MATH 203 • Tüm Sınavlar • Linear Algebra and Differential Equations
Linear Cebir ve Diferansiyel Denklemler dersi bundan önce aldığın Calculus I - II (MATH 101-102) derslerinden birer parça barındırıyor; Merak etme, biz senin icin tüm bu bilgileri düzenledik.
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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
Linear First Order Equations
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Introduction: What is a Differential Equation
Integrating Factor Method
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Separable Differential Equations
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Separable Equations
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Bernoulli Equation
1 konu anlatımı · 3 soru
Bernoulli Equations
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Homogeneous Differential Equations
1 konu anlatımı · 2 soru
Homogeneous Equations
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Other Substitution Techniques
2 konu anlatımı · 3 soru
Case 1: Given Substitution
Case 2: Equations of the form F(ax + by + c)
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Exact Differential Equations
7 konu anlatımı · 5 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
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Second Order Differential Equations
7 konu anlatımı · 4 soru
Homogeneous Equations with Constant Coefficient 1
Homogeneous Equations with Constant Coefficient 2
Homogeneous Equations with Constant Coefficient 3
Homogeneous Equations with Constant Coefficient 4
Two Complex Roots I
Two Complex Roots II
Repeated Roots
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The Wronskian Determinant
5 konu anlatımı · 3 soru
Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
Wronskian and Linear Independence
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Variation of Parameters
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Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Method of Undetermined Coefficients
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Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
Caucy Euler Equation
1 konu anlatımı · 3 soru
Caucy Euler Equation
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Exam Like Question 3
(NEW) FALL 2024 Exam Problems
8 soru
Separable Equation
Linear Equation
Exact Equation
Homogeneous Equation
Substitution Method (1st Order DE)
Undetermined Coefs. Method
Undetermined Coefs. Method
Variation of Parameters Method
(NEW) SPRING 2025 Exam Problems
4 soru
Separable Equation, Bernoulli Equation
Exact Equations
Homogeneous Equations
Method of Undetermined Coefficients
The Laplace Transform
6 konu anlatımı · 4 soru
The Laplace Transform 1
The Laplace Transform 2
The Laplace Transform 3
The Laplace Transform 4
Inverse Laplace Transform 1
Inverse Laplace Transform 2
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Solving Differential Equations by Laplace Transform
3 konu anlatımı · 6 soru
Laplace Transform of Derivative
Laplace Transform and Initial Value Problems 1
Laplace Transform and Initial Value Problems 2
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Step Functions and IVP
6 konu anlatımı · 5 soru
Step Functions 1
Step Functions 2
Step Functions 3
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Initial Value Problems with Step Functions 1
Initial Value Problems with Step Functions 2
Initial Value Problems with Step Functions 3
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The Convolution Integral
5 konu anlatımı · 4 soru
The Convolution Integral 1
The Convolution Integral 2
The Convolution Integral 3
Initial Value Problems with Convolution Integral 1
Initial Value Problems with Convolution Integral 2
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Power Series Solution of Second Order Equations
7 konu anlatımı · 7 soru
What is a Power Series?
Convergence of a Power Series
Power Series Solution of Second Order Equations 1
Power Series Solution of Second Order Equations 2
Power Series Solution of Second Order Equations 3
Power Series Solution of Second Order Equations 4
Power Series Solution of Second Order Equations 5
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Linear Combination & Span of Vectors
6 konu anlatımı · 5 soru
Vector Properties
Linear Combination 1
Linear Combination 2
Formal Definition of Linear Combination
Span of Vectors 1
Span of Vectors 2
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Linear Independence
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Linear Independent Sets
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Orthogonality and Orthogonal Complement
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Key concepts for orthogonality
Orthogonal Complement
Orthagonal Complement 2
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Gram-Schmidt Orthogonalization Process
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The Gram-Schmidt Process 1
The Gram-Schmidt Process 2
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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
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Homogeneous and Nonhomogeneous Systems
3 konu anlatımı · 3 soru
Matrix Equations and Augmented Matrix
Solutions of Homogeneous Linear Systems
Solutions of Non-Homogeneous Linear Systems
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Matrix Operations and Inverse of a Matrix
3 konu anlatımı · 7 soru
Fundamental Matrix Operations
Inverse of a Matrix 1
Inverse of a Matrix 2
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Linear Transformation
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Linear Transformations 1
Linear Transformation 2
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Matrix of a Linear Transformation
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Inverse of Linear Transformation 1
Inverse of Linear Transformation 2
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Fall 2024 Exam
4 soru
Cauchy Euler Equation
Solving DE with Laplace Tr.
Solving DE with Laplace Tr. (including Convolution)
Power Series Solution Around Ordinary Point
Spring 2025 Exam
5 soru
Cauchy Euler Equations
Solution of ODEs with Laplace Transform
Power Series Solution Around an Ordinary Point
Gram-Schmidt Process
Echelon Form
Exam Practice Problems
8 soru
Gaussian Elimination Method
Existence and Uniqueness 1
Existence and Uniqueness 2
Inverse of a Matrix 1
Inverse of a Matrix 2
Solving systems with Inverse 1
Solving Systems with Inverse 2
Solving systems with Inverse 3
Vector Spaces and Subspaces
4 konu anlatımı · 6 soru
Vector Spaces and Subspaces 1
Vector Spaces and Subspaces 2
Matrix Spaces & Matrix Subspaces
Polynomial Subspaces
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Linear Independence
1 konu anlatımı · 6 soru
Linear Independent Sets
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Basis for General Subspaces
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Basis for Vector Subspaces
Basis for Polynomial Subspaces
Basis for Matrix Subspaces
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Basis for Null, Column and Row Spaces
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Bases for Col A & Row A & Null A
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Orthogonal Basis
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Orthogonal Sets and Basis
Advantage of an Orthogonal Basis
Orthonormal Sets and Basis
Orthogonal Matrix
Orthogonal Projection
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Orthogonal Projection 1
Orthogonal Projection 2
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Matrix Equations
3 konu anlatımı · 4 soru
Matrix Equations and Augmented Matrix
Solutions of Homogeneous Linear Systems
Solutions of Non-Homogeneous Linear Systems
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Determinants
4 konu anlatımı · 11 soru
Determinant & Cofactor Expansion
Determinants of Bigger Matrices
Properties of Determinant I
Properties of Determinant II
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Adjoint of a Matrix
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Adjoint of a Matrix I
Adjoint Matrix II
Adjoint Matrix III
Adjoint Matrix IV
Adjoint Matrix V
Eigenvalues and Eigenvectors
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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
Diagonalization
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Diagonalization 1
Diagonalization 2
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Exam Practice Problems
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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 4
Cofactor Expansion
Cofactor
Inverse Matrix
Eigenvalues
Eigenvalue Eigenvector Diagonalizable
Diagonalization 1
Diagonalization 2
Diagonalization 3
Diagonalization 4
Diagonalization 5
Eigenvalue and Null Space
Fall 2025 Final Exam
5 soru
True/False Questions
Diagonalization
Power Series Solution
System of Linear Equations
Fundamental Matrix
Fall 2024 Final Exam
4 soru
Undetermined Coefs. Method
Exact Equation
Undetermined Coefs. Method
Solving DE with Laplace Tr.
Spring 2025 Final Exam
2 soru
Question 1
Question 2