MATH 225 • Tüm Sınavlar • Linear Algebra and Differential Equations
İhsan Doğramacı Bilkent Üniversitesi MATH 225 (Linear Algebra and Differential Equations) Midterm sınavına hazırlık paketi.
İşlenen konular: Systems of Linear Equations, Matrix Operations and Inverse, Matrix Equations, Elementary Matrices, Determinants, Vectors: Linear Combination and Span, Linear Independence, Vector Spaces and Subspaces, Basis for Subspaces: Row and Column Spaces, Orthogonality.
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.
Konular
Systems of Linear Equations
4 konu anlatımı · 3 soru
Augmented Matrix - Row Operations 1
Augmented Matrix - Row Operations 2
Existence and Uniqueness of Solution
Free Variables
Exam-like Questions 1
Exam-like Questions 2
Exam like Question 3
Matrix Operations and Inverse
3 konu anlatımı · 3 soru
Fundamental Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
Exam-like Question 1
Exam-like Question 2
Exam like Question 3
Matrix Equations
2 konu anlatımı · 3 soru
Matrix Equation
Solving AX = B with Inverse
Exam like Question 1
Exam-like Question 2
Exam like Question 3
Elementary Matrices
2 konu anlatımı · 3 soru
Elementary Matrix
Inverse of Elementary Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Determinants
6 konu anlatımı · 3 soru
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant
Properties of Determinant 2
Cramer's Rule
Adjoint Matrix
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Vectors: Linear Combination and Span
7 konu anlatımı · 3 soru
Vector Properties
Linear Combination 1
Linear Combination 2
Formal Definition of Linear Combination
Span of Vectors 1
Span of Vectors 2
Solutions of Homogeneous Linear Systems
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Linear Independence
3 konu anlatımı · 3 soru
Linear Independent Sets
Linear Independence of Matrices
Special Theorem for Matrix Equation
Exam-like Questions 1
Exam-like Questions 2
Exam-like Question 3
Vector Spaces and Subspaces
3 konu anlatımı · 7 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
Exam-like Question 7
Basis for Subspaces: Row and Column Spaces
6 konu anlatımı · 4 soru
Null Space & Column Space & Row Space
Bases for Col A & Row A & Null A
Basis for Vector Subspaces
Basis for Matrix Subspaces
Basis for Polynomial Subspaces
Basis for Polynomial Subspaces 2
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
Orthogonality
4 konu anlatımı · 3 soru
Key concepts for orthogonality
Orthogonal Complement
Orthagonal Complement 2
Orthogonal Sets and Basis
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
General Review Problems
24 soru
Existence and Uniqueness
Elementary Matrices
Determinant and Invertibility
Properties of Determinants
Subspace or not 1
Subspace or not 2
Subspaces or not 3
Basis for Subspaces 1
Basis for Subspaces 2
Basis for Subspaces 3
Basis for Subspaces 4
Polynomials Basis 1
Polynomials Basis 2
Polynomials Basis 3
Polynomials Basis 4
Null & Column & Row Spaces
Null & Column & Row Spaces 2
Null & Column & Row Spaces 3
Orthogonal Complement 1
Orthogonal Complement 2
Orthogonal Complement 3
Orthogonal Complement 4
Theory Problem 1
Theory Problem 2
Past Exam Problems
22 soru
Fall 2021 Exam: Existence and Uniqueness
Fall 2020 Exam: Existence and Uniqueness
Fall 2021 Exam: Elementary Matrices
Spring 2022 Exam: Inverse & Elementary Matrices
Fall 2020 Exam: Properties of Determinants
Fall 2022 Exam: Subspaces or not ?
Fall 2022 Exam: Subspaces or not ?
Spring 2023 Exam: Basis for Subspaces
Spring 2022 Exam: Basis for Subspaces
Fall 2020 Exam: Polynomials Basis
Fall 2020 Exam: Null & Column & Row Spaces
Fall 2020: Rank of a Matrix
Fall 2021 Exam: Null & Column & Row Spaces
Fall 2021 Exam: Orthogonal Complement
Spring 2023 Exam: Orthogonal Complement
Fall 2020 Exam: Orthogonal Complement
Fall 2020 Exam: Theory Problem I
Fall 2020 Exam: Theory Problem II
Fall 2020 Exam: Theory Problem III
Fall 2020 Exam: Theory Problem IV
Spring 2022 Exam: Theory Problem I
Spring 2022 Exam: Theory Problem II
Spring 2024 Exam
6 soru
Existence and Uniqueness of Solution
Determinants
Elementary Matrices
Determinant and Invertibility
Basis and Subspaces
Basis and Subspaces
Fall 2024 Exam
9 soru
Systems of Linear Equations
Row Reduction
Determinant
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Vector Spaces and Subspaces
Orthogonality
Orthogonality
Fall 2024 Midterm Prep Set
9 soru
Null Space & Column Space
Matrix Operations & Invertibility
Determinant
Theory Problem
Vector Subspaces
Vector Subspaces
Dimension of Subspaces
Inner Product Space
Orthogonal Complement & Inner Product Space
Diagonalization of Matrices
2 konu anlatımı · 4 soru
Diagonalization 1
Diagonalization 2
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
First Order Linear Differential Equations
2 konu anlatımı · 7 soru
Introduction: What is a Differential Equation
Integrating Factor Method
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
Separable Differential Equations
1 konu anlatımı · 6 soru
Separable Equations
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Exam like Question 6
The Bernoulli Equation
2 konu anlatımı · 3 soru
Bernoulli Equations I
Bernoulli Equations II
Exam like Question 1
Exam like Question 2
Exam like Question 3
Homogeneous Equations
3 konu anlatımı · 3 soru
Homogeneous Differential Equations I
Homogeneous Differential Equations II
Homogeneous or not ?
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exact Equations & Integrating Factor
8 konu anlatımı · 4 soru
Exact Differential Equations I
Exact Differential Equations II
Exact Differential Equations III
Non-Exact Equation & Integrating Factor I
Non-Exact Equation & Integrating Factor II
Non-Exact Equation & Integrating Factor III
Non-Exact Equation & Integrating Factor IV
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Past Exams & Sample Final Part I
20 soru
Integrating Factor 1
Integrating Factor 2
Integrating Factor 3
Integrating Factor 4
Integrating Factor 5
Separable Equations 1
Separable Equations 2
Separable Equations 3
Separable Equations 4
Homogeneous Equation 1
Homogeneous Equation 2
The Bernoulli Equation 1
The Bernoulli Equation 2
The Bernoulli Equation 3
Exact Equations 1
Exact Equations 2
Exact Equations 3
Exact Equations 4
Exact Equations 5
Exact Equations 6
Substitution: Reducible Equations
2 konu anlatımı · 2 soru
Case I: Variable y is missing
Exam like Question 1
Case II: Variable x is missing
Exam like Question 2
Second Order Linear ODE
8 konu anlatımı · 3 soru
Homogeneous Equations with Constant Coefficient
Homogeneous Equations with Constant Coefficient 2
Homogeneous Equations with Constant Coefficient 3
Homogeneous Equations with Constant Coefficient 4
Homogeneous Equations with Constant Coefficient 5
Two Complex Roots 1
Two Complex Roots 2
Repeated Roots 1
Exam like Question 1
Exam like Question 2
Exam like Question 3
Existence and Uniqueness Theorem
4 konu anlatımı · 3 soru
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence and Uniqueness for 2nd Order DE
Exam like Question 1
Exam like Question 2
Exam-like Question 3
The Wronskian Determinant
7 konu anlatımı · 5 soru
How to Calculate Wronskian Determinant
Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
Fundamental Set of Solution 3
Fundamental Set of Solutions 4
Exam like Question 1
Exam like Question 2
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Past Exams & Sample Final Part II
12 soru
Homogeneous Eq. with Constant Coefficients
Homogeneous Eq. with Constant Coefficients 2
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence and Uniqueness 4
From Wronskian to Equation 1
From Wronskian to Equation 2
From Wronskian to Equation 3
Fundamental Set of Solutions 1
Fundamental Set of Solutions 2
Fundamental Set of Solutions 3
General Theory of N-th Order ODEs
2 konu anlatımı · 5 soru
General Theory of nth Order DEs (Wronskian)
Homogeneous DEs with Constant Coefficients
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
The Reduction of Order Method
2 konu anlatımı · 2 soru
Reduction of Order 1
Reduction of Order 2
Exam like Question 1
Exam like Question 2
Nonhomogeneous ODEs: Variation of Parameters
3 konu anlatımı · 2 soru
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Exam-like Question 1
Exam-like Question 2
Nonhomogeneous ODEs: Undetermined Coefficients
3 konu anlatımı · 2 soru
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
Exam-like Question 1
Exam-like Question 2
Higher Order Nonhomogeneous ODEs
2 konu anlatımı · 3 soru
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Exam like Question 1
Exam like Question 2
Exam like Question 3
Past Exams & Sample Final Part III
22 soru
Higher Order Linear Equations 1
Higher Order Linear Equations 2
Reduction of Order 1
Reduction of Order 2
Reduction of Order 3
Reduction of Order 4
Reduction of Order 5
Reduction of Order 6
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
Variation of Parameter 5
Variation of Parameter 6
Higher Order: Variation of Parameter
Method of Undetermined Coefficients 1
Method of Undetermined Coefficients 2
Higher Order: Undetermined Coefficient 1
Higher Order: Undetermined Coefficient 2
Higher Order: Undetermined Coefficient 3
Finding a Trial Solution 1
Finding a Trial Solution 2
Systems of Differential Equations
5 konu anlatımı · 2 soru
Introduction
Distinct Real Eigenvalues 1
Distinct Real Eigenvalues 2
Complex Eigenvalues 1
Complex Eigenvalues 2
Exam-like Question 1
Exam-like Question 2
Nonhomogeneous Systems
2 konu anlatımı · 1 soru
Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
Exam like Question
Past Exams & Sample Final Part IV
9 soru
Systems of Differential Eq. 1
Systems of Differential Eq. 2
Systems of Differential Eq. 3
Systems of Differential Eq. 4
Systems of Differential Eq. 5
Systems of Differential Eq. 6
Systems of Differential Eq. 7
Non-hom. Systems: Given Particular Solution I
Non-hom. Systems: Given Particular Solution II
Spring 2024 Final Exam
6 soru
Theory Problem: Eigenvalues
Theory Problem: Eigenvalues
Theory Problem: Orthogonality
Exact Equations & Existence and Uniqueness
Undetermined Coefficients
Non-homogeneous Systems
Fall 2024 Final Exam
3 soru
Eigenvectors & Diagonalization
Q2: Reducible Equations
Q3: Variation of Parameters Method