This document outlines a course of calculus for IT students at Lobachevsky State University of Nizhni Novgorod. The course is divided into 3 terms covering sequences, differential calculus, integral calculus, and series. Tests and exams are given throughout each term to assess student competency in mathematical thinking and problem solving. The course aims to develop skills in applying modern mathematical tools. Plans are discussed to modernize the course by adding an introductory section to address low student preparation, using online tools like METAMATH to support independent work, and testing key concepts to address educational problems.

1. 1
A COURSE
OF CALCULUS
FOR IT-STUDENTS
Kuzenkov Oleg,
Department of Computer Mathematics and Cybernetics

2. 1. MODULE “CALCULUS”
2. TARGET COMPETENCIES
3. CONTENT OF MODULE
4. PLAN OF MODIFICATION
5. ASSESSMENTS
OUTLI NE
2
OUTLINE

3. 3
UNN educational standard
• Lobachevsky State University of Nizhni Novgorod as a National
Research University has been granted the right to develop its own
self-imposed educational standards (SIES).
• In 2010, the first UNN standard was developed in the area of
studies "010300 Fundamental Computer Science and Information
Technology (FCSIT)" (Bachelor's degree)
• In 2011, the second UNN standard was developed in the area of
studies "Applied Computer Science" (ACS) (Bachelor's degree).

4. • In 2014, UNN educational program in the area of studies "010300
Fundamental Computer Science and Information Technology (FCSIT)"
(Bachelor's degree) received the accreditation of Russian Engineer
Education Assosiation (АИОР)
• As a rule, UNN IT-students learn in 3 groups with 25 students in each one.
• Moreover, there is one group with 20 foreign students (Asia, Africa), which
learn in English
• In 2014, e-learning program has started in UNN (3 students)
FCSIT program in UNN

5. 5
Module “Calculus”
Module “Calculus” is the part of the curriculum in the area of studies
"010300 Fundamental Computer Science and Information
Technology (FCSIT)" (Bachelor's degree)
A credit cost of the module is 20 credit units (ECTS) or 720 hours:
• Lectures 206 hours
• Seminars 188 hours
• Independent work 326 hours

6. 6
TARGET COMPETENCIES
The study of module “Calculus” is aimed at the formation of two
competencies GCC1 and PC3:
• Ability to understand and apply modern mathematical means in a
research and applied activity (PC3 level 2)
• Ability to use basic analysis tools and their application in real situations
(GCC1 level 2)
The content of these competencies is determined by competence maps
and corresponds to General SEFI Competencies
1. Thinking mathematically
2. Reasoning mathematically
3. Posing and solving mathematical problems
4. Modelling mathematically
5. Representing mathematical entities
6. Handling mathematical symbols and formalism
7. Communicating in, with, and about mathematics
8. Making use of aids and tools

7. 7
CONTENT OF THE COURSE
• This module is studied by IT-students during 3 terms (from the
first to third terms) in the beginning of learning.
• In module “Calculus” the students study the fundamental methods
of an investigation of the variables by means of an analysis of
infinitesimals. The base of this course is the theory of differential
and integral calculus.
• A brief content of this module is differential and integral calculus
for the functions of one and several real variables and theory of
series.

8. 8
No
.
Section of course Term Hours
Lectures+Seminars
+Independent work
1 Introduction. Real numbers. 1 6+2+5
2 Definition of function. Basic elementary
functions.
1 8+3+4
3 Number sequence. Countable and non-
countable sets. Open and closed sets.
1 20+18+20
4 Function limit. 1 6+9+10
5 Continuous functions. 1 6+2+10
6 Derivative of function. 1 8+8+16
7 Properties of differentiable functions. 1 22+16+20
CONTENT OF TERM 1
Exam – 35 hours
The content of 1 term is sequences and differential calculus for a function of
one variable

9. 9
No. Section of course Term Hours
Lectures+Seminars
+Independent work
1 Indefinite integral 2 12+12+12
2 Definite integral 2 7+7+7
3 Application of definite integral 2 6+6+6
4 Function of several variables and limits 2 7+7+7
5 Continuous functions of several variables 2 3+3+4
6 Differentiation of functions of several
variables
2 8+8+8
7 Implicit function 2 5+5+5
8 Extremum of function of several variables 2 6+6+6
CONTENT OF TERM 2
Exam – 36 hours
The content of 2 term is integral calculus for a function of one variable and
differential calculus for a function of several variables

10. 10
CONTENT OF TERM 3
No. Section of course Term Hours
Lectures+Seminars
+Independent work
1 Multiple integral 3 12+12+12
2 Number series 3 16+16+16
3 Functional series and sequences 3 8+8+8
4 Power series 3 10+10+10
5 Improper integral 3 10+10+10
6 Fourier series 3 8+8+8
7 Line integral 3 8+8+8
8 Surface integral 3 4+4+7
Exam – 36 hours
The content of 3 term is series and integral calculus for a function of several
variables

11. 11
Comparing with SEFI Core zero
SEFI standard UNN
Core zero
Functions and their inverses
Progressions, binomial expansions
Logarithmic and exponential functions
Rates of change and differentiation
Maximum and minimum values
Indefinite integral
Definite integral, applications
Proof
level
input
input
input
input
input
input
input
input
SEFI Core zero level corresponds to the input level of UNN students

12. 12
SEFI UNN
Core level 1
Hyperbolic functions
Rational functions
Functions
Differentiations
Sequences and series
Methods of integration
Application of integration
Term
1
1
1
1
1
2
2
Comparing with SEFI Core level 1
SEFI Core level 1 corresponds to the content of 1 and 2 terms

13. 13
SEFI UNN
Level 2
Function of several variables
Fourier series
Double integrals
Further multiple integrals
Vector calculus
Line and surface integrals
Non-linear optimization
Laplace transforms
Z-transforms
Complex functions
Complex series and contour integrals
Term
2
3
3
3
3
3
2
-
-
-
-
Comparing with SEFI level 2
SEFI level 2 corresponds to the content of 2 and 3 terms. Some sections of
level 2 are studied in other courses (complex analysis).
SEFI level 3 corresponds to the master level of UNN students. Sections of level
3 aren’t studied in module “Calculus”.

14. 14
The main problems
of the mathematical education
• Low input level of students
• Reducing the volume of mathematical courses
• The need of the methodical support of the independent work
• The need of e-learning
It is necessary to modernize the module to solve these problems.
METAMATH is an important tool for the modification of the module.

15. 15
Plan of modification
• The first step of the modification plan is to include new section “Elementary
Mathematics” at the beginning of module “Calculus”
• The content of the section corresponds to SEFI Core zero:
Functions and their inverses
Progressions, binomial expansions
Logarithmic and exponential functions
Proof
• Testing students at the end of the section study (including the use of
METAMATH)
This step allows to solve the first problem: low input level of students

16. 16
Plan of modernizing
• The second step of the modification plan is the effective use of the
independent work of students during a term (including the use of
METAMATH)
• The independent work must be accompanied by regular mandatory testing
students during the term (including the use of METAMATH)
• The third step is the independent study some sections of the second level
Further multiple integrals
Vector calculus
Line and surface integrals
• Mandatory testing students at the end of these sections study (including
using METAMATH)
• These steps may be useful for solving our educational problems

17. 17
ASSESSMENTS
Tests and exams are conducted some times per each term in written,
electronic, and oral forms.
There are the following types of assessment used in UNN:
positive (perfect, excellent, very good, good, satisfactory);
negative (unsatisfactory, poor).
"Perfect" – the student displays in-depth knowledge of the main and
additional material without any mistakes and errors, can solve non-
standard problems, has acquired all the competences (parts of
competences) relating to the given subject in a comprehensive
manner and above the required level. A stable system of
competences has been formed, interrelation with other
competences is manifested

18. 18
• "Excellent" – the student displays in-depth knowledge of the main material
without any mistakes and errors, has acquired all the competences (parts of
competences) relating to the given subject completely and at a high level, a
stable system of competences has been formed;
• "Very good" – the student has sufficient knowledge of the main material with
some minor mistakes, can solve standard problems and has acquired
completely all the competences (parts of competences) relating to the given
subject;
• "Good" – the student has the knowledge of the main material with some
noticeable mistakes and has acquired in general the competences (parts of
competences) relating to the given subject);
• "Satisfactory" – the student has the knowledge of the minimum material
required in the given subject, with a number of errors, can solve main
problems, the competences (parts of competences) relating to the subject
are at the minimum level required to achieve the main learning objectives;
• "Unsatisfactory" – the knowledge of the material is insufficient, additional
training is required, the competences (parts of competences) relating to the
subject are at a level that is insufficient to achieve the main learning
objectives;
• "Poor" – lack of knowledge of the material, relevant competences have not
been acquired.
ASSESSMENTS

19. THANK YOU FOR YOUR ATTENTION
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