Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
MATHEMATICS I IKT1015 1. Semester 4 + 0 4.0 4.0

Prerequisites None

Language of Instruction English
Course Level Bachelor's Degree
Course Type Compulsory
Mode of delivery
Course Coordinator
Instructors Taylan Zafer BALİ
Assistants
Goals Function, limit, continuity, derivative, application of the derivative, curve sketching, differential, linear approximation, indefinite integral.
Course Content This lecture deals with limit, continuity, derivative, application of derivative, curve sketching and indefinite integral of univariate functions.
Learning Outcomes 1) Recognizes basic elementary functions
2) Knows the definitions of limit, continuity and derivative and evaluates limits
3) Obtains the derivatives of elementary functions. Finds the derivative of the composition of functions.
4) Uses the applications of the derivative in the areas of limit evaluation, maximum-minimum problems and physics. Explains the mean value theorem.
5) Decides some properties of the functions such as increasing, decreasing, convexity concavity by using derivative. Sketch their graphs.
6) Knows the definitions of the differential and linear approximation. Obtains the differential of composition of functions.
7) Explains the concept of antiderivative. Evaluates the indefinite integral.

Weekly Topics (Content)
Week Topics Teaching and Learning Methods and Techniques Study Materials
1. Week Definition of function. Basic elementary functions. Trigonometric functions. Lecture
Brainstorming
Project Based Learning
Homework
2. Week Inverse Trigonometric functions, Exponential and Logarithmic functions. Lecture
Brainstorming
Project Based Learning
Homework
3. Week Hyperbolic and Inverse Hyperbolic Functions. Definition of the limit, one sided limits. Lecture
Brainstorming
Project Based Learning
Homework
4. Week Basic trigonometric limits. The concept of continuity. Lecture
Brainstorming
Project Based Learning
Homework
5. Week Properties of continuous functions on the closed interval-Intermediate value theorem, Bolzano's theorem, local and absolute maxima and minima. Lecture
Brainstorming
Project Based Learning
Homework
6. Week The Derivative. Basic differentiation rules. Derivative of inverse function. Derivative of trigonometric and inverse trigonometric functions Lecture
Brainstorming
Project Based Learning
Homework
7. Week Derivatives of Logaritmic and exponential functions. Logarithmic differentiation. Derivatives of Hyperbolic functions and their inverses. Derivatives of parametric functions and implicit functions. Lecture
Brainstorming
Project Based Learning
Homework
8. Week Higher derivatives.and geometric mean of the derivative Lecture
Brainstorming
Project Based Learning
Homework
9. Week Higher derivatives.and geometric mean of the derivative Lecture
Brainstorming
Project Based Learning
Homework
10. Week Fermat's Theorem and maximum-minimum problems Lecture
Brainstorming
Project Based Learning
Homework
11. Week Some theorems about derivative, convex and concave functions, inflection points Lecture
Brainstorming
Project Based Learning
Homework
12. Week Indeterminate forms (L'Hospital's rule) Lecture
Brainstorming
Project Based Learning
Homework
13. Week Differentials and asypmtotes Lecture
Brainstorming
Project Based Learning
Homework
14. Week Curve sketching Lecture
Brainstorming
Project Based Learning
Homework

Sources Used in This Course
Recommended Sources
Edwards&Penney, Calculus and analytic geometry
Kalkülüs, Tüba Yayınları
Mustafa Balcı Genel Matematik I

Relations with Education Attainment Program Course Competencies
Program RequirementsContribution LevelDK1DK2DK3DK4DK5DK6DK7
PY150000000
PY250000000
PY350000000
PY450000000

*DK = Course's Contrubution.
0 1 2 3 4 5
Level of contribution None Very Low Low Fair High Very High
.

ECTS credits and course workload
Event Quantity Duration (Hour) Total Workload (Hour)
Course Duration (Total weeks*Hours per week) 14 4
Work Hour outside Classroom (Preparation, strengthening) 14 4
Midterm Exam 1 1
Final Exam 1 2
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
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Course Information