# 230-0405/01 – Mathematics II (MII)

 Gurantor department Department of Mathematics Credits 5 Subject guarantor Mgr. Dagmar Dlouhá, Ph.D. Subject version guarantor Mgr. Dagmar Dlouhá, Ph.D. Study level undergraduate or graduate Requirement Compulsory Year 2 Semester winter Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties HGF Intended for study types Bachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
DLO44 Mgr. Dagmar Dlouhá, Ph.D.
DUB02 RNDr. Viktor Dubovský, Ph.D.
STA50 RNDr. Jana Staňková, Ph.D.
URB0186 RNDr. Zbyněk Urban, Ph.D.
VOL18 RNDr. Jana Volná, Ph.D.
VOL06 RNDr. Petr Volný, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2

### 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

The contents of the course is the introduction of common mathematical concepts and interpretation of their relations in connection to the methods of solving selected problems of three advanced parts of mathematics, according to which the learning material is structured. In Integral Calculus, the main motive is the preparation to general use of definite and indefinite integrals of real functions of one variable. Under Linear algebra is an emphasis on interpretation of the basic methods for solving systems of linear equations. In Differential Equations is an emphasis on interpretation of the basic procedures for the solution of selected types of differential equations.

### Compulsory literature:

Kreml, Pavel: Mathematics II, VŠB – TUO, Ostrava 2005, ISBN 80-248-0798-X http://mdg.vsb.cz/portal/en/Mathematics2.pdf Kučera, Radek: Mathematics III, VŠB – TUO, Ostrava 2005, ISBN 80-248-0802-1. James, G.: Modern Engineering Mathematics, Addison-Wesley, 1992, 0-201-1805456.

### Recommended literature:

Harshbarger, Ronald; Reynolds, James: Calculus with Applications, D.C. Heath and Company 1990, ISBN 0-669-21145-1. Leon, S., J.: Linear Algebra with Aplications, Macmillan Publishing Company, New York, 1986, ISBN 0-02-369810-1. Moore,C: Math quations and inequalities, Science & Nature, 2014. James, G.: Modern Engineering Mathematics. Addison – Wesley Publishing Company, Wokingham, 1994, ISBN 0-201-18504-5.

### Way of continuous check of knowledge in the course of semester

Conditions for obtaining the course-unit credit: participation in exercises, 30% of absences can be excused, submission of programs assigned by the supervisor in the prescribed course, passing of written tests. The student will get 5 b for fulfilling the conditions. The student can get 0 - 15 b for the tests. (The student who gets the credit will be evaluated 5 - 20 b). The condition for participation in the exam is a written credit from the relevant course. The exam consists of a written and an oral part. Students must pass both parts of the exam and achieve the necessary number of points.

### Other requirements

No more requirements

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

1st Integral calculus: antiderivative and indefinite integral for functions of one variable. 2nd Integration methods - substitution, integration by parts. 3rd Integration of rational functions, irrational functions, trigonometric functions. 4th Definite integrals: basic concepts, properties, Newton-Leibniz rule. 5th Substitution method and integration by parts for the definite integral. 6th Applications of integrals in geometry. 7th Differential calculus for functions of two variables: definition, domain, limits and continuity. 8th Partial derivatives of first order and higher orders. Total differential. 9th The equation of the tangent plane and of the normal. 10th Extrema of functions of two variables. 11th Implicit function and its derivatives. 12th Ordinary differential equation of the 1st order: types of solutions, separable, homogeneous and linear. 13th Linear differential equations of the 2nd order with constant coefficients: variation of constants, determination of coefficients. 14th Linear differential equations of higher orders.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 20  5
Examination Examination 80 (80) 30
Písemná zkouška Written examination 60  25
Ústní zkouška Oral examination 20  5
Mandatory attendence parzicipation: At least 70% attendance at the exercises. Absence, up to a maximum of 30%, must be excused and the apology must be accepted by the teacher (the teacher decides to recognize the reason for the excuse).

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### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner