Course details

# Selected Parts from Mathematics 1

IVP1 FEEC BUT BPC-VPA Acad. year 2019/2020 Winter semester 5 credits

The aim of this course is to introduce the basics of calculation of improper multiple integral and basics of solving of linear differential equations using delta function and weighted function.
In the field of improper multiple integral, the main attention is paid to calculations of improper multiple integrals on unbounded regions and from unbounded functions.
In the field of linear differential equations, the following topics are covered: Eliminative solution method, a method of eigenvalues and eigenvectors, method of variation of constants, a method of undetermined coefficients, the stability of solutions.

Guarantor

Deputy Guarantor

Rebenda Josef, Mgr., Ph.D. (CEITEC BUT)

Language of instruction

Czech

Completion

Examination (written)

Time span

26 hrs lectures, 12 hrs exercises, 14 hrs pc labs

Assessment points

70 exam, 30 half-term test

Department

Lecturer

Instructor

Subject specific learning outcomes and competences

Students completing this course should be able to:
• calculate improper multiple integral on unbounded regions and from unbounded functions.
• apply a weighted function and a delta function to solving of linear differential equations.
• select an optimal solution method for the given differential equation.
• investigate the stability of solutions of systems of differential equations.

Learning objectives

The aim of this course is to introduce the basics of improper multiple integrals, systems of differential equations including of investigations of stability of solutions of differential equations and applications of selected functions with solving of dynamical systems.

Why is the course taught

The course provides students basic orientation in differential and integral calculus of functions of several variables that are necessary for the description of the behaviour of the scalar and vector-valued fields and as well for determination of characteristics of vector-valued random variables.

Prerequisite kwnowledge and skills

The student should be able to apply the basic knowledge of analytic geometry and mathematical analysis on the secondary school level: to explain the notions of general, parametric equations of lines and surfaces and elementary functions. From the BMA1 and BMA2 courses, the basic knowledge of differential and integral calculus and solution methods of linear differential equations with constant coefficients is demanded. Especially, the student should be able to calculate derivative (including partial derivatives) and integral of elementary functions.

Fundamental literature

• ŠMARDA, Z., RUŽIČKOVÁ, I.: Vybrané partie z matematiky, el. texty na PC síti. (CS)
• KRUPKOVÁ, V.: Diferenciální a integrální počet funkce více proměnných,skripta VUT Brno, VUTIUM 1999, 123s. (CS)
• BRABEC, J., HRUZA, B.: Matematická analýza II,SNTL/ALFA, Praha 1986, 579s. (CS)
• GARNER, L.E.: Calculus and Analytical Geometry. Brigham Young University, Dellen publishing Company, San Francisco,1988, ISBN 0-02-340590-2.

Syllabus of lectures

1. Basic properties of multiple integrals.
2. Improper multiple integral
3. Impulse function and delta function, basic properties
4. Derivative and integral of the delata function
5. Unit function and its relation with the delta function, the weighted function
6. Solving differential equations of the n-th order using weighted functions
7. The relation between Dirac function and weighted function
8. Systems of differential equations and their properties
9. Eliminative solution method
10. Method of eigenvalues and eigenvectors
11. Method of variation of constants and method of undetermined coefficients
12. Differential transformation solution method of ordinary differential equations
13. Differential transformation solution method of functional differential equations

Progress assessment

The student's work during the semestr (written tests and homework) is assessed by maximum 30 points.
Written examination is evaluated by maximum 70 points. It consist of seven tasks (one from improper multiple integral (10 points), three from application of a weighted function and a delta function (3 X 10 points) and three from analytical solution method of differential equations (3 x 10 points)).

Controlled instruction

Teaching methods include lectures and demonstration practises . Course is taking advantage of exercise bank and Maple exercises on server UMAT. Students have to write a single project/assignment during the course.
The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Schedule

DayTypeWeeksRoomStartEndLect.grpGroupsInfo
Monlecturelectures T8/010 09:0010:50 2BIA 2BIB 3BIT xx Šmarda
Monexerciseodd week T8/235 11:0012:50 2BIA 2BIB 3BIT xx Šmarda
Moncomp.labeven week T8/235 11:0012:50 2BIA 2BIB 3BIT xx Šmarda
Monexerciselectures T8/235 13:0014:50 2BIA 2BIB 3BIT xx Šmarda
Moncomp.labeven week T8/235 13:0014:50 2BIA 2BIB 3BIT xx Šmarda rezerva

Course inclusion in study plans

• Programme BIT, 2nd year of study, Elective
• Programme IT-BC-3, field BIT, 2nd year of study, Elective