| Ders Adı | Kodu | Yarıyıl | T+U Saat | Kredi | AKTS |
|---|---|---|---|---|---|
| Mathematıcs I | MAT 111 | 1 | 4 + 0 | 4 | 6 |
| Ön Koşul Dersleri | |
| Önerilen Seçmeli Dersler | |
| Dersin Dili | Türkçe |
| Dersin Seviyesi | Lisans |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Dr.Öğr.Üyesi EMİNE ÇELİK |
| Dersi Verenler | Prof.Dr. SELMA ALTUNDAĞ, Doç.Dr. MURAT SARDUVAN, Prof.Dr. MAHPEYKER ÖZTÜRK, Prof.Dr. MAHMUT AKYİĞİT, Doç.Dr. YALÇIN YILMAZ, Prof.Dr. ŞEVKET GÜR, Prof.Dr. METİN BAŞARIR, Prof.Dr. MEHMET ÖZEN, Prof.Dr. REFİK KESKİN, Dr.Öğr.Üyesi MEHMET GÜNER, Prof.Dr. MEHMET ALİ GÜNGÖR, Dr.Öğr.Üyesi EMİNE ÇELİK, |
| Dersin Yardımcıları | Research Assistants in mathematics department |
| Dersin Kategorisi | Alanına Uygun Temel Öğretim |
| Dersin Amacı | To give fundamental conceptions of mathematical analysis and limit,continuity, derivative and applications of derivative in single-valued functions |
| Dersin İçeriği | Foreknowledge, functions, Limit and continuity, Derivate, Application of derivative |
| # | Ders Öğrenme Çıktıları | Öğretim Yöntemleri | Ölçme Yöntemleri |
|---|---|---|---|
| 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, |
| Hafta | Ders Konuları | Ön Hazırlık |
|---|---|---|
| 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. |
| Kaynaklar | |
|---|---|
| Ders Notu | Lecture Notes |
| Ders Kaynakları | [1] Thomas, G.B., Thomas Calculus, 11.baskı, çeviri:Recep Korkmaz, Beta Basım, 2010. |
| Sıra | Program Çıktıları | Katkı Düzeyi | |||||
|---|---|---|---|---|---|---|---|
| 1 | 2 | 3 | 4 | 5 | |||
| 1 | To have sufficient foundations on engineering subjects such as science and discrete mathematics, probability/statistics; an ability to use theoretical and applied knowledge of these subjects together for engineering solutions, | X | |||||
| 2 | An ability to determine, describe, formulate and solve engineering problems; for this purpose, an ability to select and apply proper analytic and modeling methods,al background in describing, formulating, modeling and analyzing the engineering problem, with a consideration for appropriate analytical solutions in all necessary situations | X | |||||
| 3 | An ability to select and use modern techniques and tools for engineering applications; an ability to use information technologies efficiently, | X | |||||
| 4 | An ability to analyze a system, a component or a process and design a system under real limits to meet desired needs; in this direction, an ability to apply modern design methods, | X | |||||
| 5 | An ability to design, conduct experiment, collect data, analyze and comment on the results and consciousness of becoming a volunteer on research, | X | |||||
| 6 | Understanding, awareness of administration, control, development and security/reliability issues about information technologies, | ||||||
| 7 | An ability to work efficiently in multidisciplinary teams, self confidence to take responsibility, | X | |||||
| 8 | An ability to present himself/herself or a problem with oral/written techniques and have efficient communication skills; know at least one extra language, | ||||||
| 9 | An awareness about importance of lifelong learning; an ability to update his/her knowledge continuously by means of following advances in science and technology, | X | |||||
| 10 | Understanding, practicing of professional and ethical responsibilities, an ability to disseminate this responsibility on society, | ||||||
| 11 | An understanding of project management, workplace applications, health issues of laborers, environment and job safety; an awareness about legal consequences of engineering applications, | ||||||
| 12 | An understanding universal and local effects of engineering solutions; awareness of entrepreneurial and innovation and to have knowledge about contemporary problems. | ||||||
| 13 | |||||||
| Değerlendirme Sistemi | |
|---|---|
| Yarıyıl Çalışmaları | Katkı Oranı |
| 1. Ara Sınav | 70 |
| 1. Kısa Sınav | 10 |
| 2. Kısa Sınav | 10 |
| 3. Kısa Sınav | 10 |
| Toplam | 100 |
| 1. Yıl İçinin Başarıya | 50 |
| 1. Final | 50 |
| Toplam | 100 |
| AKTS - İş Yükü Etkinlik | Sayı | Süre (Saat) | Toplam İş Yükü (Saat) |
|---|---|---|---|
| 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 |
| Toplam İş Yükü | 161 | ||
| Toplam İş Yükü / 25 (Saat) | 6,44 | ||
| Dersin AKTS Kredisi | 6 | ||