Course details

Calculus 1

IMA1 Acad. year 2020/2021 Summer semester 4 credits

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

Guarantor

Fuchs Petr, RNDr., Ph.D. (DMAT FEEC BUT)

Deputy Guarantor

Language of instruction

Czech

Completion

Credit+Examination (written)

Time span

26 hrs lectures, 26 hrs exercises

Assessment points

80 exam, 20 exercises

Department

Department of Mathematics (DMAT FEEC BUT)

Lecturer

Instructor

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.

Prerequisite kwnowledge and skills

Secondary school mathematics.

Study literature

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

Fundamental literature

  • Knichal, V., Bašta, A., Pišl, M., Rektorys, K., Matematika I, II, SNTL Praha, 1966. (in Czech).
  • 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.

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. Numerical integration.
  11. Improper integral.

Syllabus of numerical exercises

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

Progress assessment

Home assignments during the semester.

Controlled instruction

Classes are not compulsory.

Exam prerequisites

The condition for receiving the credit is obtaining at least a given minimum of points from the activities during the semester.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Monexerciselectures T8/522 08:0009:50 1BIA 1BIB 2BIA 2BIB xx Fusek
Monlecturelectures D105 09:0010:50 1BIB 2BIA 2BIB xx Fuchs
Monlecturelectures D105v 09:0010:50 FIT YT, ZP; Fuchs
Monexerciselectures T8/522 10:0011:50 1BIA 1BIB 2BIA 2BIB xx Fusek
Monexerciselectures D0207 11:0012:50 1BIA 1BIB 2BIA 2BIB xx Fuchs
Monexerciselectures T8/522 16:0017:50 1BIA 1BIB 2BIA 2BIB xx Vítovec
Tueexerciselectures T8/522 12:0013:50 1BIA 1BIB 2BIA 2BIB xx Fusek
Tueexercise1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 13. of lectures A113v 13:0014:50YT, ZP, bez projekce; Hliněná
Tuelecturelectures D0206 D105 13:0014:50 1BIA 2BIA 2BIB xx Hliněná
Tueexerciselectures A113 15:0016:50 1BIA 1BIB 2BIA 2BIB xx Hliněná
Tueexercise5., 7., 9., 10. of lectures A113v 15:0016:50YT, ZP, bez projekce; Hliněná
Wedexerciselectures A113 10:0011:50 1BIA 1BIB 2BIA 2BIB xx Hliněná
Wedexerciselectures A113v 10:0011:50YT, ZP, bez projekce; Hliněná
Wedexerciselectures T8/522 10:0011:50 1BIA 1BIB 2BIA 2BIB xx Fuchs
Wedexerciselectures D0207 14:0015:50 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Wedexerciselectures D0207 16:0017:50 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Thuexerciselectures A113 08:0009:50 1BIA 1BIB 2BIA 2BIB xx Fusek
Thuexerciselectures A113 10:0011:50 1BIA 1BIB 2BIA 2BIB xx Fusek
Thuexerciselectures A113 14:0015:50 1BIA 1BIB 2BIA 2BIB xx Hliněná
Thuexerciselectures T8/522 16:0017:50 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Friexercise2021-04-30 A113v 10:0011:50YT, ZP, bez projekce; Hliněná

Course inclusion in study plans

  • Programme BIT, 1st year of study, Compulsory
  • Programme IT-BC-3, field BIT, 1st year of study, Compulsory
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