Analysis 4

Mathematics BSc
Course description
2013.

Eötvös Loránd University
Faculty of Science
Institute of Mathematics

Borromean Rings

All courses
Core courses
- Algebra, number theory
- Analysis
- Geometry
  - Geometry 1
- Discrete mathematics
  - Discrete mathematics 1
  - Discrete mathematics 2
- Elementary mathematics
  - Elementary mathematics 1
- Informatics
  - Prog. fundamentals
Pure mathematics
- Algebra, number theory
- Analysis
  - Analysis 3
  - Analysis 4
  - Applied analysis
    - Numerical analysis
    - Appl. anal. comp.
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Topology
    - Introduction
    - Algebraic topology
  - Complex analysis
  - Functional analysis
  - Function series
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Informatics
- Computer science
- Foundations of math.
  - Set theory
  - Mathematical logic
Applied mathematics
- Analysis
  - Analysis 3
  - Analysis 4
  - Analysis 5
  - Applied analysis
  - Differential equations
    - Differential equations
    - Partial diff. equations
  - Complex analysis
  - Functional analysis
- Geometry
- Operations research
  - Operations research 1
  - Operations research 2
- Probability theory
- Applied modules
- Informatics
- Algorithms
- Algebra
- Elementary mathematics
  - Elementary mathematics 2
  - Elementary mathematics 3
- Foundations of math.
BSc: general information
Studies

Analysis 4

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
4 + 2	4 + 3	exam + term grade	pure math.	mm1c1an4m mm1c2an4m	4	compulsory

Course coordinator

Géza Kós
Department of Analysis
Institute of Mathematics

Strong	Weak	Prerequisites
Practice class
Practice class		Strong: Analysis3L-p (mm1c1an3m)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

Syllabus

Line integrals. The length of a curve. The Newton-Leibniz formula. Connection with the existence of the primitive function. Divergence and rotation. Integral theorems.
Measure theory. Convergence almost everywhere. The Egoroff theorem. The Lusin theorem. The Lebesgue integral. Signed measure. The total variation. Hahn's theorem. The Radon-Nikodym theorem. The product of measure spaces. The Fubini theorem. Absolutely continuous functions. L_p classes. The convolution.