Course Information


Course Information
Course Title Code Semester L+U Hour Credits ECTS
MATHEMATICS 1 AYBS105 1. Semester 0 + 0 0 5.0

Prerequisites None

Language of Instruction Turkish
Course Level Bachelor's Degree
Course Type Compulsory
Mode of delivery
Course Coordinator
Instructors ANKUZEF ANKUZEF
Assistants
Goals This lecture deals with limit, continuity, derivative, application of derivative, curve sketching and indefinite integral of univariate functions.
Course Content Function, limit, continuity, derivative, application of the derivative, curve sketching, differential, linear approximation, indefinite integral.
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; Question Answer
Colloquium
Problem Based Learning 		Homework
2. Week Inverse Trigonometric functions, Exponential and Logarithmic functions. Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
3. Week Hyperbolic and Inverse Hyperbolic Functions. Definition of the limit, one sided limits. Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
4. Week Basic trigonometric limits. The concept of continuity. Lecture; Question Answer; Problem Solving
Colloquium
Problem 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; Question Answer
Colloquium
Problem Based Learning 		Homework
6. Week The Derivative. Basic differentiation rules. Derivative of inverse function. Derivative of trigonometric and inverse trigonometric functions Lecture; Question Answer
Colloquium
Problem 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; Question Answer
Colloquium
Problem Based Learning 		Homework
8. Week Higher derivatives.and geometric mean of the derivative Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
9. Week Increasing and decreasing functions, local extramums Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
10. Week Fermat's Theorem and maximum-minimum problems Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
11. Week Some theorems about derivative, convex and concave functions, inflection points Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
12. Week Indeterminate forms (L'Hospital's rule) Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
13. Week Differentials and asypmtotes Lecture; Question Answer
Colloquium
Problem Based Learning 		Homework
14. Week Curve sketching Lecture; Question Answer
Colloquium
Problem 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
PY155555555
PY255555555
PY355555555
PY455555555
PY755555555

*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
Homework 4 4
Midterm Exam 1 2
Time to prepare for Midterm Exam 1 10
Final Exam 1 2
Time to prepare for Final Exam 1 10
Total Workload
Total Workload / 30 (s)
ECTS Credit of the Course
Quick Access Hızlı Erişim Genişlet
Course Information
  • Course Information
  • Weekly Topics (Content)
  • Sources Used in This Course
  • Relations with Education Attainment Program Course Competencies
  • ECTS credits and course workload