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 | Turkish |
Course Level | Bachelor's Degree |
Course Type | Compulsory |
Course Coordinator | Doç.Dr. SELMA ALTUNDAĞ |
Course Lecturers | Doç.Dr. SELMA ALTUNDAĞ, Doç.Dr. MURAT SARDUVAN, Doç.Dr. MAHPEYKER ÖZTÜRK, Doç.Dr. MAHMUT AKYİĞİT, Doç.Dr. YALÇIN YILMAZ, Prof.Dr. MEHMET ÖZEN, Prof.Dr. REFİK KESKİN, Dr.Öğr.Üyesi MEHMET GÜNER, Prof.Dr. MEHMET ALİ GÜNGÖR, Öğr.Gör.Dr. EMİNE ÇELİK, |
Course Assistants | Research Assistants in mathematics department |
Course Category | Available Basic Education in the Field |
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, 11.baskı, çeviri:Recep Korkmaz, Beta Basım, 2010. |
Order | Program Outcomes | Level of Contribution | |||||
---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |||
1 | X | ||||||
2 | X | ||||||
3 | X | ||||||
4 | X | ||||||
5 | X | ||||||
6 | |||||||
7 | |||||||
8 | X | ||||||
9 | X | ||||||
10 | |||||||
11 | |||||||
12 |
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 |
ECTS - Workload Activity | Quantity | Time (Hours) | Total Workload (Hours) |
---|---|---|---|
Course Duration (Including the exam week: 16x Total course hours) | 16 | 4 | 64 |
Hours for off-the-classroom study (Pre-study, practice) | 16 | 3 | 48 |
Mid-terms | 1 | 10 | 10 |
Assignment | 1 | 15 | 15 |
Quiz | 2 | 12 | 24 |
Total Workload | 161 | ||
Total Workload / 25 (Hours) | 6.44 | ||
dersAKTSKredisi | 6 |