230-0306/02 – Mathematics II (MII)
Gurantor department | Department of Mathematics | Credits | 4 |
Subject guarantor | Mgr. Jakub Stryja, Ph.D. | Subject version guarantor | Mgr. Jakub Stryja, Ph.D. |
Study level | undergraduate or graduate | Requirement | Compulsory |
Year | 1 | Semester | summer |
| | Study language | Czech |
Year of introduction | 2020/2021 | Year of cancellation | |
Intended for the faculties | FBI | 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 courses than a goal. Thus the goal of mathematics is train logical reasoning than mere list of mathematical notions, algorithms and methods.
Students should learn how to:
analyze problems,
distinguish between important and unimportant,
suggest a method of solution,
verify each step of a method,
generalize achieved results,
analyze correctness of achieved results with respect to given conditions,
apply these methods while solving technical problems,
understand that mathematical methods and theoretical advancements outreach the field mathematics.
Teaching methods
Lectures
Individual consultations
Tutorials
Summary
Mathematics II is divided in three parts:
1. Integral calculus of functions of one real variable - indefinite integral, some properties, elementary methods of integration.
2. Differential calculus of functions of two real variables - the partial derivations, extremes of functions of two variables.,
3. Ordinary differential equations - ordinary differential equation of the 1st and 2nd order.
Compulsory literature:
Recommended literature:
Way of continuous check of knowledge in the course of semester
Passing the course, requirements
Course-credit (full-time study):
5 points:
-participation on tutorials is obligatory, 20% of absence can be accepted,
-submition of semestral project in predefined form.
5 – 15 poinst:
-accomplish the written tests,
-each test can be repeated once,
-it is necessary to get at least 5 out of 15 points.
Student has to gain at least 10 points in total to obtain credit and procced to final exam.
Course-credit (distance study):
Based on participation in consultations student can get 5 - 20 points, in case of absence student can get 5 points for elaboration of additional project.
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.
Point quantification National grading scheme
100 – 86 excellent
85 – 66 very good
65 – 51 satisfactory
50 – 0 failed
E-learning
http://mdg.vsb.cz/portal/en/Mathematics2.pdf
Other requirements
There are no additional requirements.
Prerequisities
Subject has no prerequisities.
Co-requisities
Subject has no co-requisities.
Subject syllabus:
1. Integral calculus: antiderivative and indefinite integral for functions of one variable.
2. Integration methods - substitution, integration by parts.
3. Integration of rational functions, irrational functions, trigonometric functions.
4. Definite integrals: basic concepts, properties, Newton-Leibniz rule.
5. Substitution method and integration by parts for the definite integral.
6. Geometric and physical application of definite integrals.
7. Differential calculus for functions of two variables: definition, domain, limits and continuity.
8. Partial derivatives of first order and higher orders. Total differential.
9. The equation of the tangent plane and of the normal.
10. Extrema of functions of two variables.
11. Implicit function and its derivatives.
12. Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear.
13. Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients.
14. Linear differential equations of higher orders.
Conditions for subject completion
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction