Course description

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A course is the basic teaching unit, it's design as a medium for a student to acquire comprehensive knowledge and skills indispensable in the given field. A course guarantor is responsible for the factual content of the course.
For each course, there is a department responsible for the course organisation. A person responsible for timetabling for a given department sets a time schedule of teaching and for each class, s/he assigns an instructor and/or an examiner.
Expected time consumption of the course is expressed by a course attribute extent of teaching. For example, extent = 2 +2 indicates two teaching hours of lectures and two teaching hours of seminar (lab) per week.
At the end of each semester, the course instructor has to evaluate the extent to which a student has acquired the expected knowledge and skills. The type of this evaluation is indicated by the attribute completion. So, a course can be completed by just an assessment ('pouze zápočet'), by a graded assessment ('klasifikovaný zápočet'), or by just an examination ('pouze zkouška') or by an assessment and examination ('zápočet a zkouška') .
The difficulty of a given course is evaluated by the amount of ECTS credits.
The course is in session (cf. teaching is going on) during a semester. Each course is offered either in the winter ('zimní') or summer ('letní') semester of an academic year. Exceptionally, a course might be offered in both semesters.
The subject matter of a course is described in various texts.

BIE-ZMA Elements of Calculus Extent of teaching: 3P+2C

Instructor: Marchesiello A. Completion: Z,ZK

Department: 18105 Credits: 6 Semester: Z

Annotation:
Students acquire knowledge and understanding of the fundamentals of classical calculus so that they are able to apply mathematical way of thinking and reasoning and are able to use basic proof techniques. They get skills to practically handle functions of one variable in solving the problems in informatics. They understand the links between the integrals and sums of sequences. They are able to estimate lower or upper bounds of values of real functions and to handle simple asymptotic expressions.

Lecture syllabus:

1. Introduction, real numbers, basic properties of functions.

2. Limits.

3. Continuity, introduction to derivatives.

4. Properties of derivatives, implicit differentiation, numerical and symbolic differentiation on a computer.

5. Classical theorems (Rolle, mean value, etc.), differentiation using limits, finding limits using derivatives (l'Hospital's rule).

6. Taylor polynomials and approximation, error estimation, root finding (bisection, regula falsi, Newton's method), monotony, extremes and optimization.

7. Convexity, function graph, primitive function, substitution.

8. Integration by parts, partial fractions.

9. Definite integral (properties, N-L formula).

10. Improper integral.

11. Uses of integrals, numerical methods for definite integrals.

12. Sequences and their limits.

13. Extended scales of infinity, small- and big-O notation, theta. Space and time complexity of algorithms.

Seminar syllabus:

1. Differentiating.

2. Domain of a function.

3. Basic properties of functions.

4. Limits of functions.

5. Tangents/normals, implicit differentiation, related rates.

6. Limits of functions.

7. Approximation, optimization.

8. Graphs of functions, primitive functions.

9. Indefinite integral.

10. Definite integral.

11. Improper integral.

12. Applications of integrals.

13. Sequences.

Literature:

1. Strang, G. ''Calculus.'' Wellesley-Cambridge Press, 2009. ISBN 0961408820.

Requirements:
The ability to think mathematically and knowledge of a high school mathematics.

Information about the course and courseware are available at https://courses.fit.cvut.cz/BIE-ZMA/

The course is also part of the following Study plans:

Study Plan Study Branch/Specialization Role Recommended semester

BIE-TI.2015_ORIGINAL Computer Science (Bachelor, in English) PP 1

BIE-BIT.2015 Computer Security and Information technology (Bachelor, in English) PP 1

BIE-TI.2015 Computer Science (Bachelor, in English) PP 1

BIE-WSI-SI.2015 Software Engineering (Bachelor, in English) PP 1

Page updated 19. 4. 2024, semester: L/2020-1, L/2021-2, Z/2023-4, Z/2024-5, Z/2019-20, Z/2022-3, L/2019-20, L/2022-3, Z/2020-1, Z/2021-2, L/2023-4, Send comments to the content presented here to Administrator of study plans Design and implementation: J. Novák, I. Halaška

BIE-ZMA	Elements of Calculus			Extent of teaching:	3P+2C
Instructor:	Marchesiello A.			Completion:	Z,ZK
Department:	18105	Credits:	6	Semester:	Z

1.		Introduction, real numbers, basic properties of functions.
2.		Limits.
3.		Continuity, introduction to derivatives.
4.		Properties of derivatives, implicit differentiation, numerical and symbolic differentiation on a computer.
5.		Classical theorems (Rolle, mean value, etc.), differentiation using limits, finding limits using derivatives (l'Hospital's rule).
6.		Taylor polynomials and approximation, error estimation, root finding (bisection, regula falsi, Newton's method), monotony, extremes and optimization.
7.		Convexity, function graph, primitive function, substitution.
8.		Integration by parts, partial fractions.
9.		Definite integral (properties, N-L formula).
10.		Improper integral.
11.		Uses of integrals, numerical methods for definite integrals.
12.		Sequences and their limits.
13.		Extended scales of infinity, small- and big-O notation, theta. Space and time complexity of algorithms.

1.		Differentiating.
2.		Domain of a function.
3.		Basic properties of functions.
4.		Limits of functions.
5.		Tangents/normals, implicit differentiation, related rates.
6.		Limits of functions.
7.		Approximation, optimization.
8.		Graphs of functions, primitive functions.
9.		Indefinite integral.
10.		Definite integral.
11.		Improper integral.
12.		Applications of integrals.
13.		Sequences.