230-0202/15 – Mathematics II (BcM II)
| Gurantor department | Department of Mathematics | Credits | 5 |
| Subject guarantor | RNDr. Petr Volný, Ph.D. | Subject version guarantor | RNDr. Petr Volný, Ph.D. |
| Study level | undergraduate or graduate | | |
| | Study language | Czech |
| Year of introduction | 2026/2027 | Year of cancellation | |
| Intended for the faculties | FAST | Intended for study types | Bachelor |
Subject aims expressed by acquired skills and competences
Mathematics is essential part of education on technical universities. It should be considered rather the method in the study of technical subjects than a goal.
The aim of the subject is therefore to teach students not only basic mathematical knowledge, procedures and methods, but also to deepen their logical thinking. Students should learn to analyze a problem, distinguish the essential from the unessential, propose a solution procedure, check individual steps of the solution, generalize the conclusions, evaluate the correctness of the results with respect to the given conditions, apply tasks to solving technical problems, and understand that mathematical methods and thought processes are applicable in areas other than mathematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Other activities
Summary
The course includes three chapters – integral calculus of functions of one real variable, introduction to differential calculus of functions of two real variables and ordinary differential equations. The aim of the first chapter is to master the basic techniques of integration and, above all, to become familiar with the geometric and physical applications of the definite integral. The second chapter deals with the basics of differential calculus of functions of two variables, creating a geometric idea of a graph, determining local extrema and the tangent plane to a surface. The third chapter introduces the basic types of ordinary differential equations and their solutions.
Compulsory literature:
Hass, J.R.; Heil, C.E.; Bogacki, P.; Weir, M.D.: Thomas' Calculus, 15th Ed., Pearson, 2023.
Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, http://mdg.vsb.cz/portal/en/Mathematics2.pdf
Volná, J.; Volný, P.: Worksheets for Mathematics II, VŠB-TUO, 2021; http://mdg.vsb.cz/portal/en/Mathematics2_worksheets.pdf
Recommended literature:
Additional study materials
Way of continuous check of knowledge in the course of semester
Ongoing submission of tasks assigned during the exercises on the dates set by the teacher. Written tests, discussion on specialized topics covered in the lectures.
E-learning
http://www.studopory.vsb.cz
http://mdg.vsb.cz
Other requirements
Passing the course, requirements
Course-credit
-participation on tutorials is obligatory, 30% of absence can be apologized,
-elaborate programs,
-pass the written tests,
Point classification: 5-20 points.
Exam
Practical part of an exam is classified by 0 - 60 points. Practical part is successful if student obtains at least 25 points.
Theoretical part of the exam is classified by 0 - 20 points. Theoretical part is successful if student obtains at least 5 points.
Prerequisities
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Integral calculus of functions of one variable. Antiderivatives and indefinite integrals. Integration of elementary functions.
2. Integration by substitutions, integration by parts.
3. Integration of rational functions.
4. Definite integral and methods of integration.
5. Geometric and physical application of definite integrals.
6. Differential calculus of functions of two or more real variables. Functions of two or more variables, graphs, partial derivatives of the first and higher orders.
7. Differential of functions of two variables, tangent plane and normal to a surface, derivatives of implicit functions.
8. Extrema of functions.
9. Ordinary differential equations. General, particular and singular solutions. Separable and homogeneous equations.
10. Linear differential equations of the first order, method of variation of arbitrary constant.
11. 2nd order linear differential equations with constant coefficients, linearly independent solutions, Wronskian, fundamental system of solutions.
12. 2nd order LDE with constant coefficients - method of variation of arbitrary constants.
13. 2nd order LDE with constant coefficients - method of undetermined coefficients.
Conditions for subject completion
Conditions for completion are defined only for particular subject version and form of study
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction
Předmět neobsahuje žádné hodnocení.