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Transition Math and Algebra with Geometry

General data

Course ID: 103A-CTxxx-ISA-ETMAG Erasmus code / ISCED: (unknown) / (unknown)
Course title: Transition Math and Algebra with Geometry Name in Polish: Transition Math and Algebra with Geometry
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) ETMAG

(in Polish) Numer wersji:

(in Polish) 1

Short description:

The aim of the lecture is to introduce fundamental concepts of the theory of linear algebra and basics of a single variable calculus. The course covers the following topics: field of complex numbers, polynomials, vector spaces, matrices, linear equations, determinants, sequences, exponential and logarithmic functions, inverse trigonometric functions, limits of functions and continuity, derivatives.

Full description:

The aim of the lecture is to introduce fundamental concepts of the theory of linear algebra and basics of a single variable calculus. The course covers the following topics: field of complex numbers, polynomials, vector spaces, matrices, linear equations, determinants, sequences, exponential and logarithmic functions, inverse trigonometric functions, limits of functions and continuity, derivatives.

Lecture contents

  1. Sets and functions (2h): basic definitions and properties.
    "One-to-one" functions ?onto? functions and permutations. Function
    composition and inversion.

  2. Complex numbers (2h): definition and properties. Polynomials over
    the field of real and complex numbers. Remainder theorem. Roots of
    polynomials. Main Theorem of Algebra.

  3. Vector spaces (2h): basic definitions. Examples of vector spaces
    over the field of real and complex numbers. Subspaces: definitions and
    properties. Linear independence of a finite set of vectors in
    finite dimensional vector spaces. Basis and dimension of a vector
    space: definition and properties.

  4. Matrices (2h): basic definitions and properties. Matrix
    operations: addition, scaling, multiplication, transposition. Square
    matrices, symmetric matrices. Rank of a matrix.

  5. System of linear equations (4h). General and homogeneous systems.
    Matrix form of a system of linear equations. Solution space.
    Kronecker-Capelli theorem. Gauss elimination.

  6. Determinant of a matrix (2h): definition and properties. Cramer`s
    rule. Nonsingular matrices: matrix inversion.

  7. Axioms for real numbers (2h). Sequences. Arithmetic and geometric
    sequences. Monotonicity and boundedness of a sequence. Convergence and
    divergence. Properties of the limit.

  8. Basic convergent sequences (2h). The number e. Evaluating limits.

  9. Functions and graphs (2h). Exponential and logarithmic functions.
    Inverse trigonometric functions.

  10. Limits (2h): one-sided limits and limits at infinity; continuity,
    theorems on continuous functions; extreme values.

  11. Derivatives (2h): definitions, physical and geometric
    interpretation. Rolle`s theorem. Lagrange`s theorem. Cauchy`s theorem.

  12. Evaluation of derivatives (2h). Applications of derivatives. De
    l`Hospital rule.

  13. Derivatives of higher order (4h): graphing functions using y` and
    y``. Monotonicity and convexity.


Tutorial contents
The fundamental aim of the tutorials is to demonstrate how to apply the knowledge from lectures in problem solving. The tutorials cover the following topics: field of complex numbers, polynomials, vector spaces, matrices, linear equations, determinants, sequences, exponential and logarithmic functions, inverse trigonometric functions, limits of functions and continuity, derivatives.

Bibliography:

Textbooks:

  • S. Lipschutz, M. Lipson: Schaum`s Outline of Linear Algebra,
    McGraw-Hill; 3rd edition (2000)

  • R. L. Finney, G. B. Thomas :Calculus. Pearson Education; 2nd
    edition (1993)


Additional reading:

  • R. L. Finney, F. D. Demana, B. K. Waits, D. Kennedy: Calculus: A complete course. Addison Wesley; 2 edition ( 1999)

Assessment methods and assessment criteria:

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

    s 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:

5.0: 91-100 points

4.5: 81-90 points

4.0: 71-80 points

3.5: 61-70 points

3.0: 51-60 points

2.0: 0 -50 points

Classes in period "Summer Semester 2019/2020"

Time span: 2020-02-22 - 2020-09-30

Choosen plan division:


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see course schedule
Type of class: lectures, 30 hours, 60 places more information
tutorials, 30 hours, 60 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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, 120 places more information
tutorials, 30 hours, 120 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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, 100 places more information
tutorials, 30 hours, 100 places more information
Coordinators: Tomasz Traczyk
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: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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, 100 places more information
tutorials, 30 hours, 100 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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, 40 places more information
tutorials, 30 hours, 40 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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:


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see course schedule
Type of class: lectures, 30 hours, 70 places more information
tutorials, 30 hours, 70 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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:


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Type of class: lectures, 30 hours, 55 places more information
tutorials, 30 hours, 55 places more information
Coordinators: Tomasz Traczyk
Group instructors: Tomasz Traczyk
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:


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Type of class: lectures, 30 hours, 40 places more information
tutorials, 30 hours, 40 places more information
Coordinators: Tomasz Brengos
Group instructors: Tomasz Brengos
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, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Brengos
Group instructors: Tomasz Brengos
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: Tomasz Brengos
Group instructors: Tomasz Brengos
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, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Brengos
Group instructors: Tomasz Brengos
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: Tomasz Brengos
Group instructors: Tomasz Brengos
Students list: (inaccessible to you)
Examination: Exam
(in Polish) Jednostka realizująca:

(in Polish) 112000 - Wydział Matematyki i Nauk Informacyjnych

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

Time span: 2012-10-01 - 2013-02-19
Choosen plan division:


magnify
see course schedule
Type of class: lectures, 30 hours, 45 places more information
tutorials, 30 hours, 45 places more information
Coordinators: Tomasz Brengos
Group instructors: Tomasz Brengos
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.