Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
APPLIED MATRIX EQUATIONS MAT 462 8 2 + 0 2 5
Ön Koşul Dersleri Students are assumed to be familiar with Linear Algebra I-II, and Generalized and Conditional Inverses.
 Dersin Dili Türkçe Dersin Seviyesi Lisans Dersin Türü SECMELI Dersin Koordinatörü Prof.Dr. HALİM ÖZDEMİR Dersi Verenler Dersin Yardımcıları Res.Assist. Emre Kişi- Res.Assist. Tuğba Petik Dersin Kategorisi Alanına Uygun Öğretim Dersin Amacı An important property of the generalized inverse is that it enables us to find explicit solutions of systems of linear equations. For this reason, the main aim of this course is to present systems of linear equations and computational applications using rather generalized inverse. Dersin İçeriği Basic concepts and theorems, Summary of the generalized and conditional inverses, Existence of solution to Ax=g, The number of solutions of the system Ax=g, Approximate solution to inconsistent system of linear equations, Existence of solution to AXB=C, The number of solutions of the system AXB=C, Statistical applications, Least squares solutions and inverses, Computational applications.
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - 1) He/she summarizes the culture of general mathematics. 14 - 15 - 1 - 2 - 3 - 4 - 9 - A - B - 2 - He/she describes a generalized inverse of any matrix. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B - 3 - He/she restates the existence of solution to any equation system. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B - 4 - He/she explains the existence of solution to any matrix equation. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B - 5 - He/she establishes the connection between the equation system and matrix equation. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B - 6 - He/she finds an approximate solution to the matrix equation when it doesnt have any solution. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B - 7 - He/she applies these to statistics.. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B - 8 - He/she compares the approximate solution obtained with the least square solution. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - C - 9 - He/she uses the solution for constructing computer program. 1 - 2 - 3 - 4 - 9 - 14 - 15 - A - B -
 Öğretim Yöntemleri: 14:Self Study 15:Problem Solving 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 9:Simulation Ölçme Yöntemleri: A:Testing B:Oral Exam C:Homework

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Introduction [4] pages 44-160; [1] pages 138-139
2 Basic concepts and theorems [1] pages 95-135
3 Summary of the generalized and conditional inverses [1] pages 95-135
4 Existence of solution to Ax=g [1] pages 139-142
5 The number of solutions of the system Ax=g [1] pages 142-146
6 Approximate solution to inconsistent system of linear equations [1] pages 146-150
7 Approximate solution to inconsistent system of linear equations (continue) [1] pages 146-150
8 Statistical applications [1] pages 150-153
9 Midterm exam
10 Existence of solution to AXB=C [2] pages 55-61
11 The number of solutions of the system AXB=C [2] pages 55-61
12 Least squares solutions [1] pages 153-158
13 Statistical applications [1] pages 159-160; [2] pages 136-154
14 Computational applications [1] pages 160-162; [5] completely

#### Kaynaklar

Ders Notu [1] Freanklin A. GRAYBILL, Introduction to matrices with applications in statistics, Wadsworth publishing company, Inc., Belmont California, 1969.
Ders Kaynakları [2] C. Radhakrishna RAO, Sujit Kumar MITRA, Generalized inverse of matrices and its applications, John Wiley & Sons Inc., Canada, 1971.
[3] Thomas N. F. GREVILLE, Adi BEN-ISRAEL, Generalized Inverses Theory and Applications, John Wiley & Sons, Inc., Canada, 1974.
[4] Stewart VENIT, Wayne BISHOP, Elementary linear algebra, McGraw Hill, Boston, 1985.
[5] M. Uzunoğlu, A.Kızıl, Ö.Ç. Onar, Her yönüyle Matlab, 2003

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 He/ she has the ability to use the related materials about mathematics, constructed on competency, achieved in secondary education and also has the further knowledge equipment. X
2 Evaluating the fundamental notions, theories and data with academic methods, he/ she determines and analyses the encountered problems and subjects, exchanges ideas, improves suggestions propped up proofs and inquiries. X
3 He/ she has the competency of executing the further studies of undergraduate subjects independently or with shareholders. X
4 He/ she follows up the knowledge of mathematics and has the competency of getting across with his (or her) professional colleagues within a foreign language. X
5 He/ she has the knowledge of computer software information as a mathematician needs. X
6 He/ she has scientific and ethic assets in the phases of congregating, annotating and announcing the knowledge about mathematics. X
7 He/ she has the ability to make the mathematical models of contemporary problems and solving them. X
8 He/ she uses the ability of abstract thinking. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 55
KisaSinav 1 15
KisaSinav 2 15
KisaSinav 3 15
Toplam 100
Yıliçinin Başarıya Oranı 60
Finalin Başarıya Oranı 40
Toplam 100

#### AKTS - İş Yükü

Etkinlik Sayısı Süresi(Saat) Toplam İş yükü(Saat)
Course Duration (Including the exam week: 16x Total course hours) 16 2 32
Hours for off-the-classroom study (Pre-study, practice) 16 2 32
Mid-terms 1 16 16
Quiz 3 9 27
Final examination 1 16 16
Toplam İş Yükü 123
Toplam İş Yükü /25(s) 4.92
Dersin AKTS Kredisi 4.92
; ;