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Analysis 3

Semester 2, 2015/2016

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

  1. Equations, from linear to nonlinear.
  2. Applications.

Integration

  1. Basics of integration.
  2. Iterated integral.
  3. Lebesgue's criterion for Riemann integrability.
  4. Linear change of variables.
  5. Nonlinear change of variables.
  6. Improper integral.

Summary

TEXTBOOKS

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

EXAMS (in Hebrew)

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 (?) - ...