Course details

# Mathematical Analysis 1

IMA1 Acad. year 2022/2023 Summer semester 4 credits

Limit, continuity and derivative of a function. Extrema and graph properties. Approximation and interpolation. Indefinite and definite integrals.

Guarantor

Course coordinator

Language of instruction

Czech, English

Completion

Credit+Examination (written)

Time span

• 26 hrs lectures
• 26 hrs exercises

Assessment points

• 80 pts final exam
• 20 pts numeric exercises

Department

Lecturer

Instructor

Course Web Pages

Subject specific learning outcomes and competences

The ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.

Learning objectives

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis is put on handling the practical use of these methods for solving specific tasks.

Why is the course taught

Fundamentals of calculus are a necessary part of a study at a technical university because virtually all technical and physical subjects employ the concepts of a derivative and integral.

Prerequisites

Prerequisite knowledge and skills

Secondary school mathematics.

Study literature

• Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966.
• Fong, Y., Wang, Y., Calculus, Springer, 2000.
• Ross, K. A., Elementary analysis: The Theory of Calculus, Springer, 2000.
• Small, D. B., Hosack, J. M., Calculus (An Integrated Approach), McGraw-Hill Publ. Comp., 1990.
• Thomas, G. B., Finney, R. L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.

Fundamental literature

• Krupková, V., Fuchs, P., Matematická analýza pro FIT, elektronický učební text, 2019.

Syllabus of lectures

1. The concept of a function of a real variable, properties of functions and basic operations with functions.
2. Elementary functions of a real variable.
3. Limit and continuity of a function. Limit of a sequence.
4. Derivative and a differential of a function.
5. Higher-order derivatives. Taylor polynomial. Extrema of a function.
6. Graph properties.
7. Interpolation and approximation.
8. Numerical solutions of equations.
9. Indefinite integral, basic methods of integration.
10. Definite Riemann integral, its applications.
11. Improper integral.
12. Numerical integration.

Syllabus of numerical exercises

Problems discussed at numerical classes are chosen so as to complement suitably the lectures.

Progress assessment

Written tests during the semester (maximum 30 points).

Controlled instruction

Classes are compulsory (presence at lectures, however, will not be controlled), absence at numerical classes has to be excused.

Exam prerequisites

The condition for receiving the credit is active work during the semestr and obtaining at least 12 points from the tests during the semester.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise *) 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12. of lectures T8/T 5.22 08:0009:500 1BIA 1BIB 2BIA 2BIB xx Fusek
Mon lecture 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12. of lectures D105 09:0010:50316 1BIB 2BIA 2BIB xx 30 - 49 Fuchs
Mon exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12. of lectures T8/T 5.22 10:0011:5050 1BIA 1BIB 2BIA 2BIB xx Fusek
Mon exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12. of lectures D0207 11:0012:5059 1BIA 1BIB 2BIA 2BIB xx Fuchs
Mon exercise *) 1., 2., 3., 4., 5., 6., 7., 8., 9., 11., 12. of lectures T8/T 5.22 16:0017:500 1BIA 1BIB 2BIA 2BIB xx Fuchs
Tue exercise lectures T8/T 5.22 10:0011:5050 1BIA 1BIB 2BIA 2BIB xx Fusek
Tue exam 2023-05-09 A112 A113 D0206 D0207 D105 E104 E105 E112 G202 12:0014:50řádná
Tue exercise lectures T8/T 5.22 12:0013:5050 1BIA 1BIB 2BIA 2BIB xx Fusek
Tue lecture lectures D0206 D105 13:0014:50550 1BIA 2BIA 2BIB xx 10 - 29 Hliněná
Tue exercise lectures A113 15:0016:5064 1BIA 1BIB 2BIA 2BIB xx Hliněná
Wed exercise lectures T8/T 5.22 08:0009:5050 1BIA 1BIB 2BIA 2BIB xx Tůma
Wed exercise lectures D0207 10:0011:5064 1BIA 1BIB 2BIA 2BIB xx Hliněná
Wed exercise lectures T8/T 5.22 10:0011:5045 1BIA 1BIB 2BIA 2BIB xx Fuchs
Wed exercise lectures D0207 14:0015:5063 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Wed exercise lectures D0207 16:0017:5060 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Thu exercise lectures A113 08:0009:5060 1BIA 1BIB 2BIA 2BIB xx Fusek
Thu exercise lectures A113 10:0011:5060 1BIA 1BIB 2BIA 2BIB xx Fusek
Thu exam 2023-06-01 D0206 D0207 D105 E112 12:0014:501. oprava
Thu exercise lectures A113 14:0015:5059 1BIA 1BIB 2BIA 2BIB xx Fuchs
Thu exercise lectures T8/T 5.22 16:0017:5050 1BIA 1BIB 2BIA 2BIB xx Tůma
Fri exercise lectures T8/T 5.22 08:0009:5050 1BIA 1BIB 2BIA 2BIB xx Tůma
Fri exercise lectures T8/T 5.22 10:0011:5050 1BIA 1BIB 2BIA 2BIB xx Tůma
Fri exam 2023-06-09 A113 D0206 E104 E105 E112 G202 12:0014:502. oprava
It is not possible to register this class in Studis. (Some exercises may be opened later if needed, but this is not guaranteed.)

Course inclusion in study plans

• Programme BIT, 1st year of study, Compulsory
• Programme BIT (in English), 1st year of study, Compulsory
• Programme IT-BC-3, field BIT, 1st year of study, Compulsory