MATH 259 • Final • Linear Algebra and Differential Equations
“Kesinlikle ders anlatimlari başarılıydı soru çözümleri ve konu anlatımları kaliteliydi”
Ege Turgal
Elektrik-Elektronik Mühendisliği
Bu dersimizde sunduğumuz tüm konular, sırasıyla: 1) Vector spaces 2) Linear independence, bases and dimension 3) Linear transformations 4) Eigenvalues and eigenvectors 5) Higher order linear ODEs 6) Method of undetermined coefficients and variation of parameters 7) Systems of fi rst order linear ODEs
Eğitmenler
Dorukhan Özcan
Co-Founder & CEO
Unicourse şirketinin kurucu ortağıyım. 2016 senesinde Galatasaray Lisesinden mezun oldum. Geçtiğimiz dört sene içerisinde 2000 saatten fazla ders anlattım. Anlattığım dersler sırasıyla; Calculus, Çok değişkenli Calculus, Lineer Cebir, Differansiyel Denklemler, Uygulamalı İstatistik ve Stokastik Modelleme dersleridir. Doping Hafıza şirketinde 2017 - 2022 seneleri arasında CEO danışmanlığı yaptım. Koç Üniversitesi Endüstri Mühendisliği ve Ekonomi çift anadal programını tam burslu olarak, 3.96/4.00 not ortalamasıyla bitirdim. Kadıköy Modalıyım.
Tolga Temiz
Eğitmen
2016 senesinde başladığım Koç Üniversitesi Matematik bölümünden 2020 senesinde fakülte üçüncüsü olarak mezun oldum. Lisans ve yüksek lisans eğitimlerim boyunca çeşitli derslerde asistanlık yaptım. 2021'de Koç Üniversitesi'nde Matematik yüksek lisansına başladım ve 2023 yılında mezun oldum. Şimdi Michigan State Üniversitesi'nde doktora yapıyorum. Topoloji alanıyla ilgilenmekteyim.
Kerem Başol
Eğitmen
2019 senesinde Koç Üniversitesi Matematik bölümüne başladım. Geçtiğimiz senelerde Calculus ve Linear Algebra derslerinde Tutor ve Teaching Assistant pozisyonlarında görev aldım. Halen Koç Üniversitesi Matematik ve Bilgisayar Mühendisliği çift anadal programını 4.00/4.00 ortalamayla fakülte birincisi olarak sürdürüyorum. Trigonometrik fonksiyonların elips üzerinde nasıl tanımlanabileceğini merak etmemle başlayan Matematik tutkumu aktarmak için Unicourse Matematik Zümresine katıldım.
Konular
Systems of Linear Equations
4 konu anlatımı · 5 soru
Augmented Matrix - Row Reduction 1
Augmented Matrix - Row Reduction 2
Existence and Uniqueness of Solution
Free Variables
Exam-like Questions 1
Exam-like Questions 2
Exam-like Questions 3
Exam-like Questions 4
Exam like Question 5
Matrix Operations & Algebra
1 konu anlatımı · 9 soru
Fundamental Matrix Operations
Problem 1
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Problem 8
Problem 9
The Inverse of a Matrix
2 konu anlatımı · 4 soru
Inverse of a Matrix 1
Inverse of a Matrix 2
Practice Problem 1
Practice Problem 2
Practice Problem 3
Practice Problem 4
Matrix Equations (AX = B Formu)
3 konu anlatımı · 4 soru
Matrix Equation
Solving AX = B with Inverse
Invertible or not ?
Exam like Question 1
Exam like Question 2
Exam-like Question 3
Exam like Question 4
Determinants and Properties
4 konu anlatımı · 11 soru
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant I
Properties of Determinant II
Exam like Question 1
Exam-like Question 2
Exam like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 5
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
Exam-like Question 9
Exam Practice Part I
28 soru
Gaussian Elimination
Gaussian Elimination
Gaussian Elimination
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence and Uniqueness
Existence and Uniqueness 3
Matrix Operations
Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Inverse of a Matrix 3
Solving systems with Inverse 1
Solving Systems with Inverse 2
Solving systems with Inverse 3
Solving systems with Inverse 4
Determinant and Invertibility
Determinant and Invertibility
Existence, Determinant and Invertibility 1
Existence, Determinant and Invertibility 2
Properties of Determinants 1
Properties of Determinants 2
Properties of Determinants 3
Properties of Determinants
Theory Problem 1
Theory Problem 2
Theory Problem 3-4
Vectors: Linear Combination
7 konu anlatımı · 3 soru
Vector Properties
Linear Combination 1
Linear Combination 2
Formal Definition of Linear Combination
Span of Vectors I
Span of Vectors II
Span of Vectors III
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Vectors: Linear Independence
2 konu anlatımı · 2 soru
Linear Independent Sets
Linear Independence of Matrices
Exam-like Questions 1
Exam-like Questions 2
Vector Spaces and Subspaces
3 konu anlatımı · 6 soru
Vector Spaces and Subspaces
Polynomial Subspaces
Matrix Spaces & Matrix Subspaces
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Bases and Dimension (Null, Column and Row Spaces)
2 konu anlatımı · 3 soru
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Bases for General Subspaces
3 konu anlatımı · 5 soru
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Eigenvalues and Eigenvectors
8 konu anlatımı
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Algebraic and Geometric Multiplicities 1
Algebraic and Geometric Multiplicities-2
Eigenspace of Matrices
Complex Eigenvalues
Complex Eigenvalues-2
Higher Order Linear ODEs
4 konu anlatımı · 15 soru
General Theory of nth Order DEs (Wronskian)
Exam like Question 1
Exam like Question 2
Homogeneous DEs with Constant Coefficients
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Exam like Question 9
Exam like Question 10
Exam like Question 11
Exam like Question 12
Exam like Question 13
Exam like Question 14
Exam like Question 15
Systems of First Order Differential Equations
7 konu anlatımı · 11 soru
Introduction
Homogeneous Systems: Distinct Real Eigenvalues 1
Homogeneous Systems: Distinct Real Eigenvalues 2
Homogeneous Systems: Complex Eigenvalues 1
Homogeneous Systems: Complex Eigenvalues 2
Homogeneous Systems: Repeated Eigenvalues 1
Homogeneous Systems: Repeated Eigenvalues 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
Exam-like Question 9
Exam-like Question 10
Exam-like Question 11
Exam Practice Part II
29 soru
Trivial & Nontrivial Solution
Inverse Matrix
Linear Independence
Linear Independence
Linear Independence 2
Span of Vectors
Span of Vectors
Wronskian
Wronskian
Vectors & Span
Vectors & Span
Vector Subspaces
Vector Subspaces
Polynomial Basis
Polynomial Basis
Polynomial Basis
Polynomial Basis
Column, Null and Row Spaces
Linear Systems and Basis
Eigenvalues, Eigenspaces and Diagonalization
Eigenvalues, Eigenspaces and Diagonalization
Eigenvalues, Eigenspaces and Diagonalization
Homogeneous System of Differential Equations
Homogeneous System of Differential Equations
Homogeneous System of Differential Equations
Homogeneous System of Differential Equations
Second Order DE
Higher Order DE
Undetermiend Coefficient
Değerlendirmeler
2 öğrenci değerlendirmesi
Değerlendirme yapmak için bu derse sahip olman gerekiyor.
Mustafa Mert Çetin
Genetik ve Biyomühendislik
Ada Şağra Elgün
Genetik ve Biyomühendislik
Paketi Tamamla
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