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Ders Tanıtım Bilgileri (İngilizce)
DERS TANITIM BİLGİLERİ (İNGİLİZCE)
Course Information
Course
Name
Single
Variable
Calculus
Code Semester
Math
104
Spring
Theory
Application Laboratuary National ECTS
(Saat/Hafta) (Saat/hafta) (hours/week) Credit
3
2
0
4
6
Prequisites
Course
Language
Couse Type
Mode of
Delivery
(face to
face,
distance
learning)
Learning
and
Teaching
Strategies
Instructor(s)
Course
Objective
Math 103
English
Learning
Outcomes
1) use the fundamentals notions of functions,
2) understand limit of a function,
3) understand the derivative and take the derivative of a function,
4) understand the integral and take the integral of a function,
5) understand the applications of the derivative and the integral.
Course
Content
Review of Functions, Trigonometric Functions, Exponential and Logarithmic
Functions, Limit and Continuity, Derivative, Applications of the Derivative,
Definite and Indefinite Integrals, Techniques of Integration, Areas and
Volumes.
Course Book
B.E. Blank and S.G. Krantz, Single Variable Calculus, 2.ed., John Wiley & Sons,
Inc 2011.
Other Sources
1) J. Stewart, Single Variable Calculus: Early Transcendentals, Brooks Cole, 6
ed., 2007
2) Matematik II, Atılım Üniversitesi Matematik Bölümü Uzaktan Eğitim Ders
Notu
References
Compulsory
Face to face
Lecture, Question and Answer, Discussion, Problem Solving
The objective of this course is to recall and use the functions and their
properties, to teach the fundamental operations such as limit, derivative and
integral and their applications, also it is aimed to develop the problem solving
and analytic thinking skills of the student and to increase their ability to apply
problems to real life.
1
Ders Tanıtım Bilgileri (İngilizce)
Weekly Course outline
Weeks
Topics
1. Week
Review of Functions: Domain, Range of a function; Equal
functions; Examples of functions of a real variable,
piecewise-defined functions, graphs of functions,
sequences, combining functions
Inverse Functions: Onto, One-to-one Functions, The
Graph of the Inverse Function, Vertical and Horizontal
Translations, Even and Odd Functions, Parameterized
Curves and Graphs of Functions, Trigonometric functions
The concept of limit, Limit Theorems: One-sided limits,
Basic limit theorems, A rule that tells when a limit does
not exist, The Pinching Theorem, Some important
trigonometric limits, The definition of a continuous
function
Continuous Extensions, One-Sided Continuity, Some
Theorems about Continuity, Infinite Limits and
Asymptotes, Exponential Functions and Logarithms
Rates of Change and Tangent Lines, The Derivative, Rules
for Differentiation
Differentiation of Some Basic Functions, The Chain Rule,
Derivatives of Exponential Functions, Derivatives of
Inverse Functions
2. Week
3. Week
4. Week
5. Week
6. Week
Pre-study
pp.34-52
pp. 52-75
pp. 85-108
pp. 108-155
pp. 164-200
pp. 200-223
7. Week
Midterm
8. Week
Derivatives of Logarithms, Logarithmic Differentiation,
Higher Derivatives, Implicit Differentiation, Differentials pp. 223-253
and Approximation of Functions: Linearization,
Differentials
Inverse Trigonometric Functions, Derivatives of Inverse pp. 253-268,282-289
Trigonometric Functions, Related Rates
The Mean Value Theorem, Maxima and Minima of pp. 289-320
Functions, Applied Maximum-Minimum Problems
9. Week
10. Week
11. Week
Concavity, Graphing Functions, l’Hopital’s Rule
12. Week
Antidifferentiation and Applications: Indefinite Integral,
Rules for Integration, The Fundamental Theorem of
Calculus
Integration by Substitution, Calculating of Area,
Techniques of Integration: Integration by Parts
Techniques of Integration: Powers and Products of
Trigonometric Functions, Trigonometric Substitution,
Partial Fractions—Linear Factors
Techniques of Integration: Partial Fractions—Irreducible
Quadratic Factors, Applications of the Integral: Volumes
Final Exam
13. Week
14. Week
15. Week
16. Week
pp. 320-348
pp. 357-366, 399-417
pp. 428 - 446, 470-479
pp. 479-506
pp. 506-551
2
Ders Tanıtım Bilgileri (İngilizce)
Assesment methods
Course Activities
Number
Attendance
Laboratory
Application
Field Activities
Specific Practical Training (if any)
Assignments
Presentation
Projects
Seminars
Midterms
Final Exam
Percentage %
2
1
60
40
Total 3
100
60
Percentage of semester activities contributing grade
success
Percentage of final exam contributing grade success
40
100
Total
Course Category
Core Courses
Major Area Courses
Supportive Courses
Media and Management Skills Courses
Transferable Skill Courses
Workload and ECTS Calculation
Activities
Course Duration ( Including Exam Week:
16 x Total Hours)
Laboratory
Application
Specific practical training (if any)
Field Activities
Study Hours Out of Class (Preliminary
work, reinforcement, ect)
Presentation / Seminar Preparation
Projects
Homework assignment
Number
Duration
(Hours)
Total Work Load
16
3
48
14
2
28
14
4
56
3
Ders Tanıtım Bilgileri (İngilizce)
Midterms ( Study duration )
2
Final ( Study duration )
1
Total Workload
13
22
4
26
22
180
Matrix of the Course Learning Outcomes Versus Program Outcomes
Program Outcomes
1 Acquires skills to use the advanced theoretical and applied
knowledge obtained at the mathematics bachelors program to do
further academic and scientific research in both mathematics-based
graduate programs and public or private sectors.
2 Transplants and applies the theoretical and applicable knowledge
gained in their field to the secondary education by using suitable tools
and devices.
Contribution Level*
1
2
3
4
5
Ders Tanıtım Bilgileri (İngilizce)
3 Acquires the skill of choosing, using and improving problem solving
techniques which are needed for modeling and solving current
problems in mathematics or related fields by using the obtained
knowledge and skills.
4 Acquires analytical thinking and uses time effectively in the process
of deduction.
5 Acquires basic software knowledge necessary to work in the
computer science related fields and together with the skills to use
information technologies effectively.
6 Obtains the ability to collect data, to analyze, interpret and use
statistical methods necessary in decision making processes.
7 Acquires the level of knowledge to be able to work in the
mathematics and related fields and keeps professional knowledge and
skills up-to-date with awareness in the importance of lifelong learning.
8 Takes responsibility in mathematics related areas and has the ability
to work affectively either individually or as a member of a team.
9 Has proficiency in English language and has the ability to
communicate with colleagues and to follow the innovations in
mathematics and related fields.
10 Has the ability to communicate ideas with peers supported by
qualitative and quantitative data.
11 Has professional and ethical consciousness and responsibility which
takes into account the universal and social dimensions in the process of
data collection, interpretation, implementation and declaration of
results in mathematics and its applications.
1: Lowest, 2: Low, 3: Average, 4: High, 5: Highest
5