Course Syllabus

Course Code: __ MCM 103

Department: __ Mathematics and Natural Sciences______________________________
Course Title: __Calculus 1_______________________________________________
Semester: __ 1_____________________________________________________
Credits/ECTS: __5_____________________________________________________

Degree Cycle (Level): __Bachelor________________________________________________

Course Type: __Compulsary_____________________________________________
Language of Instruction:_English ________________________________________________

Requisites

The table below is automatically filled in if it is included in the Education Program

Type Program Educational program Course Title Consent status

Code

● AR 10XXX

● CR (Co- Calculus 2
requisite)

● PR
(Prerequisite)

Programmes on which course is available

If your course is taught in another Educational Program, that Educational Program

automatically will be displayed in this table

Program Program Title Degree Program Learning

Code Outcome

● LO1

● LO2
 Mode of Delivery

● On campus

Course Description
The course includes: functions, limits of functions, continuity, derivatives, applications of
derivatives, extreme values of functions, graphing by the first and second derivatives, graphing
rational functions: asymptotes and dominant terms, integration, indefinite integrals, techniques of
integration, the existence of definite integrals, the fundamental theorem of calculus, application
of integrals.

Instructor (s)

Name Surname Degree Contact information

Aiman Shakulikova Candidate of Science aiman.shakulikova@sdu.edu.kz

Kuralay Apseit

Skills and competences

Academic skills Subject-specific skills

Mastering mathematical modes of thought; Students should understand concept of function

of one single and be able to sketch graphs of the
common functions;

Solving different kinds of mathematical Students will be able to investigate functions

problems (pure or applied); using the first and second derivatives and sketch
their graphs

Distinguishing between different kinds of Students should understand concept of the

mathematical statements (including definite integral and be able to find definite
integral using different methods and prove main
conditioned assertions (‘if-then’), definitions, properties of them;
theorems, conjectures, cases);

Uncovering the basic ideas in a given argument Students will be able to apply the concept of
derivative for solving extreme problems;
(especially a proof), ideas from technicalities;

Weekly course plan

№ Topics Activity
1 Functions and their graphs. [1]: Sec 1.1, 1.2, 1.6
Common functions. Combining functions, shifting and Homework
scaling graphs. Inverse functions
2 Limits of a function and limit laws. One-sided limits. [1]: Sec 2.2, 2.3, 2.4
Homework
3 Continuity. Limits involving infinity, asymptotes of graphs [1]: Sec 2.5, 2.6
Homework, quiz
4 Tangents and the derivative at a point, The derivative as a [1]: Sec 3.1, 3.2, 3.6
function. Differentiation rules. The derivative as a rate of Homework
change. The Chain rule. Second and higher order derivatives
5 Implicit differentiation. Derivatives of inverse functions and [1]: Sec 3.7, 3.8, 3.11
logarithms. Linearization and differentials Homework
6 Applications of derivatives. [1]: Sec 4.2, 4.3
Extreme values of functions. The mean value theorem. Homework, quiz
Monotonic functions and the first derivative test
7 Concavity and curve sketching. Indeterminate forms and [1]: Sec 4.4, 4.5
L’Hopital’s rule
7 Midterm 1 Midterm quiz

8 Indefinite integrals. Antiderivatives. Techniques of [1]: Sec 4.8, 5.5

integration, basic Integration formulas. Substitution method Homework
and integration by parts.
9- Trigonometric integrals, trigonometric substitutions, [1]: Sec 8.1, 8.2, 8.4
10 integration of rational functions by partial fractions Homework, quiz
11 Area and estimating with finite sums. The definite integral. [1]: Sec 5.2, 5.3, 5.4
The fundamental theorem of calculus. Substitution and area Homework
between curves.

12- Applications of definite integrals. Volumes using cross- [1]: Sec 5.6, 6.1, 6.2
13 sections, arc length. Areas of surfaces of revolution Homework
[1]: Sec 6.3, 6.4, 11.1, 11.2
Homework, quiz
14 Numerical integration and improper integrals [1]: Sec 8.6, 8.7
Homework
15 Preparations. Final Exam

Course Learning Outcomes

№ Active verbs What will be How this learning outcome
done/produced will be achieved
1 State and explain Students will be able to Students should attach
state the concepts of the importance to the definitions
 indefinite and definite of the indefinite and definite
integrals explain their integrals.
meanings.
2 Apply Students will be able to Students should put together
apply main methods of all main methods of
integration. integration derived in class.
3 Prove Students will be able to Students should attach
obtain main properties of importance to the definition
the definite integrals. of the definite integral.
4 Prove Students will be able to Students should attach
state and prove the basic importance to the main
theorems considered in concepts and their definitions
the course. and properties.
5 Test Students will be able to Students should put together
investigate functions all tests for monotonicity and
using the first and second concavity and asymptotes.
derivatives.
6 Apply Students will be able to Students should attach
find the areas, volumes importance to the definitions
and length of the lines and properties of the definite
using definite integrals. integral.

Planned Learning Activities and Teaching Method

● Lecture
● Questions & Answer
● Discussion
● Problem Solving
● Other
*if other _______________________

Reading List

If the number of Required / Recommended / Other reading list is more than one, you
can add a line below
Type Author Title Publishing ISBN Publisher/
year Web site
● Required Joel Hass, Thomas’ Calculus 2004 Pearson
Christopher
Heil, Maurice
Weir

● Required Stewart James Calculus 2012 USA

 ● Required Рябушкo Индивидуальные 2003 Минск
А.П. задания по высшей
математике. Часть
1-3

● Other

Assessment Methods and Criteria

The University’s normative rules regarding assessment apply. See the Code of Practice on
Assessments.
These norms set the boundary conditions for all instructors of University.

If the pre-final grade is more than one, you can insert a row below in the table.
Assessment Description Quantity %

● Pre-final Quiz 2 10

● Pre-final Midterm 1 1 15

● Pre-final Midterm 2 1 15

● Pre-final Activity 11 10

● Pre-final Home work 12 10

● Final Writing - oral final 1 40

work

Total 100 100

THE FORM THE SCHEDULE OF PERFORMANCE AND DELIVERY OF

WORKS
№ Type of Week Total
evaluation 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
1 Activity * * * * * * * * * * * 10

2 Home work * * * * * * * * * * * * 10
3 Quiz * * 10
4 Mid-term exam * * 30
5 Final exam * 40
6 Active * * * * * * * * * * * * * * * 10
 participation bonus
Total 100

Student Workload
* Student workload filling example
Resource

Academic Integrity

Students must ensure that all work completed for this course is their own work. Any evidence of
plagiarism, data falsification, fabrication, collusion, self-plagiarism and/or other forms of
academic misconduct will be punished. Further, information can be found in the Code of Practice
on Academic Integrity.

Late/Non Submission and Attendance Policy

Academic excellence and high achievement are only possible in an environment where the
highest standards of academic honesty and integrity are maintained: students at SDU must ensure
they adhere to this requirement. Active participation is an integral part of teaching and learning
at SDU. Therefore, regular class attendance is required of all students and records of any
absences are kept for each class: a student whose attendance falls below 70% will fail the course.
Students are also expected to be in class on time: poor punctuality is seen as being discourteous
to the teacher and other students, therefore repeat incidences of late arrivals are subject to a
penalty. The use of electronic devices (e.g.: computers, tablets, phones) is only permitted upon
tutor instruction. Any other activities (e.g.: texting, surfing, gaming, social emails, online
shopping...etc.) are strictly forbidden during class time. Students found to be engaged in any
non-class activity may lose marks for overall participation.

Course Specific Policy

The instructor reserves the right to use pre-final grades for the final assessment, if such a need arises .
There is required to attend no less than 70% of all sessions.

Approved by Head of Department

Bayan Bekbolat________________________________________________________________