About this Course
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Doğrusal cebir ikili dizinin ikincisi olan bu ders birinci derste verilen temel bilgilerin üzerine eklemeler yapılarak tamamen matris işlemleri ve uygulamalarını kapsamaktadır. Cebirsel denklem sistemleri, sonuçların tekilliği ve var olup olmadığı, determinantlar ve onların doğal olarak nasıl oluştuğu, öz değer problemleri ve onların matris fonksiyonlarına uygulanışı vb. konulara derste değinilmektedir. Ders gerçek yaşamdan gelen uygulamaları da tanıtmaya önem veren “içerikli yaklaşımla” tasarlanmıştır. Bölümler: Bölüm 1: Doğrusal Cebir I'in Özeti Bölüm 2: Kare Matrislerde Determinant Bölüm 3: Kare Matrislerin Tersi Bölüm 4: Kare Matrislerde Özdeğer Sorunu Bölüm 5: Matrislerin Köşegenleştirilmesi Bölüm 6: Matris Fonksiyonları Bölüm 7: Matrislerle Diferansiyel Denklem Takımları ----------- This second of the sequence of two courses builds on the fundamentals of the first course, is entirely on matrix algebra and applications. Specifically, the studies include systems of algebraic equations including the existence and uniqueness of solutions, determinants and how they arise naturally, eigenvalue problems with their applications to diagonalization and matrix functions. The course is designed in the same spirit as the first one with a “content based” emphasis, answering the “why” and “where“ of the topics, as much as the traditional “what” and “how” leading to “definitions” and “proofs”. Chapters: Chapter 1: Summary of Linear Algebra I Chapter 2: Determinant Chapter 3: Inverse of Square Matrices Chapter 4: Eigenvalue Problem in Square Matrices Chapter 5: Diagonalization of Matrices Chapter 6: Matrix Functions Chapter 7: Matrices and Systems of Differential Equations ----------- Kaynak: Attila Aşkar, “Doğrusal cebir”. Bu kitap dört ciltlik dizinin üçüncü cildidir. Dizinin diğer kitapları Cilt 1 “Tek değişkenli fonksiyonlarda türev ve entegral”, Cilt 2: "Çok değişkenli fonksiyonlarda türev ve entegral" ve Cilt 4: “Diferansiyel denklemler” dir. Source: Attila Aşkar, Linear Algebra, Volume 3 of the set of Vol1: Calculus of Single Variable Functions, Volume 2: Calculus of Multivariable Functions and Volume 4: Differential Equations....
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Flexible deadlines

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Clock

Suggested: 7 weeks, 4 hours per week

Approx. 12 hours to complete
Comment Dots

Turkish

Subtitles: Turkish, English
Globe

100% online courses

Start instantly and learn at your own schedule.
Calendar

Flexible deadlines

Reset deadlines in accordance to your schedule.
Clock

Suggested: 7 weeks, 4 hours per week

Approx. 12 hours to complete
Comment Dots

Turkish

Subtitles: Turkish, English

Syllabus - What you will learn from this course

1

Section
Clock
24 minutes to complete

Doğrusal Cebir I'in Özeti / Summary of Linear Algebra I

...
Reading
1 video (Total 14 min), 1 reading
Reading1 reading
Modül Slaytları / Slides10m

2

Section
Clock
3 hours to complete

Kare Matrislerde Determinant / Determinant in Square Matrices

...
Reading
7 videos (Total 147 min), 1 reading, 1 quiz
Video7 videos
2x2 ve 3x3 lü Matrislerden Öğrendiklerimiz / Observations in 2 x 2 and 3x3 Matrices25m
Determinant Hesaplama Yöntemi 1: Laplace Hesaplama Zinciri / Method 1 for Evaluating Matrices: Laplace Algorithm17m
Determinantların Temel Özellikleri / Basic Properties of Determinants9m
Determinantların Temel Özelliklerden İspatlanan Yeni Özellikler / New Properties of Determinants Proven by the Basic Properties24m
Determinantın Önermelerle Tanımı / Axiomatic Definition of Determinants27m
Determinant Hesaplama Yöntemi 4: Gauss - Jordan Elemeleriyle / Method 4 for Evaluating Matrices: Gauss - Jordan Eliminations20m
Reading1 reading
Modül Slaytları / Slides10m
Quiz1 practice exercise
Kısa Sınav 1 / Quiz 120m

3

Section
Clock
1 hour to complete

Kare Matrislerin Tersi / Inverse of Square Matrices

...
Reading
3 videos (Total 52 min), 1 reading, 1 quiz
Video3 videos
Gauss - Jordan Elemeleriyle Hesaplama: Yöntem 2 / Method 2 for Evaluating Matrices: Gauss - Jordan Eliminations12m
Cramer Kuralı / Cramer's Rule11m
Reading1 reading
Modül Slaytları / Slides10m
Quiz1 practice exercise
Kısa Sınav 2 / Quiz 220m

4

Section
Clock
3 hours to complete

Kare Matrislerde Özdeğer Sorunu / Eigenvalue Problem in Square Matrices

...
Reading
6 videos (Total 93 min), 1 reading, 1 quiz
Video6 videos
Özdeğer ve Öz Vektörlerin Hesaplanması / Evaluation of Eigenvalues and Eigenvectors9m
Çözümlü Problemler / Solved Problems34m
Simetrik Matrislerde Özdeğer Problemi / Eigenvalue Problem of Symmetric Matrices9m
Çözümlü Problemler / Solved Problems13m
Hermite Matrislerinde Öz Değer ve Öz Vektörler / Eigenvalues and Eigenvectors of Hermitian Matrices12m
Reading1 reading
Modül Slaytları / Slides10m
Quiz1 practice exercise
Kısa Sınav 3 / Quiz 348m

Instructor

Attila Aşkar

Prof. Dr.
Matematik Bölümü (Department of Mathematics)

About Koç University

Koç University is a leading liberal arts university located in Istanbul, Turkey; also recognized globally for facilitating cutting edge research in its full collection of Colleges, including Administrative Sciences & Economics, Engineering, Natural Sciences, Humanities & Social Sciences, Law, Nursing and Medicine. With its strong academic structure, research opportunities, international achievements, vivid social environment and wide range of job opportunities upon graduation, Koç University distinctively attracts attention. Now available online....

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