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Course info KMA / MATX3 : Course description

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Department/Unit / Abbreviation	KMA / MATX3			Academic Year	2023/2024
Academic Year	2023/2024
Title	Mathematics 3			Form of course completion	Exam
Form of course completion	Exam
Accredited / Credits	Yes, 5 Cred.			Type of completion	Combined
Type of completion	Combined
Time requirements	lecture 2 [Hours/Week] practical class 2 [Hours/Week]			Course credit prior to examination	No
Course credit prior to examination	No
Automatic acceptance of credit before examination	No
Included in study average	YES
Language of instruction	Czech, English
Occ/max				Automatic acceptance of credit before examination	No
Summer semester	0 / -	0 / -	0 / -	Included in study average	YES
Winter semester	0 / 0	0 / 0	0 / 0	Repeated registration	NO
Repeated registration	NO
Timetable	Yes			Semester taught	Winter semester
Semester taught	Winter semester
Minimum (B + C) students	not determined			Optional course	Yes
Optional course	Yes
Language of instruction	Czech, English			Internship duration	0
No. of hours of on-premise lessons				Evaluation scale	A|B|C|D|E|F
Periodicity	every year
Specification periodicity				Fundamental theoretical course	No
Fundamental course	No
Fundamental theoretical course	No
Evaluation scale	A|B|C|D|E|F
Substituted course	None
Preclusive courses	KMA/MATH3 and KMA/XMAT3 and KMA/XMAX3 and KMA/2MAT3
Prerequisite courses	N/A
Informally recommended courses	N/A
Courses depending on this Course	N/A
Histogram of students' grades over the years: Graphic PNG ,  XLS

Course objectives:
Elements of topology, differential calculus of functions of several variables. Ordinary differential equation (ODE), basic terminology, the initial Cauchy problem for ODE of the 1st order, equation with separable variables, homogeneous differential equations, linear differential equations of the 1st order, Bernoulli differential equation, linear differential equations of 2nd order. Function of several variables, partial derivatives and differentiability. Basic use of differential and finding extrema of functions of several variables.
Requirements on student
During the seminar the students have to pass three written tests. Students have the right to retake the test once. The overall grade is calculated by taking three best scores from four tests. If the student gains mark "excellent" or "very good" from the test written in the seminar, he/she has the right not to sit at written examination and the grade is recognized as the final grade. Course completion: written and oral examination. The evaluation of the course including the classification is carried out in accordance with the Study and Examination Regulations OU.
Content
1. Ordinary differential equation (ODE), the types of solutions of ODE-general, particular, singular. 2. ODE if the 1st order, Cauchy initial value problem for the ODE of the 1st order, the theorem on the existence and uniqueness of the ODE of the 1st order. 3. Basic types of the ODEs of the 1st order: the equation with separable variables, homogeneous differential equation. Linear differential equations of the 1st order, Bernoulli differential equation. 4. Linear differential equations of higher orders. Homogeneous linear differential equations of the 2nd order. Non homogeneous linear differential equations of the 2nd order, method of variation of parameters. Method of undetermined coefficients in the special case of the right side. 5. Examples of differential equations in mechanics and their solutions. 6. Functions of several variables. Domain, the graph of the function of two variables. Limit and continuity of functions of several variables. 7. Partial functions. Partial derivatives. Gradient. 8. Differentiability of functions of more variables. Total differential and its use for approximate calculations. 9. Equation for the plane tangent to the graph of a function. Stationary points of functions of several variables. Classification of stationary points. 10. Local extremes. Necessary condition for extrema of differentiable function. Sufficient condition for extrema of the function of two variables. 11. Constrained extrema. Solving the extremas.
Activities
Fields of study
Guarantors and lecturers
Guarantors: doc. RNDr. Jan Šustek, Ph.D. (100%),  Lecturer: RNDr. Martin Swaczyna, Ph.D. (100%),  doc. RNDr. Jan Šustek, Ph.D. (100%),  doc. Ing. Ondřej Turek, Ph.D. (100%),  Tutorial lecturer: Mgr. Jakub Poruba (100%),  doc. RNDr. Jan Šustek, Ph.D. (100%),
Literature
Basic: V. Jarník. Diferenciální počet II. Academia, Praha, 1976. ISBN cnb000459025. Basic: Gillman, L., Mc Dowell, R.H. Matematická analýza. SNTL, Praha, 1980. ISBN cnb000141373. Basic: O. Krupková. Matematika 3, Diferenciální počet funkcí více proměnných,. učební text OU, Ostrava, 2004. Basic: Vrbenská, H. -- Bělohlávková, J. Základy matematiky pro bakaláře I. Ostrava: VŠB, 2003. ISBN 80-248-0519-7. Extending: Thomas, G., Finney, I. Calculus and analytic geometry. Addison-Wesley Publishing Company, 1988. ISBN 0-201-16320-9. Extending: Sikorski, R. Diferenciální a integrální počet: Funkce více proměnných. Academia Praha, 1973. ISBN cnb000156402. Extending: Kluvánek,I., Mišík,L., Švec,M. Matematika I. a II.. SVTL Bratislava, 1959. Extending: REKTORYS,K. A KOLEKTÍV. Přehled užité matematiky. Praha, 1981. ISBN 80-85849-92-5. Recommended: M. Ráb. Metody řešení obyčejných diferenciálních rovnic. skriptum MU, Brno, 1998. ISBN 80-210-1818-6. Recommended: Anton, H. Multivariable calculus. John Wiley and Sons, 1992. ISBN 978-0-495-11890-9. Recommended: J. Kalas, M. Ráb. Obyčejné diferenciální rovnice. učebnice MU, Brno, 1995. ISBN 80-210-1130-0. On-line library catalogues
Time requirements
All forms of study Activities Time requirements for activity [h] Being present in classes 52 Preparation for test 3 Self-tutoring 26 Consultation of work with the teacher/tutor (incl. electronic) 5 Continuous tasks completion (incl. correspondence tasks) 13 Preparation for an exam 30 Books of fiction reading in the Czech language 13 Total 142
Prerequisites
Learning outcomes
Knowledge - knowledge resulting from the course: Student knows the basic structures of mathematical analysis (topological and metrical structure of Euclid spaces) knows the basic terminology and examples of mapping of Euclidean spaces and can work with them is familiar with terminology of limits and derivatives, gains the ability to apply his/her knowledge to particular mapping knows the basic characteristics of differentiable mapping and acquires the ability to use them knows the basic theorems of differential calculus of several variables, acquires the ability to apply them in simple situations develops the knowledge of the theory of free and bounded extrema of functions of several variables develops the ability to search extremes of functions and to study their properties acquires the ability to study relevant technical literature can use computer to display functions and to study their properties
Assessment methods
Knowledge - knowledge achieved by taking this course are verified by the following means: Continuous analysis of student´s achievements Oral examination Written examination
Teaching methods
Knowledge - the following training methods are used to achieve the required knowledge: Computer-based tutoring Dialogic (discussion, dialogue, brainstorming) Monologic (explanation, lecture, briefing) Projection (static, dynamic) Working with text (coursebook, book)