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A COURSE OF CALCULUS FOR IT-STUDENTS

Kuzenkov Oleg,

Department of Computer Mathematics and Cybernetics

1. MODULE “CALCULUS” 2. TARGET COMPETENCIES3. CONTENT OF MODULE4. PLAN OF MODIFICATION5. ASSESSMENTS

OUTLINE

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OUTLINE

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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).

• 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

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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

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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 mathematically2. Reasoning mathematically3. Posing and solving mathematical problems4. Modelling mathematically5. Representing mathematical entities6. Handling mathematical symbols and formalism7. Communicating in, with, and about mathematics8. Making use of aids and tools

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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.

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No.

Section of course Term HoursLectures+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+167 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

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No. Section of course Term HoursLectures+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

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CONTENT OF TERM 3

No. Section of course Term HoursLectures+Seminars+Independent work

1 Multiple integral 3 12+12+12

2 Number series 3 16+16+163 Functional series and sequences 3 8+8+8

4 Power series 3 10+10+105 Improper integral 3 10+10+106 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

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Comparing with SEFI Core zero

SEFI standard UNN

Core zeroFunctions and their inversesProgressions, binomial expansionsLogarithmic and exponential functionsRates of change and differentiationMaximum and minimum valuesIndefinite integralDefinite integral, applicationsProof

levelinputinput inputinputinputinputinputinput

SEFI Core zero level corresponds to the input level of UNN students

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SEFI UNN

Core level 1Hyperbolic functionsRational functionsFunctionsDifferentiationsSequences and seriesMethods of integrationApplication of integration

Term11 11122

Comparing with SEFI Core level 1

SEFI Core level 1 corresponds to the content of 1 and 2 terms

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SEFI UNN

Level 2Function of several variablesFourier seriesDouble integralsFurther multiple integralsVector calculusLine and surface integralsNon-linear optimizationLaplace transformsZ-transformsComplex functionsComplex series and contour integrals

Term23 33332- - - -

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”.

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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.

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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 inversesProgressions, binomial expansionsLogarithmic and exponential functionsProof

• 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

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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 levelFurther multiple integralsVector calculusLine 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

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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

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• "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

THANK YOU FOR YOUR ATTENTION

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