Ders Bilgileri

#### Ders Tanımı

Ders Kodu Yarıyıl T+U Saat Kredi AKTS
MATRICES IN APPLIED SCIENCES I MAT 569 0 3 + 0 3 6
Ön Koşul Dersleri Students are assumed to be familiar with Linear Algebra, Probability, Statistics, Generalized and Conditional Inverse, and Applied Matrix Equations.
 Dersin Dili Türkçe Dersin Seviyesi Yüksek Lisans Dersin Türü SECMELI Dersin Koordinatörü Doç.Dr. MURAT SARDUVAN Dersi Verenler Doç.Dr. MURAT SARDUVAN Dersin Yardımcıları Res. Assist. Emre KİŞİ- Res. Assist. Tuğba PETİK Dersin Kategorisi Dersin Amacı Linear algebra and matrix theory have long been fundamental tools in mathematical and statistical disciplines as well as applied sciences for example, sociology, education, chemistry, and engineering for research in their own right. The aim of this course is to introduce some information and facilities related to special types of matrices mainly used in many applied sciences. Dersin İçeriği Partitioned matrices; The inverses, the determinants and the characteristic equations and roots of certain patterned matrices; Triangular matrices and Correlation matrix; Direct product and sum of matrices; Circulants, Dominant diagonal matrices; Vandermonde, Fourier, Permutation, Hadamard, Band and Toeplitz Matrices; Vector of a matrix and trace; Commutation Matrices
 Dersin Öğrenme Çıktıları Öğretim Yöntemleri Ölçme Yöntemleri 1 - He/she consolidates the culture of linear algebra. 1 - 2 - 3 - A - C - 2 - He/she sees the concept of partitioned matrix. 1 - 2 - 3 - 4 - 15 - A - C - D - 3 - He/she recognizes some of usefulness and easiness of patterned matrices, which are supplied in applied sciences. 2 - 3 - 4 - 15 - A - C - D - 4 - He/she understands direct product and sum. 2 - 3 - 4 - 15 - A - C - 5 - He/she recognizes some of easiness in finding determinant, inverse and eigenvalue for special types of matrices. 1 - 2 - 3 - 4 - 15 - A - C - D - 6 - He/she understands the concept of vector of a matrix. 2 - 3 - 4 - 15 - A - C - 7 - He/she sees Commutation matrices and their application areas. 1 - 2 - 3 - 4 - 15 - A - C -
 Öğretim Yöntemleri: 1:Lecture 2:Question-Answer 3:Discussion 4:Drilland Practice 15:Problem Solving Ölçme Yöntemleri: A:Testing C:Homework D:Project / Design

#### Ders Akışı

Hafta Konular ÖnHazırlık
1 Partitioned matrices and the inverse of certain patterned matrices [1] pages 182-200
2 The determinants and characteristic roots of some patterned matrices [1] pages 201-206
3 Triangular matrices and Correlation matrix [1] pages 207-214
4 Direct product and sum of matrices [1] pages 215-229
5 Additional theorems [1] pages 230-249
6 Dominant diagonal matrices [1] pages 250-264
7 Vandermonde and Fourier matrices [1] pages 265-273
8 Permutation, Hadamard matrices [1] pages 274-281
9 Band and Toeplitz matrices [1] pages 282-288
10 Solutions of some problems [1] pages 289-297
11 Trace of a matrix and its properties [1] pages 298-308
12 Vector of a matrix [1] pages 309-314
13 Commutation Matrices [1] pages 315-321
14 Solutions of some problems [1] pages 322-325

#### Kaynaklar

Ders Notu Graybill, F. A., Introduction to Matrices with Applications in Statistics, United States, 1969.
Ders Kaynakları [1] Searle, S. R., Matrix Algebra Useful For Statistics, Canada, 1982.
[2] Johnson, R. A. and Wichern, D. W., Applied Multivariate Statistical Analysis, Englewood Cliffs, New Jersey, 1982.
[3] Horn, R. A., Johnson, C. R., Matrix Analysis, Cambridge University Press, Cambridge, 1985.

#### Dersin Program Çıktılarına Katkısı

No Program Öğrenme Çıktıları KatkıDüzeyi
1 2 3 4 5
1 Develop strategic, political and practice plans and evaluate the results by taking into account the quality process in his/her area of expertise X
2 Student follows the current journals in his/her field and puts forward problems. X
3 Student understands the relations between the disciplines pertaining to the undergraduate programs of Mathematics X
4 Student gets new knowledge by relating the already acquired experience and knowledge with the subject-matters out of his/her field. X
5 Student uses different proof methods to come to a solution by analyzing the problems encountered. X
6 Student determines the problems to be solved within his/her field and if necessary takes the lead. X
7 Student conveys, in team work, his/her knowledge in the studies done in different disciplines by applying the dynamics pertaining to his/her own field. X
8 Student critically evaluates the knowledge got at the bachelor´s degree level, makes up the missing knowledge and focuses on the current subject-matters X
9 Student knows a foreign language to communicate orally and in writing and uses the foreign language in a way that he/she can have a command of the Maths terminology and can do a source research. X
10 Student improves himself/herself at a level of expertness in Mathematics or in the fields of application by improving the knowledge got at the bachelor´s degree level. X
11 Student considers the scientific and cultural ethical values in the phases of gathering and conveying data or writing articles. X

#### Değerlendirme Sistemi

YARIYIL İÇİ ÇALIŞMALARI SIRA KATKI YÜZDESİ
AraSinav 1 40
Odev 1 20
PerformansGoreviSeminer 1 40
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 3 48
Hours for off-the-classroom study (Pre-study, practice) 16 3 48
Mid-terms 1 15 15
Assignment 1 8 8
Performance Task (Seminar) 1 20 20
Final examination 1 20 20
Toplam İş Yükü 159
Toplam İş Yükü /25(s) 6.36
Dersin AKTS Kredisi 6.36
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