MATH 225 • Final • Linear Algebra and Differential Equations
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.
Paketi Tamamla
🎓 Bilkent Üniversitesinde öğrencilerin %92'si tüm paketi alarak çalışıyor.
Konular
Eigenvalues and Eigenvectors
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Algebraic and Geometric Multiplicities
Eigenspace of Matrices
Complex Eigenvalues
Complex Eigenvalues 2
Diagonalization of Matrices
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
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
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
Bernoulli Equations I
Bernoulli Equations II
Exam like Question 1
Exam like Question 2
Exam like Question 3
Homogeneous Equations
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
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
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
Case I: Variable y is missing
Exam like Question 1
Case II: Variable x is missing
Exam like Question 2
Second Order Linear ODE
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
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
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
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
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
Reduction of Order 1
Reduction of Order 2
Exam like Question 1
Exam like Question 2
Nonhomogeneous ODEs: Variation of Parameters
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Exam-like Question 1
Exam-like Question 2
Nonhomogeneous ODEs: Undetermined Coefficients
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
Exam-like Question 1
Exam-like Question 2
Higher Order Nonhomogeneous ODEs
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
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
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
Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
Exam like Question
Past Exams & Sample Final Part IV
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
Theory Problem: Eigenvalues
Theory Problem: Eigenvalues
Theory Problem: Orthogonality
Exact Equations & Existence and Uniqueness
Undetermined Coefficients
Non-homogeneous Systems
Fall 2024 Final Exam
Eigenvectors & Diagonalization
Q2: Reducible Equations
Q3: Variation of Parameters Method
Değerlendirmeler
Ders İçeriği
Eigenvalues and Eigenvectors
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Algebraic and Geometric Multiplicities
Eigenspace of Matrices
Complex Eigenvalues
Complex Eigenvalues 2
Diagonalization of Matrices
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
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
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
Bernoulli Equations I
Bernoulli Equations II
Exam like Question 1
Exam like Question 2
Exam like Question 3
Homogeneous Equations
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
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
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
Case I: Variable y is missing
Exam like Question 1
Case II: Variable x is missing
Exam like Question 2
Second Order Linear ODE
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
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
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
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
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
Reduction of Order 1
Reduction of Order 2
Exam like Question 1
Exam like Question 2
Nonhomogeneous ODEs: Variation of Parameters
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Exam-like Question 1
Exam-like Question 2
Nonhomogeneous ODEs: Undetermined Coefficients
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
Exam-like Question 1
Exam-like Question 2
Higher Order Nonhomogeneous ODEs
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
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
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
Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
Exam like Question
Past Exams & Sample Final Part IV
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
Theory Problem: Eigenvalues
Theory Problem: Eigenvalues
Theory Problem: Orthogonality
Exact Equations & Existence and Uniqueness
Undetermined Coefficients
Non-homogeneous Systems
Fall 2024 Final Exam
Eigenvectors & Diagonalization
Q2: Reducible Equations
Q3: Variation of Parameters Method
Sıkça Sorulan Sorular
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