MATH 202 • Midterm II + Final • 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.
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.
Paketi Tamamla
🎓 Sabancı Üniversitesi öğrencilerinin %92'si tüm paketi alarak çalışıyor.
Konular
Linear Independence of Solutions (Wronskian)
Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
Exam like Question 1
Exam like Question 2
4.6-4.7: Variation of Parameters
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
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 12
4.7: Reduction of Order
Reduction of Order 1
Reduction of Order 2
Exam like Question
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
4.7: Existence and Uniqueness Theorem
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence & Uniqueness for 2nd Order DE
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
4.7: Cauchy-Euler Equations
Cauchy - Euler Equations
Exam like Question 1
Exam like Question 2
6.1-6.4: High Order Linear Equations
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
7.1-7.4: The Laplace Transform
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
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
7.5: Solving Differential Equations by Laplace Transform
Laplace Transform of Derivative
Laplace Transform and Initial Value Problems 1
Laplace Transform and Initial Value Problems 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
7.6: Step Functions and IVP
Step Functions 1
Step Functions 2
Step Functions 3
Exam-like Question 4
Exam-like Question 5
Initial Value Problems with Step Functions 1
Initial Value Problems with Step Functions 2
Initial Value Problems with Step Functions 3
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
7.7: The Convolution Integral
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
Exam-like Question 8
Exam-like Question 9
Exam-like Question 10
Exam-like Question 11
8.1-8.3: Power Series Solution of Second Order Equations
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
Exam-like Question 1
Exam-like Question 2
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
8.5-8.6: Regular Singular Points and Euler Equations
Solution Near an Regular Singular Point-1
Classification of Singular Points
Solution Near an Regular Singular Point-2
Euler Equation I
Euler Equation II
Euler Equation III
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
9.1-9.3: Linear Algebra Review (Hiç hatırlamayanlar)
Matrix Equations and Augmented Matrix
Homogeneous Linear Systems
Inverse of a Matrix
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Complex Eigenvalues
Complex Eigenvalues-2
9.1-9.3: Linear Algebra Review (Temelim sağlam diyenler)
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Complex Eigenvalues
Complex Eigenvalues-2
9.4-9.6: Systems of First Order Differential Equations
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
9.4-9.6: Fundamental Matrix
Fundamental Matrices
Solving systems with Fundamental Matrices
Exam-like Question 1
Exam-like Question 2
9.7: Non-homogeneous Systems Part I
Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
Exam like Question 1
Review of Diagonalization
Method of Diagonalization I
Method of Diagonalization II
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam-like Question 5
Exam-like Question 6
9.7: Non-homogeneous Systems Part II
Variation of Parameters Method 1
Variation of Parameters Method 2
Exam-like Question 1
Exam like Question 2
Boundary Value Problems: Eigen-Functions
Eigen-Functions 1
Eigen-Functions 2
Eigen-Functions 3
(NEW) Past Exam Spring 23
Fundamental Matrix
Fundamental Matrix and Nonhomogeneous System
First Order Differential Equation
Laplace Transform
(NEW) Past Exam Summer 20
Second Order ODE and Systems
Eigenvalues and Eigenvectors
Homogeneous System
Laplace Transform
(NEW) Past Exam Spring 24
Laplace Transform
Higher Order HE
Second Order DE
(NEW) Past Exam Spring 25
Laplace
Homogeneous DE
Linear 1st Order Homogeneous DE
Fundamental Matrix
Değerlendirmeler
Sıkça Sorulan Sorular
Örneğin, Koç Üniversitesi - MATH 101 (Calculus) veya başka bir okulun benzer dersi olsun, paketlerimiz tam da o derse göre tasarlanır. Böylece nokta atışı çalışır, zaman kazanırsın.
Sınava özel videolar —konu anlatımları, çıkmış sorular ve çözümleri, özet notlar—içerir. Sınavda sıkça çıkan soruları hedefler. Eğitmenlerimiz, üniversitenin akademik takvimini takip ederek paketleri sürekli günceller. Böylece, gereksiz detaylarla vakit kaybetmeden başarını artırmaya odaklanabilirsin.
Ders İçeriği
Linear Independence of Solutions (Wronskian)
Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
Exam like Question 1
Exam like Question 2
4.6-4.7: Variation of Parameters
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
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 12
4.7: Reduction of Order
Reduction of Order 1
Reduction of Order 2
Exam like Question
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
4.7: Existence and Uniqueness Theorem
Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence & Uniqueness for 2nd Order DE
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
4.7: Cauchy-Euler Equations
Cauchy - Euler Equations
Exam like Question 1
Exam like Question 2
6.1-6.4: High Order Linear Equations
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
7.1-7.4: The Laplace Transform
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
Exam-like Question 2
Exam-like Question 3
Exam-like Question 4
7.5: Solving Differential Equations by Laplace Transform
Laplace Transform of Derivative
Laplace Transform and Initial Value Problems 1
Laplace Transform and Initial Value Problems 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
7.6: Step Functions and IVP
Step Functions 1
Step Functions 2
Step Functions 3
Exam-like Question 4
Exam-like Question 5
Initial Value Problems with Step Functions 1
Initial Value Problems with Step Functions 2
Initial Value Problems with Step Functions 3
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
7.7: The Convolution Integral
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
Exam-like Question 8
Exam-like Question 9
Exam-like Question 10
Exam-like Question 11
8.1-8.3: Power Series Solution of Second Order Equations
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
Exam-like Question 1
Exam-like Question 2
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
8.5-8.6: Regular Singular Points and Euler Equations
Solution Near an Regular Singular Point-1
Classification of Singular Points
Solution Near an Regular Singular Point-2
Euler Equation I
Euler Equation II
Euler Equation III
Exam-like Question 3
Exam-like Question 4
Exam-like Question 5
Exam-like Question 6
Exam-like Question 7
Exam-like Question 8
9.1-9.3: Linear Algebra Review (Hiç hatırlamayanlar)
Matrix Equations and Augmented Matrix
Homogeneous Linear Systems
Inverse of a Matrix
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Complex Eigenvalues
Complex Eigenvalues-2
9.1-9.3: Linear Algebra Review (Temelim sağlam diyenler)
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Complex Eigenvalues
Complex Eigenvalues-2
9.4-9.6: Systems of First Order Differential Equations
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
9.4-9.6: Fundamental Matrix
Fundamental Matrices
Solving systems with Fundamental Matrices
Exam-like Question 1
Exam-like Question 2
9.7: Non-homogeneous Systems Part I
Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
Exam like Question 1
Review of Diagonalization
Method of Diagonalization I
Method of Diagonalization II
Exam like Question 2
Exam like Question 3
Exam like Question 4
Exam-like Question 5
Exam-like Question 6
9.7: Non-homogeneous Systems Part II
Variation of Parameters Method 1
Variation of Parameters Method 2
Exam-like Question 1
Exam like Question 2
Boundary Value Problems: Eigen-Functions
Eigen-Functions 1
Eigen-Functions 2
Eigen-Functions 3
(NEW) Past Exam Spring 23
Fundamental Matrix
Fundamental Matrix and Nonhomogeneous System
First Order Differential Equation
Laplace Transform
(NEW) Past Exam Summer 20
Second Order ODE and Systems
Eigenvalues and Eigenvectors
Homogeneous System
Laplace Transform
(NEW) Past Exam Spring 24
Laplace Transform
Higher Order HE
Second Order DE
(NEW) Past Exam Spring 25
Laplace
Homogeneous DE
Linear 1st Order Homogeneous DE
Fundamental Matrix