| 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 | İngilizce |
| Dersin Seviyesi | Lisans |
| Dersin Türü | Zorunlu |
| Dersin Koordinatörü | Dr.Öğr.Üyesi EMİNE ÇELİK |
| Dersi Verenler | Dr.Öğr.Üyesi EMİNE ÇELİK, |
| Dersin Yardımcıları | Research Assistants in mathematics department |
| Dersin Kategorisi | Diğer |
| 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. | Anlatım, Soru-Cevap, Tartışma, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Sözlü Sınav, Ödev, |
| 2 | He/she recognizes functions and its properties. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Ödev, |
| 3 | He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Ödev, |
| 4 | He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Ödev, |
| 5 | He/she defines right and left approached limit. Knows the undetermined conditions. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Ödev, |
| 6 | He/she defines the concept of continuity and discontinuity. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Sözlü Sınav, Ödev, |
| 7 | He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Ödev, |
| 8 | Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Ödev, |
| 9 | He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. | Anlatım, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Sözlü Sınav, Ödev, |
| 10 | Defines the increasing and decreasing functions with the help of tangent and normal equations. | Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Gösteri, Gösterip Yaptırma, | Sınav, Sözlü Sınav, |
| 11 | Can calculate the limit of undetermined conditions with the help of derivatives. | Anlatım, Soru-Cevap, Problem Çözme, | Sınav, Sözlü Sınav, |
| 12 | Can define the maximum, minimum and asymptote of functions. | Anlatım, Soru-Cevap, Alıştırma ve Uygulama, Problem Çözme, | Sınav, Sözlü Sınav, Ödev, |
| 13 | Expresses the curve plot. | Anlatım, Soru-Cevap, Problem Çözme, | Sınav, Sözlü Sınav, |
| 14 | Solves the engineering problems with the help of derivative and approximates with differential approach. | Anlatım, Soru-Cevap, Problem Çözme, | Sınav, Sözlü Sınav, Ödev, |
| 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, 13e, Pearson Education, 2013. [2] Larson, R., Edwards, B., Calculus, 11e, Cengage Learning, 2018. [3] Stewart, J. Calculus, 8e, Cengage Learning, 2016. |
| # | Ders Öğrenme Çıktılarının Program Çıktılarına Katkısı |
|---|---|
| 1 | He/she defines sets and number set concepts. Explains equality, inequality and equation concepts. |
| 2 | He/she recognizes functions and its properties. |
| 3 | He/she expresses trigonometric, reverse trigonometric and hyperbolic functions, partial function and special functions ( Absolute value, exact value and sign functions) |
| 4 | He/she expresses concept of limit and calculates. Can prove the rules which are used for limit. |
| 5 | He/she defines right and left approached limit. Knows the undetermined conditions. |
| 6 | He/she defines the concept of continuity and discontinuity. |
| 7 | He/she can explain concept of derivative and calculates derivatives with this definition. Proves the derivative rules with the definition of derivative. |
| 8 | Can define the derivative of trigonometric, reverse trigonometric functions, Exponential and logarithmic function, hyperbolic and revere hyperbolic functions. |
| 9 | He/she calculates high order derivatives. Can define the derivatives of given functions and parametric equations. Express the derivative of implicit functions. |
| 10 | Defines the increasing and decreasing functions with the help of tangent and normal equations. |
| 11 | Can calculate the limit of undetermined conditions with the help of derivatives. |
| 12 | Can define the maximum, minimum and asymptote of functions. |
| 13 | Expresses the curve plot. |
| 14 | Solves the engineering problems with the help of derivative and approximates with differential approach. |
| 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) |
|---|---|---|---|
| Ders Süresi (Sınav haftası dahildir: 16x toplam ders saati) | 16 | 4 | 64 |
| Sınıf Dışı Ders Çalışma Süresi(Ön çalışma, pekiştirme) | 16 | 3 | 48 |
| Ara Sınav | 1 | 10 | 10 |
| Kısa Sınav | 1 | 25 | 25 |
| Ödev | 1 | 15 | 15 |
| Toplam İş Yükü | 162 | ||
| Toplam İş Yükü / 25 (Saat) | 6,48 | ||
| dersAKTSKredisi | 6 | ||