Mathematics

……………….
Course code
Course item
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1. INFORMATION ABOUT THE COURSE
A. Basic information
Course title
Mathematics
Field of study
Environmental Engineering
Cycle
first
Study profile
academic
Study mode
full-time
Specialisation
Lecturer
Faculty of Civil and Environment Engineering and
Architecture, Department of Structural Mechanics
Mykhaylo Delyavskyy, Professor
Introductory courses
Mathematics
Prerequisites
basic knowledge of mathematics
Unit responsible for the field of study
B. Semester/ weekly timetable
Semester
Lectures
Classes
winter/
summer
1
1
Laboratories
Project
classes
Seminars
Field
experience
ECTS
credits
3
2. LEARNING OUTCOMES (acc. to National Qualifications Framework)
No.
K1
S1
SC1
Description of learning outcomes
KNOWLEDGE
Student has basic knowledge - theoretical and
practical - of higher mathematics in range of
mathematical analysis and linear algebra
SKILLS
Student knows how to solve tasks and problems of
higher mathematics
SOCIAL COMPETENCES
Student is ready for further education in technical
subjects
Reference to
learning
outcomes for
the field of
study
Reference to learning
outcomes for the area
of study
K_W01
T1A_W01
K_U02
K_U04
T1A_U01
T1A_U02
T1A_U05
T1A_U06
K_K01
T1A_K01
3. TEACHING METHODS
Lectures and classes – traditional methods, ‘board and chalk’, in individual cases use of multimedia
technology. Classes-students are provided with manuals for exercises
4. METHODS OF EXAMINATION
Lectures- written and oral examination, classes –colloquium, participation in lessons.
5. COURSE CONTENT
Lectures
Real function of one variable and basic properties. Numerical sequences, limit of
sequence. Limit of function and its use. Function derivative, its properties and
uses. Analysis functions variation. Matrices, operations on matrices. Linear
transformations, matrix of linear transformation. Determinants, properties of
determinants. Inverse matrix. Systems of equations. Elements of analytic
geometry in the plane. Elements of analytic geometry in space. Functions of many
variables. Indefinite integral. Integrals of rational functions. Integrals of irrational
functions. Integrals of trigonometric functions. Definite integral and its applications.
Multiple integrals and their applications. Ordinary differential equations of first
rank. The equation with separated variables, linear differential equation, Bernoull’si
equation.
Solving tasks covering a range of lectures.
Project classes
6. VALIDATION OF LEARNING OUTCOMES
(Each learning outcome from the list requires validation methods to ensure that it was achieved by a
student.)
Learning
outcome
Form of assessment
Oral
examination
K1
S1
SC1
x
Written
examination
x
x
x
Colloquium
Project
…………
Report
x
x
7. LITERATURE
Basic literature
Supplementary
literature
Jurlewicz T., Skoczylas Z., 2008. Algebra liniowa 1. Oficyna Wydawnicza GiS,
Wrocław
Jurlewicz T., Skoczylas Z., 2008. Algebra liniowa 2. Oficyna Wydawnicza GiS,
Wrocław
Gewert M., Skoczylas Z., 2008. Analiza matematyczna 1. Oficyna Wydawnicza GiS,
Wrocław
Gewert M., Skoczylas Z., 2008. Analiza matematyczna 2. Oficyna Wydawnicza GiS,
Wrocław
Gewert M., Skoczylas Z., 2008. Równania różniczkowe zwyczajne. Oficyna
Wydawnicza GiS, Wrocław
Krysicki W., Włodarski L., 2006. Analiza matematyczna w zadaniach. PWN Warszawa
Lassak M., 2007. Matematyka dla studiów technicznych. Wydawnictwo Supremum,
Bydgoszcz
Gdowski B., Pluciński E., 2000. Zbiór zadań z rachunku wektorowego i geometrii
analitycznej. Oficyna Wydawnicza Politechniki Warszawskiej
8. TOTAL STUDENT WORKLOAD REQUIRED TO ACHIEVE EXPECTED LEARNING OUTCOMES
EXPRESSED IN TIME AND ECTS CREDITS
Student workload–
number of hours
Student’s activity
Participation in classes indicated in point 2.2
30
Preparation for classes
10
Reading assignments
15
Strona 2 z 3
Other (preparation for exams, tests, carrying out a project etc)
20
Total student workload
75
Number of ECTS credits allocated by the lecturer
3
Final number of ECTS credits (determined by the Programme Council for
the Field of Study)
3