathoverflow).
3. Applications.

Integration

4. Basics of integration.
5. Iterated integral.
6. Lebesgue's criterion for Riemann integrability.
7. Linear change of variables.
8. Nonlinear change of variables.
9. Improper integral.
• Appendix: Monotone convergence for Riemann integral (if you are interested).

Summary

• Summary.

TEXTBOOKS

For "Differentiation": Courant, Fleming, Hubbard, Lang, Shifrin, Shurman, Zorich I,II.
For "Integration": Burkill, Hubbard, Lang, Shifrin, Shurman, Zorich II.

• J.C. BURKILL, H. BURKILL, "A second course in mathematical analysis" (1970 Cambridge).
• Richard COURANT, Fritz JOHN, "Introduction to calculus and analysis", vol. 2 (1989 Springer). (Our library has 8 copies.)
• Wendell FLEMING, "Functions of several variables" (1977 Springer). (Our library has 2 copies.)
• John H. HUBBARD, Barbara Burke HUBBARD, "Vector calculus, linear algebra, and differential forms" (2002 Prentice).
• Serge LANG, "Undergraduate analysis" (1997 Springer).
• Theodore SHIFRIN, "Multivariable mathematics" (2005 Wiley).
• Jerry SHURMAN, "Multivariable calculus". (Online only, not printed.)
• Vladimir A. ZORICH, "Mathematical analysis I" (2004 Springer). (Our library has 8 copies.)
• Vladimir A. ZORICH, "Mathematical analysis II" (2004 Springer). (Our library has 8 copies.)

EXAMS (in Hebrew)

• 2016, sample
• 21.06.2016; see also some solutions and typical errors, comments etc.
• 05.08.2016; see also some solutions and typical errors, comments etc.

Two quotes:

The world is not one-dimensional, and calculus doesn't stop with a single independent variable.

James Nearing, Chapter 8 "Multivariable Calculus" of the course "Mathematical Tools for Physics ".

There is nothing more practical than a good theory.

Immanuel Kant 1793 (?) - Gustav Kirchhoff (?) - Ludwig Boltzmann (?) - ...