Title:

Mathematical Analysis

Code:IMA
Ac.Year:2017/2018
Term:Summer
Curriculums:
ProgrammeFieldYearDuty
IT-BC-3BIT1stCompulsory
Language of Instruction:Czech
Credits:6
Completion:examination (written)
Type of
instruction:
Hour/semLecturesSem. ExercisesLab. exercisesComp. exercisesOther
Hours:39100106
 ExaminationTestsExercisesLaboratoriesOther
Points:60010030
Guarantor:Krupková Vlasta, RNDr., CSc., DMAT
Lecturer:Hliněná Dana, doc. RNDr., Ph.D., DMAT
Krupková Vlasta, RNDr., CSc., DMAT
Instructor:Fuchs Petr, RNDr., Ph.D., DMAT
Fusek Michal, Ing., Ph.D., DMAT
Hliněná Dana, doc. RNDr., Ph.D., DMAT
Krupková Vlasta, RNDr., CSc., DMAT
Novák Michal, RNDr., Ph.D., DMAT
Šafařík Jan, Mgr. et Mgr., FEEC
Faculty:Faculty of Electrical Engineering and Communication BUT
Department:Department of Mathematics FEEC BUT
Prerequisites: 
Discrete Mathematics (IDA), DMAT
Follow-ups:
Numerical Methods and Probability (INM), DMAT
Schedule:
DayLessonWeekRoomStartEndLect.Gr.St.G.EndG.
Monexam - Náhradní pszk2018-04-16A11210:0010:50
Wedexam - předtermín (min. 30 bodů ze cv.)2018-05-02T12/2.17309:0011:501BIA
Wedexam - předtermín (min. 30 bodů ze cv.)2018-05-02T12/2.17309:0011:501BIB
Wedexam - předtermín (min. 30 bodů ze cv.)2018-05-02T12/2.17309:0011:502BIA
Wedexam - předtermín (min. 30 bodů ze cv.)2018-05-02T12/2.17309:0011:502BIB
Wedexam - 1. oprava Út 11:00-12:50 Fuchs2018-05-30T8/01011:0013:501BIB3839
Wedexam - 1. oprava Út 11:00-12:50 Fusek2018-05-30T8/01011:0013:501BIB4041
Wedexam - 1. oprava Po 14:00 -15:50 Fusek2018-05-30D10511:0013:501BIA1415
Wedexam - 1. oprava Po 16:00 - 17:50 Fusek2018-05-30D10511:0013:501BIA1617
Wedexam - 1. oprava Pá 09:00-12:50 Hliněná2018-05-30D10511:0013:501BIA1013
Wedexam - 1. oprava St 14:00 -15:50 Fuchs2018-05-30D10511:0013:501BIA1819
Wedexam - 1. oprava St 16:00 -17:50 Fuchs2018-05-30D10511:0013:501BIA2021
Wedexam - 1. oprava2018-05-30D10511:0013:502BIA
Wedexam - 1.oprava Út 11-12:50 Fusek+Fuchs2018-05-30T8/01011:0013:502BIB
Wedexam - 1. oprava St 08-09:50 Krupková2018-05-30T8/02011:0013:501BIB3233
Wedexam - 1. oprava St 10-11:50 Krupková2018-05-30T8/02011:0013:501BIB3031
Wedexam - 1. oprava St 10-11:50 Fusek2018-05-30T8/02011:0013:501BIB3637
Wedexam - 1. opr. St 8-12 Krup.+10-12 Fus.2018-05-30T8/02011:0013:502BIB
Thuexam - řádná Út 11:00-12:40 Fuchs2018-05-10T10/1.3611:0013:501BIB3839
Thuexam - řádná Út 11:00-12:40 Fusek+Fuchs2018-05-10T10/1.3611:0013:502BIB
Thuexam - řádná Po 16:00-17:40 Fusek2018-05-10D10511:0013:501BIA1617
Thuexam - řádná Po 16-17:40 Fusek + Pá2018-05-10D10511:0013:502BIA
Thuexam - řádná St 14:00-15:40 Fuchs2018-05-10D020611:0013:501BIA1819
Thuexam - řádná Po 14:00-15:40 Fusek2018-05-10D020711:0013:501BIA1415
Thuexam - řádná Út 11:00-12:40 Fusek2018-05-10T10/1.3611:0013:501BIB4041
Thuexam - řádná St 8:00-9:40 Krupková2018-05-10T12/2.17311:0013:501BIB3233
Thuexam - řádná St 8-11:40 Krupková+Fusek2018-05-10T12/2.17311:0013:502BIB
Thuexam - řádná St 10:00-11:40 Krupková2018-05-10T12/2.17311:0013:501BIB3031
Thuexam - řádná St 10:00-11:40 Fusek2018-05-10T12/2.17311:0013:501BIB3637
Thuexam - řádná Pá 9:00-12:40 Hliněná2018-05-10D10511:0013:501BIA1011
Thuexam - řádná Pá 11:00-12:40 Hliněná2018-05-10D10511:0013:501BIA1213
Thuexam - řádná Po 14:00-15:40 Fusek2018-05-10D020711:0013:502BIA
Thuexam - řádná St 14:00 - 17:40 Fuchs2018-05-10D020611:0013:502BIA
Thuexam - řádná St 16:00-17:40 Fuchs2018-05-10D020611:0013:501BIA2021
Friexam - 2. oprava2018-06-08T12/2.17311:0013:501BIB
Friexam - 2. oprava2018-06-08T12/2.17311:0013:502BIB
Friexam - 2. oprava2018-06-08D020611:0013:501BIA
Friexam - 2. oprava2018-06-08D020611:0013:502BIA
 
Learning objectives:
  The main goal of the calculus course is to explain the basic principles and methods of higher mathematics that are necessary for the study of computer science. The practical aspects of applications of these methods and their use in solving concrete problems (including the application of contemporary mathematical software in the laboratories) are emphasized.
Description:
  Limit and continuity, derivative of a function. Partial derivatives. Basic differentiation rules. Elementary functions. Extrema for functions (of one and of several variables). Indefinite integral. Techniques of integration. The Riemann (definite) integral. Multiple integrals. Applications of integrals. Infinite sequences and infinite series. Taylor polynomials.
Knowledge and skills required for the course:
  Secondary shool mathematics and the kowledge from Discrete Mathematics course.
Learning outcomes and competences:
  The ability of orientation in the basic problems of higher mathematics and the ability to apply the basic methods. Solving problems in the areas cited in the annotation above by using basic rules. Solving these problems by using modern mathematical software.
Syllabus of lectures:
 
  1. Function of one variable, limit, continuity.
  2. Differential calculus of functions of one variable I: derivative, differential, Taylor theorem.
  3. Differential calculus of functions of one variable II: maximum, minimum, behaviour of the function.
  4. Integral calculus of functions of one variable I: indefinite integral, basic methods of integration.
  5. Integral calculus of functions of one variable II: definite Riemann integral and its application.
  6. Infinite number and power series.
  7. Taylor series.
  8. Functions of two and three variables, geometry and mappings in three-dimensional space.
  9. Differential calculus of functions of more variables I: directional and partial derivatives, Taylor theorem.
  10. Differential calculus of functions of more variables II: funcional extrema, absolute and bound extrema.
  11. Integral calculus of functions of more variables I: two and three-dimensional integrals.
  12. Integral calculus of functions of more variables II: method of substitution in two and three-dimensional integrals.
Syllabus of numerical exercises:
 The class work is prepared in accordance with the lecture.
Syllabus of computer exercises:
 Trained tasks are prepared to follow and complete study matter from lectures and seminar practice.
Syllabus - others, projects and individual work of students:
 
  • Limit, continuity and derivative of a function. Partial derivative. Derivative of a composite function.
  • Differential of function of one and several variables. L'Hospital's rule. Behaviour of continuous and differentiable function. Extrema of functions of one and several variables.
  • Primitive function and undefinite integral. Basic methods of integration. Definite one-dimensional and multidimensional integral.
  • Methods for solution of definite integrals (Newton-Leibnitz formula, Fubini theorem).
  • Indefinite number series. Convergence of series. Sequences and series of functions. Taylor theorem. Power series.
Fundamental literature:
 
  • Edwards, C.H., Penney, D.E., Calculus with Analytic Geometry, Prentice Hall, 1993.
  • 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), Mc Graw-Hill Publ. Comp., 1990.
  • Thomas, G.B., Finney, R.L., Calculus and Analytic Geometry, Addison-Wesley Publ. Comp., 1994.
  • Zill, D.G., A First Course in Differential Equations, PWS-Kent Publ. Comp., 1992.
Study literature:
 
  • Brabec B., Hrůza,B., Matematická analýza II, SNTL, Praha, 1986.
  • Švarc, S. a kol., Matematická analýza I, PC DIR, Brno, 1997.
  • Krupková, V. Matematická analýza pro FIT, electronical textbook, 2007.
Progress assessment:
  Practice tasks: 28 points.
Homeworks: 12 points.
Semestral examination: 60 points.
 

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