Course Name Code Semester T+U Hours Credit ECTS
Mathematics I MAT 111 1 4 + 0 4 6
 Precondition Courses Recommended Optional Courses Course Language English Course Level Bachelor's Degree Course Type Compulsory Course Coordinator Öğr.Gör.Dr. EMİNE ÇELİK Course Lecturers Öğr.Gör.Dr. EMİNE ÇELİK, Course Assistants Research Assistants in mathematics department Course Category Course Objective To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions Course Content Foreknowledge, functions, Limit and continuity, Derivate, Application of derivative
# Course Learning Outcomes Teaching Methods Assessment Methods
1 He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. Lecture, Question-Answer, Discussion, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
2 He/she recognizes functions and its properties. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
3 He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) Lecture, Drilland Practice, Problem Solving, Testing, Homework,
4 He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
5 He/she defines right and left approached limit. Knows the undetermined conditions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
6 He/she defines the concept of continuity and discontinuity. Lecture, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
7 He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
8 Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. Lecture, Drilland Practice, Problem Solving, Testing, Homework,
9 He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. Lecture, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
10 Defines the increasing and decreasing functions with the help of tangent and normal equations. Lecture, Question-Answer, Drilland Practice, Demonstration, Motivations to Show, Testing, Oral Exam,
11 Can calculate the limit of undetermined conditions with the help of derivatives. Lecture, Question-Answer, Problem Solving, Testing, Oral Exam,
12 Can define the maximum, minimum and asymptote of functions. Lecture, Question-Answer, Drilland Practice, Problem Solving, Testing, Oral Exam, Homework,
13 Expresses the curve plot. Lecture, Question-Answer, Problem Solving, Testing, Oral Exam,
14 Solves the engineering problems with the help of derivative and approximates with differential approach. Lecture, Question-Answer, Problem Solving, Testing, Oral Exam, Homework,
Week Course Topics Preliminary Preparation
1 Sets. Number sets. Equations. Equality and inequality.
2 Concept of function. Types of functions (Polynomial sets, rational function, exponential and logarithmic functions and the definition set of these functions)
3 Function types (Trigonometric, reverse trigonometric and hyperbolic functions, Partial functions , special defined functions (Absolute value, exact value, sign functions).
4 Concept of limit and limit calculation with the definition of limit. Proof of the rules used for limit rule. Sandwich theorem. Limit of trigonometric functions.
5 Right and left limit. Undetermined conditions (0/0,infinity/infinity, 0.infinity, infinity-infinity,1^infinity)
6 Continuity concept in functions. Types of discontinuity and characteristics of continuous functions (Mid value theorem, absolute maximum and minimum, concept of local maximum and minimum. )
7 Concept of derivative, and calculation with derivative rule. Proof of derivate with derivative rule. Derivative of reverse function.
8 Derivative of trigonometric and reverse trigonometric functions. Derivative of exponential and logarithmic functions. Derivative of hyperbolic and reverse hyperbolic functions.
9 High order derivatives. Derivatives of functions with parametric equations. Derivative of implicit functions.
10 Equation of tangent and normal. Increasing and decreasing functions.
11 Undetermined conditions ( Analyses of 8 condition with L’hopital Rule )
12 Maximum, minimum and asymptote of functions.
13 Curve plotting.
14 Engineering problems. Approximation with differential.
Resources
Course Notes <p>Lecture Notes</p>
Course Resources

[1] Thomas, G.B., Thomas` Calculus, 13e, Pearson Education, 2013.

[2] Larson, R., Edwards, B., Calculus, 11e, Cengage Learning, 2018.

[3] Stewart, J.  Calculus, 8e, Cengage Learning, 2016.

Evaluation System
Semester Studies Contribution Rate
1. Ara Sınav 70
1. Kısa Sınav 10
2. Kısa Sınav 10
3. Kısa Sınav 10
Total 100
1. Yıl İçinin Başarıya 50
1. Final 50
Total 100