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Mathematical Analysis

General data

Course ID: 103A-CTxxx-ISA-EMANA Erasmus code / ISCED: (unknown) / (unknown)
Course title: Mathematical Analysis Name in Polish: Mathematical Analysis
Department: The Faculty of Electronics and Information Technology
Course groups: ( Courses in English )--eng.-EITI
( Mathematics )--B.Sc.-EITI
( Technical Courses )---EITI
( Technical Courses )--eng.-EITI
ECTS credit allocation (and other scores): 6.00
Language: English
(in Polish) Jednostka decyzyjna:

(in Polish) 103000 - Wydział Elektroniki i Technik Informacyjnych

(in Polish) Kod wydziałowy:

(in Polish) EMANA

(in Polish) Numer wersji:

(in Polish) 1

Short description:

Topics include: Infinite series: convergence and divergence, tests for convergence of series. Power series: radius and domain of convergence. Taylor Expansion Theorem, expansions of basic functions. Integral calculus: indefinite and definite integrals, basic theorems and techniques of integration, applications of integration. Multivariables calculus; limits and continuity, partial and directional derivatives, tangent planes, extremal points. Multiple integrals.

Full description:

Topics include: Infinite series: convergence and divergence, tests for convergence of series. Power series: radius and domain of convergence. Taylor Expansion Theorem, expansions of basic functions. Integral calculus: indefinite and definite integrals, basic theorems and techniques of integration, applications of integration. Multivariables calculus; limits and continuity, partial and directional derivatives, tangent planes, extremal points. Multiple integrals.

Lecture contents

  1. Infinite series (2): convergence and divergence. Absolute and
    conditional convergence. Geometric and harmonic series. Tests of
    convergence of series

  2. Power series (2): radius and domain of convergence.

  3. Taylor Expansion Theorem (2). Taylor and Maclaurine series.
    Expansions of basic functions

  4. Indefinite integrals (2): techniques for evaluations of
    integrals. Integrations by parts and substitution. Integrations
    of rational functions. Some integrals involving trigonometric and
    irrational functions.

  5. Definite integrals (2): basic properties. Definite integrals as
    limits of Riemann sums.

  6. Applications of integrals (2): finding the area of a region, the
    volume of a solid of revolution, the length of a curve.

  7. Improper integrals (2): definitions and applications. Integral
    test for convergence of infinite series.

  8. Functions of several variables (2): graphical representations for
    two variable functions: graphs and level curves, limits and continuity.

  9. Partial and directional derivatives (2): gradients. Tangent
    planes and linear approximation, differentiability.

  10. The chain rule (2). Implicit functions.

  11. Local maxima and minima (2): saddle points. Absolute maxima and
    minima in the closed bounded regions.

  12. Double integrals over rectangles (2): double integrals over
    general regions, changing the order of integration. Geometrical
    applications of double integrals.

  13. Change of variables in double integrals (2): double integrals in
    polar coordinates.

  14. Triple integrals (2). Coordinate transformations. Triple
    integrals in cylindrical and spherical coordinates.

  15. Applications of multiple integrals (2).


  16. Tutorial contents
    The fundamental aim of the tutorials is to demonstrate how to apply the knowledge from lectures in problem solving.


Prerequisites
Prerequisite TypePrerequisite NumberCodeName
Recommended1103A-CTxxx-ISA-EIDMAIntroduction to Discrete Mathematics

Bibliography:

    1. R. Finney, G. Thomas, Calculus, Massachusetts Institute of
      Technology, Addison-Wesley Publishing Company, 2001.

    2. J.R.L. Webb, Functions of Several Real Variables, Ellis Horwood
      series in mathematics and its applications, England, 1991.

Assessment methods and assessment criteria:

During the tutorials it is possible to score up to 40 points:

10 points for activity

15 points for mid-term test (7th week)

15 points for end-term test (14th week)

The maximum score for the final examination is 60 points.



The final result is based on the following pattern:

A: 91-100 points

B+: 81-90 points

B: 71-80 points

C+: 61-70 points

C: 51-60 points

D: 0 -50 points

Classes in period "Winter Semester 2020/2021" (in progress)

Time span: 2020-10-01 - 2021-02-12
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Agnieszka Geras, Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2019/2020" (past)

Time span: 2020-02-22 - 2020-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 70 places more information
tutorials, 30 hours, 70 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Agnieszka Geras, Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2019/2020" (past)

Time span: 2019-10-01 - 2020-02-21
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Agnieszka Geras, Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2018/2019" (past)

Time span: 2019-02-18 - 2019-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Agnieszka Geras, Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2018/2019" (past)

Time span: 2018-10-01 - 2019-02-17
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: (unknown)
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2017/2018" (past)

Time span: 2018-02-19 - 2018-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2017/2018" (past)

Time span: 2017-10-01 - 2018-02-18
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2016/2017" (past)

Time span: 2017-02-20 - 2017-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 55 places more information
tutorials, 30 hours, 55 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2016/2017" (past)

Time span: 2016-10-01 - 2017-02-19
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2015/2016" (past)

Time span: 2016-02-23 - 2016-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2015/2016" (past)

Time span: 2015-10-01 - 2016-02-22
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2014/2015" (past)

Time span: 2015-02-23 - 2015-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2014/2015" (past)

Time span: 2014-09-29 - 2015-02-22
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2013/2014" (past)

Time span: 2014-02-24 - 2014-09-28
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Winter Semester 2013/2014" (past)

Time span: 2013-10-01 - 2014-02-23
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Classes in period "Summer Semester 2012/2013" (past)

Time span: 2013-02-20 - 2013-09-30
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 30 places more information
tutorials, 30 hours, 30 places more information
Coordinators: Barbara Roszkowska-Lech
Group instructors: Barbara Roszkowska-Lech
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

Course descriptions are protected by copyright.
Copyright by Warsaw University of Technology.