Course details

# Mathematical Analysis 1

IMA1 Acad. year 2023/2024 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

Learning objectives

The main goal of the course is to explain the basic principles and methods of calculus. The emphasis ismput on handling the practical use of these methods for solving specific tasks and the ability to understand the basic problems of calculus and use derivatives and integrals for solving specific problems.

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.

Recommended prerequisites

Prerequisite knowledge and skills

Secondary school mathematics.

Study literature

• 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. Indefinite integral, basic methods of integration.
8. Definite Riemann integral, its applications.
9. Improper integral.
10. Numerical integration.
11. Numerical solutions of equations.
12. Interpolation and approximation.

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 20 points). Classes are compulsory. Presence at lectures will not be controlled, absence at numerical classes has to be excused.

Exam prerequisites

The condition for receiving the credit is obtaining at least 8 points from the tests during the semester and active work at classes.

Schedule

DayTypeWeeksRoomStartEndCapacityLect.grpGroupsInfo
Mon exercise 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures T8/T 5.22 08:0009:5050 1BIA 1BIB 2BIA 2BIB xx Fusek
Mon lecture 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures D105 09:0010:50316 1BIB 2BIA 2BIB 30 - 49 xx Fuchs
Mon exercise 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. 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., 10., 11., 12., 13. of lectures D0207 11:0012:5060 1BIA 1BIB 2BIA 2BIB xx Fuchs | Cvičení je určeno pouze pro studenty, kteří navštěvují přednášku od 9 hodin, protože na tuto přednášku přímo navazuje.
Mon exercise 1., 2., 3., 4., 5., 6., 7., 8., 10., 11., 12., 13. of lectures T8/T 5.22 16:0017:5050 1BIA 1BIB 2BIA 2BIB xx Polický
Tue exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures T8/T 5.22 10:0011:5050 1BIA 1BIB 2BIA 2BIB xx Fusek
Tue exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures T8/T 5.22 12:0013:5050 1BIA 1BIB 2BIA 2BIB xx Fusek
Tue lecture lectures D0206 D105 13:0014:50500 1BIA 2BIA 2BIB 10 - 29 xx Hliněná
Tue exercise 1., 2., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 15:0016:5064 1BIA 1BIB 2BIA 2BIB xx Hliněná
Tue exercise *) lectures A113 17:0018:500 1BIA 1BIB 2BIA 2BIB xx Hliněná
Wed exercise *) 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures T8/T 5.22 08:0009:500 1BIA 1BIB 2BIA 2BIB xx Tůma
Wed exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures D0207 10:0011:5060 1BIA 1BIB 2BIA 2BIB xx Hliněná
Wed exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures T8/T 5.22 10:0011:5050 1BIA 1BIB 2BIA 2BIB xx Fuchs
Wed exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures D0207 14:0015:5062 1BIA 1BIB 2BIA 2BIB xx Hlavičková
Wed exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures A113 16:0017:5060 1BIA 1BIB 2BIA 2BIB xx Polický
Thu exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 08:0009:5060 1BIA 1BIB 2BIA 2BIB xx Fusek
Thu exercise 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12., 13. of lectures A113 10:0011:5060 1BIA 1BIB 2BIA 2BIB xx Fusek
Thu exam 2024-05-09 Aula profesora Braunera Aula profesora Kalendovského D0206 D105 E112 T12/SF 1.141 T12/SF 2.162 T8/T 0.10 T8/T 0.20 T8/T 0.30 13:3015:30 1. termín
Thu exercise 1., 2., 3., 4., 5., 6., 7., 8., 9., 10., 11., 12. of lectures A113 14:0015:5060 1BIA 1BIB 2BIA 2BIB xx Polický
Thu exercise *) lectures T8/T 5.22 16:0017:500 1BIA 1BIB 2BIA 2BIB xx Fuchs
Fri exercise 1., 2., 3., 4., 5., 6., 7., 9., 10., 11., 12., 13. of lectures T8/T 5.22 08:0009:5050 1BIA 1BIB 2BIA 2BIB xx Tůma
Fri exercise 1., 2., 3., 4., 5., 6., 7., 9., 10., 11., 12., 13. of lectures T8/T 5.22 10:0011:5050 1BIA 1BIB 2BIA 2BIB xx Tůma
Fri exam 2024-05-24 Aula profesora Kalendovského D0206 D105 E112 T12/SF 1.141 T8/T 0.10 T8/T 0.20 T8/T 0.30 13:3015:30 2. termín
Fri exam 2024-06-07 Aula profesora Braunera Aula profesora Kalendovského T12/SF 1.141 T12/SF 2.162 T8/T 0.10 T8/T 0.20 T8/T 0.30 14:0016:00 3. termín
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