Linear and quadratic equations with applications. Linear inequalities. Absolute value. Elementary functions, their compositions and graphs in Cartesian coordinates. Linear and quadratic functions. Systems of linear equations. Matrices and operations with matrices. Determinant and Inverse of a matrix. Solutions of systems of linear equations.
Vertical Tabs
Course Learning Outcomes
| Learning Outcomes | Teaching Methods | Assessment Methods | |
| 1) Repeats the notion of real numbers and some of its properties, remembers simple algebraic techniques of: factoring, linear equation systems and linear inequalities. | 1 | A | |
| 2) Learns the notion of function, learns: graphs of functions, composition of functions, the notion of inverse function and absolute value. | 1 | A | |
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3) Learns symetry, reflection and rotations in cartesian coordinates. Observes systems of linear equations and graphs and applications of quadratic equations in cartesian coordinates.
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1 | A | |
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4) Learns matrix operations and the notian of inverse matrix.
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1 | A | |
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5) Can solve systems of linear equations through matrices.
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1 | A |
Course Flow
| Hafta | Konular | Ön Hazırlık | |
| 1 |
Bölüm 0:Cebir Tekrarı
Reel sayılar kümesi, Reel sayılar kümesinin bazı özellikleri, Üstel ve Radikaller, |
0.1, 0.2, 0.3
|
|
| 2 | Cebirsel ifadelerle yapılan işlemler, Çarpanlara Ayırma, Kesirler, | 0.4, 0.5, 0.6 | |
| 3 | Doğrusal denklemler, İkinci dereceden denklemler ve uygulamaları, | 0.7, 0.8 | |
| 4 |
Bölüm1: Uygulamalar ve Cebir’in Devamı
Denklemlerin uygulamaları, Doğrusal eşitsizlikler, |
1.1, 1.2 | |
| 5 | Eşitsizliklerin uygulamaları, Mutlak değer | 1.3, 1.4 | |
| 6 |
Bölüm 2: Fonksiyonlar ve Grafikler
Temel fonksiyonlar, Özel fonksiyonlar, Fonksiyonların bileşkeleri, Ters fonksiyonlar |
2.1, 2.2, 2.3, 2.4 | |
| 7 | Kartezyen kordinatlarda grafikler, simetri, yansıma ve döndürmeler | 2.5, 2.6, 2.7 | |
| 8 | Tekrar | ||
| 9 |
Bölüm 3:Doğrular, Paraboller ve Sistemler
Doğrular, Uygulamalar ve Doğrusal Fonksiyonlar |
3.1, 3.2 | |
| 10 | İkinci Dereceden Fonksiyonlar, Doğrusal Denklem Sistemleri | 3.3, 3.4 | |
| 11 |
Bölüm 6: Matrix Cebri
Matrisler, Matris İşlemleri |
6.1, 6.2 | |
| 12 | Matris Çarpımı, Denklem Sistemlerini Matrise İndirgeyerek Çözmek | 6.3, 6.4 | |
| 13 |
Denklem Sistemlerini Matrise İndirgeyerek Çözmek (devam)
Matris Tersleri |
6.5, 6.6 | |
| 14 | Tekrar | ||
Recommended Sources
| Lecture Book |
Introductory Mathematical
Analysis, 13th Edition by Ernest Haeussler, Richard S. Paul, Richard Wood, Pearson Prentice Hall |
Assessment
| WORKS IN SEMESTER | TIME | CONTRIBUTION PERCENTAGE |
| Mid-terms | 1 | 100 |
| Quizzes | ||
| Assignments | ||
| Total | 100 | |
| CONTRIBUTION OF FINAL EXAMINATION TO OVERALL GRADE | 60 | |
| CONTRIBUTION OF IN-TERM STUDIES TO OVERALL GRADE | 40 | |
| Total | 100 |
ECTS
| Activity | Number |
Time (Hour) |
Total Work Load (Saat) |
| Course Duration (14x Total course hours) | 14 | 3 | 42 |
| Hours for off-the-classroom study (Pre-study, practice) | 14 | 4 | 56 |
| Mid-terms (Including self study) | 1 | 12 | 12 |
| Final examination (Including self study) | 1 | 15 | 15 |
| Total Work Load | 125 | ||
| Total Work Load / 25 (h) | 5 | ||
| ECTS Credit of the Course | 5 |