MATH 241 • Tüm Sınavlar • Differential Equations
Diferansiyel Denklemler dersi bundan önce aldığın Calculus (Math 131) ve Linear Algebra (Math 221) 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
First Order Linear Differential Equations
2 konu anlatımı · 7 soru
Introduction: What is a Differential Equation
Integrating Factor Method
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Separable Differential Equations
1 konu anlatımı · 6 soru
Separable Equations
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Homogeneous Equations
1 konu anlatımı · 2 soru
Homogeneous Equations
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Bernoulli Equations
1 konu anlatımı · 3 soru
Bernoulli Equations
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Applications: Modelling with Differential Equations
1 konu anlatımı · 2 soru
Modeling with Differential Equations
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Discontinuous Functions: First Order Equations
2 konu anlatımı · 1 soru
Discontinuous Functions: Case 1
Discontinuous Functions: Case 2
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Ricatti Equations
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Ricatti Equations
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Clairaut Equations
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Clairaut 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
8 konu anlatımı · 3 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
Homogeneous Equations with Constant Coefficient
Homogeneous Equations with Constant Coefficient 2
Homogeneous Equations with Constant Coefficient 3
Two Complex Roots 1
Two Complex Roots 2
Repeated Roots 1
Repeated Roots 2
Existence and Uniqueness Theorem
1 konu anlatımı · 1 soru
Existence and Uniqueness Theorem
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The Wronskian Determinant
4 konu anlatımı · 2 soru
Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
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Reduction of Order
3 konu anlatımı · 2 soru
Reduction of Order 1
Reduction of Order 2
Reduction of Order 3
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Cauchy - Euler Equations
1 konu anlatımı · 1 soru
Cauchy - Euler Equations
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Variation of Parameters
4 konu anlatımı · 3 soru
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
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Method of Undetermined Coefficients
3 konu anlatımı · 2 soru
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
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Sınav Provası 1: Fall 2021 Exam
3 soru
Discontinuous Functions: First Order Equations
Exact Equation (with Integrating Factor)
Undetermined Coefs. Method
Sınav Provası 2: Fall 2022 Exam
3 soru
Separable Equation
Bernoulli Equation
Reduction of Order
(NEW) Sınav Provası 3: Spring 2024 Exam
2 soru
Homogeneous Equation
Exact Equation (with Integrating Factor)
(NEW) Sınav Provası 4: Fall 2024 Exam
4 soru
Types of DE, Bernoulli Eqn.
Cauchy Euler Eqn.
Exact DE with Integrating Factor
Undetermined Coefs. Method
(NEW) Sınav Provası 5: Spring 2025 Exam
3 soru
Exact Equations and Integrating Factors
Caucy-Euler Equation, Reduction of Order
Existence- Uniqueness Theorem, Separable Equations
General Review Problems
21 soru
Linear First Order Equations
Linear First Order Equations
Linear First Order Equations
Separable Equations
Separable Equations
Separable Equations
Bernoulli Equation
Bernoulli Equation
Exact Equations
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Constant Coefficient 2nd Order Equations
Wronskian & Fundamental Set of Solutions
Wronskian & Linear Independence
Wronskian & Linear Independence
Reduction of Order
Reduction of Order
Method of Undetermined Coefficients
Method of Undetermined Coefficients
Method of Undetermined Coefficients
High Order Linear Equations
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General Theory of nth Order DEs (Wronskian)
Homogeneous DEs with Constant Coefficients
The Method of Undetermined Coefficients
Power Series Solution of Second Order Equations
6 konu anlatımı · 3 soru
Power Series Review
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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Regular Singular Points and Euler Equations
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Solution Near an Regular Singular Point-1
Classification of Singular Points
Solution Near an Regular Singular Point-2
Euler Equation-1
Euler Equation-2
Euler Equation-3
The Laplace Transform
5 konu anlatımı · 3 soru
Definition of Laplace Transform
Transforms of Basic Functions (without using table)
Transforms Advanced Functions (using table)
Inverse Laplace Transform I
Inverse Laplace Transform 2
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Solving Differential Equations by Laplace Transform
3 konu anlatımı · 3 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 · 4 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 · 2 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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Review of Math 221
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Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
Complex Eigenvalues
Complex Eigenvalues-2
Systems of First Order Linear Equations
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Introduction
Homogeneous Systems Solution for Distinct Real Eigenvalues 1
Homogeneous Systems Solution for Distinct Real Eigenvalues 2
Homogeneous Systems Solution for Complex Eigenvalues 1
Homogeneous Systems Solution for Complex Eigenvalues 2
Homogeneous Systems Solution for Repeated Eigenvalues 1
Homogeneous Systems Solution for Repeated Eigenvalues 2
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Fall 2021 Final Exam
4 soru
Variation of Parameters Method
Power Series Solution Around Regular Singular Point
System of Linear DE (EVP Solution)
Solving DE with Laplace Tr.
Fall 2022 Final Exam
4 soru
Undetermined Coefs. Method
Power Series Solution Around Regular Singular Point
Solving DE with Laplace Tr.
Laplace Transform Involving a Convolution Integral
Spring 2022 Final Exam
4 soru
Variation of Parameters Method
Power Series Solution Around Regular Singular Point
Solving DE with Laplace Tr.
System of Linear DE (EVP Solution)
Fall 2024 Final Exam
4 soru
Variation of Parameters Method
Power Series Solution Around Ordinary Point
System of Linear DE (EVP Solution)
Solving DE with Laplace Tr.
Bonus Part: General Review Problems
11 soru
Variation of Parameter
Power Series Solution
Power Series Solution
Power Series Solution
Solving Equations with Laplace Transform
Solving Equations with Laplace Transform
Laplace Transform: Step Function
Laplace Transform: Step Function
Laplace Transform: Convolution Integral
System of DE: Distinct Real Eigenvalues
System of DE: Complex Eigenvalues