MATH 259 • Tüm Sınavlar • Linear Algebra and Differential Equations
Diferansiyel Denklemler dersi bundan önce aldığın Calculus (MATH 169), Multivariable Calculus (MATH 170), derslerinden birer parça barındırıyor; Merak etme, biz senin icin tüm bu bilgileri düzenledik.
Bu dersimizde sunduğumuz tüm konular, sırasıyla: 1) First-Order Differential Equations 2) Separable Equations 3) Method of Integrating Factor 4) Homogeneous Equations 5) Bernoulli Equations 6) Çıkmış Sınav Soruları Part I 7) Exact Equations & Integrating Factor 8) Substitution for some Second Order Equations 9) Çıkmış Sınav Soruları Part II
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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
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
Substitution: The Bernoulli Equation
1 konu anlatımı · 2 soru
Bernoulli Equations
Exam like Question 1
Exam like Question 2
Change of Variables: 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
Past Exams Problems Part I
10 soru
Integrating Factor
Integrating Factor (Summer 2020)
Integrating Factor (Fall 2018)
Integrating Factor
Integrating Factor (Spring 2019)
Homogeneous Eq. (Summer 2020)
Homogeneous Equation
Homogeneous Eq. (Spring 2019)
The Bernoulli Equation 1
The Bernoulli Equation 2
Exact Equations & Integrating Factor
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
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam like Question 5
Past Exam Problems Part II
6 soru
Exact Equations 1
Exact Equations 2 (Spring 2023)
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 Differential Equations
5 konu anlatımı
Homogeneous Equations with Constant Coefficient
Homogeneous Equations with Constant Coefficient 2
Homogeneous Equations with Constant Coefficient 3
Two Complex Roots
Repeated Roots
Wronskian Determinant
4 konu anlatımı
How to Calculate Wronskian Determinant
Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution
Variation of Parameters
3 konu anlatımı
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Method of Undetermined Coefficients
3 konu anlatımı
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
Reduction of Order
2 konu anlatımı · 1 soru
Reduction of Order 1
Reduction of Order 2
Exam like Question
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
(NEW) Fall 25 Exam
6 soru
Separable DE
Homogeneous DE
1st Order Linear DE
Integrating Factor
Exact DE
Matrices
Ch 7.2: 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
Ch 7.2: 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
Ch 7.2-7.3: 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
Ch 7.3: 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
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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
Ch 7.3: 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
Ch 7.3: 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
Ch 7.3: 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
Ch 5.1-5.2: Series Solutions: Ordinary Points
6 konu anlatımı
Power Series Review
Power Series Solutions I
Power Series Solutions II
Power Series Solutions III
Power Series Solutions IV
Power Series Solutions V
Ch 6.1: The Laplace Transform
6 konu anlatımı · 5 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
Exam-like Question 1-2-3
Exam-like Question 4-5-6
Exam-like Question 7-8-9
Exam-like Question 10-11
Exam-like Question 12
Ch 6.2: Solving Equations by Laplace Transform
3 konu anlatımı
Laplace Transform of Derivative
Laplace Transform and Initial Value Problems 1
Laplace Transform and Initial Value Problems 2
Ch 7.4-7.5-7.6-7.8: 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
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
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