Analysis 2

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 2

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
3 + 3	3 + 4	exam + term grade	all	mm1c1an2 mm1c2an2	2	alternative

Course coordinator

Strong	Weak	Prerequisites
Practice class
Practice class		Strong: Analysis1L (mm1c1an1)
Lecture
Lecture		Weak: practice class

Remarks

You have to take exactly one of the following two equivalent sets of courses: {Analysis 1, Analysis 2} or {Calculus 1, Calculus 2, Foundations of analysis}.

Syllabus designed by:

Syllabus

Differentiability, the rules of differentiation. The derivative of elementary functions. Higher derivatives. Connection with monotonicity and convexity.
Mean value theorems.
The Taylor formula. L'Hospital's rule.
Primitive functions. Integration by parts. Integration by substitution. Integration of rational functions.
The Riemann integral. The Newton-Leibniz formula. Conditions for integrability. Applications.
Improper integrals. Conditions for the convergence of improper integrals.
Infinite series. Convergence and absolute convergence. Convergence tests.