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Analysis 3,4

2014/2015

Lecturer
Prof. Boris Tsirelson (School of Mathematical Sciences).
Instructors
Adi Glücksam
Yonatan Shelah
Prerequisites
Analysis 2; Linear algebra 2a
Grading policy
First semester exam (01.02; 03.03)
Final exam (01.07; 08.09)

LECTURE NOTES

Preliminaries

  1. Conventions, notation, terminology etc.
  2. Euclidean space Rn.
  3. Basics of differentiation.

Differentiation

  1. Open mappings and constrained optimization.
  2. Inverse function theorem.
  3. Implicit function theorem.

Integration

  1. Basics of integration.
  2. Iterated integral.
  3. A glimpse into Lebesgue's theory.
  4. Change of variables.
  5. Improper integral.

Manifolds and differential forms

  1. From path functions to differential forms.
  2. Manifolds in Rn.
  3. Integration, from local to global.
  4. Divergence, flux, Laplacian.
  5. From boundary to exterior derivative.
  6. Stokes' theorem.

Summary

TEXTBOOKS

ADDITIONAL LITERATURE

Solutions to selected exercises

EXAMS (in Hebrew)

A quote:

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".