Calculus 1

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

Calculus 1

Hours lect+pc	Credits lect+pc	Assessment	Specialization	Course code lect/pc	Semester	Status
2 + 4	2 + 4	exam + term grade	all	mm1c1ka1 mm1c2ka1	1	alternative

Course coordinator

Strong	Weak	Prerequisites
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:

Prerequisites

A thorough understanding of High school mathematics.

Course objectives

Introduce the basic rules of calculus.

Literature

George B. Thomas, Maurice D. Weir, Joel Hass, Frank R. Girodano: Calculus I and III. Pearson Addison Wesley, 2005.

Syllabus

Introduction: functions, graphs, basic logic.
Limit of functions: one sided, inifinite limts, limit at infinity - a graphical approach.
Continuity, Bolzano's theorem. Tangent and derivative, differentiation rules.
Applications: determination of extrema, mean value theorems, monotone functions, convexity, L'Hospital's rule.
Antiderivatives.
Limit of a sequence, sequences of different order.