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Course info KMA / 2MAT1 : Course description

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Department/Unit / Abbreviation	KMA / 2MAT1			Academic Year	2023/2024
Academic Year	2023/2024
Title	Mathematics 1			Form of course completion	Exam
Form of course completion	Exam
Accredited / Credits	Yes, 6 Cred.			Type of completion	Written
Type of completion	Written
Time requirements	Lecture 4 [Hours/Semester] Tutorial 35 [Hours/Semester]			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
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			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	KMA/XMAT1
Preclusive courses	KFY/UVMA1 and KFY/XUVM1 and KMA/INDIP and KMA/MATH1 and KMA/MA2OB and KMA/XINDP and KMA/XMAA1 and KMA/XMAT1 and KMA/XUVM1 and KMA/7MAT1
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:
Fundamentals of the differential and integral calculus. Limit and continuity of a function. Derivatives and sketching the graph of a function. Primitive functions, integration by substitution and by parts. Riemann integral, Newton integral. Examples.
Requirements on student
A student has to write 2 homeworks. The homeworks must be handed in before the exam. The exam is written. Students can earn maximum 100 points. The evaluation of the course including the classification is carried out in accordance with the Study and Examination Regulations OU.
Content
1. Basic concepts. Interval, function, domain and range of a function, graph of a function. Even and odd functions. Injective, surjective and inverse function. 2. Elementary transcendental functions and their inverses (power and root, exponential and logarithmic function, trigonometric and cylometric functions). 3. Continuity of functions. Operations with functions (sum, difference, product, quotient). Composite function. 4. Limit of a function. The concept of the (non-isolated point and of the) limit. Links between limit and continuity. Limit from the left and from the right. Limits at infinity. Infinite limits. Theorem on the limit of the sum, difference, product, and quotient of functions, limit of a composite function. 5. Derivatives of functions. Examples: the instantaneous velocity, and the tangent to the graph of a function. The concept of the derivative. Rules to calculate derivatives (derivative of the sum, difference, product, and quotient of functions, chain rule). 6. L'Hospital's rule. Derivatives of higher orders. 7. Sketching the graph of a function. Monotonicity and convexity/concavity. Increasing, non-decreasing, non-increasing, decreasing functions. Convex, strictly convex, strictly concave, concave functions. Theorem on the relationship between the monotonicity of a function (increasing/decreasing functions) and its first derivative. Theorem on the relationship between convexity/concavity of a function and its second derivative. 8. Sketching the graph of a function. Local extrema (maxima and minima) and inflection points. Monotonicity of a function at a point, strict convexity/concavity of a function at a point. The relationship of local extremum and the first derivative. The relationship of inflection point and the second derivative. 9. Sketching the graph of a function. Theorem on the monotonicity of a differentiable function at a point and on the strict local extremum of a differentiable function at a point. Theorem on the strict convexity/concavity of a differentiable function at a point and on the inflection point of a differentiable function. 10. Elements of the integral calculus. (Cauchy)-Riemann definition of the integral by the summation. Sum of integrals, product of a constant and of an integral. The Fundamental Theorem of Calculus. Newton-Leibniz formula. 11. Elements of the integral calculus. Newton definition of the integral. Indefinite integral or primitive function. Integration by substitution and by parts. Geometric interpretation of definite integral. Volume and surface area of a solid of revolution. 12. Revision. Examples.
Activities
Fields of study
Guarantors and lecturers
Guarantors: prof. RNDr. Jaroslav Hančl, CSc. (100%),  Lecturer: Mgr. Věra Ferdiánová, Ph.D. (100%),  Mgr. Lukáš Novotný, Ph.D. (100%),  Mgr. Nicole Škorupová (100%),  Tutorial lecturer: Mgr. Věra Ferdiánová, Ph.D. (100%),  Mgr. Lukáš Novotný, Ph.D. (100%),  Mgr. Nicole Škorupová (100%),
Literature
Basic: Breviář vyšší matematiky (Kalus, R. -- Hrivňák, D.) Basic: Stewart, J. Calculus. [s.l.]: Thomson Brooks/Cole, 2008. ISBN 978-0-495-38362-8. Basic: Matematická analýza 1 (Hančl, J. -- Šustek, J.) Basic: Matematická analýza 2 (Hančl, J. -- Štěpnička, J.) Basic: Vrbenská, H. -- Bělohlávková, J. Základy matematiky pro bakaláře I. Ostrava: VŠB, 2003. ISBN 80-248-0519-7. Basic: Vrbenská, H. -- Bělohlávková, J. Základy matematiky pro bakaláře II. Ostrava: VŠB, 2003. ISBN 80-248-0406-9. Extending: Rektorys, K. Co je a k čemu je vyšší matematika. Praha: Academia, 2001. ISBN 80-200-0883-7. Extending: Jarník, V. Diferenciální počet I. Praha: Academia, 1984. ISBN cnb000021007. Extending: Jarník, V. Integrální počet I. Praha: Academia, 1984. ISBN cnb000007988. Extending: Rektorys, K. Přehled užité matematiky. Praha: Prometheus, 2000. ISBN 80-7196-179-5. Extending: Děmidovič, B. P. Sbírka úloh a cvičení z matematické analýzy. Havlíčkův Brod: Fragment, 2003. ISBN 80-7200-587-1. Recommended: Votava, M. Cvičení z matematické analýzy 3. díl. Ostrava: Ped. fakulta OU, 1998. ISBN 80-7042-139-8. Recommended: Ošťádalová, E. -- Ulmannová, V. Integrální počet (cvičení pro 1. ročník EkF, VŠB-TU Ostrava). Ostrava: VŠB, 2001. ISBN 80-7078-538-1. Recommended: Kopecký, M. -- Kubíček, Z. Vybrané kapitoly z matematiky. Praha: SNTL, 1981. ISBN cnb000047484. On-line library catalogues
Time requirements
All forms of study Activities Time requirements for activity [h] Being present in classes 4 Self-tutoring 52 Preparation for an exam 32 Consultation of work with the teacher/tutor (incl. electronic) 6 Continuous tasks completion (incl. correspondence tasks) 4 Unaided e-learning tasks completion 13 Total 111
Prerequisites
Learning outcomes
Knowledge - knowledge resulting from the course: Gained competencies a student understands differential and integral calculus of functions of one variable, understands the concepts of limit, continuity, derivative, primitive function, can investigate a behaviour of a function can determine a primitive functions by substitution and by parts
Assessment methods
Knowledge - knowledge achieved by taking this course are verified by the following means: Dialogue Written examination
Teaching methods
Knowledge - the following training methods are used to achieve the required knowledge: Dialogic (discussion, dialogue, brainstorming) Monologic (explanation, lecture, briefing) Working with text (coursebook, book)