Analysis 3

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 3

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
4 + 3	4 + 4	exam + term grade	applied math.	mm1c1an3a mm1c2an3a	3	compulsory

Course coordinator

Strong	Weak	Prerequisites
Practice class
		Strong: Analysis2L (mm1c1an2) or Foundations of analysisL (mm1c1ap2)
		Weak: Algebra2P (mm1c2al2)
Lecture
Lecture		Weak: practice class

Remarks

Syllabus designed by:

Literature

G. B. Thomas - M. D. Weil - J. Hass - F. R. Giordano: Thomas' Calculus. Pearson 2009.
J. E. Marsden- A. J. Tromba: Vector calculus. W. H. Freeman & Co., New York 2003.

Syllabus

Sequences of functions, convergence notions.
Series of functions, convergence notions.
Power series, Taylor series.
Functions in several variables, coordinates, topological notions.
Limit and continuity in several variables.
Differentiation in several variables, Taylor formula.
Extreme values, implicit functions.
Vector fields and operators, intergration by paths.
Integration in several variables, applications.