MATH 207 • Tüm Sınavlar • Introduction to Differential Equations I
Diferansiyel Denklemler dersi bundan önce aldığın Calculus I - II ve Linear Algebra 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.
Gürkan Hoca
Öğr. Üy.
Orta Doğu Tekn. Üni.'den derece ile mezun olduktan sonra yüksek lisans ve doktora çalışmalarımı da yurt dışında tamamladım. Ardından aynı üniversitede öğretim üyesi olarak görev yaptım. Üniversite öğrencisi olmanın ne demek olduğunu unutmayarak, dersleri öğrencilerimin gözünden anlatmanın ve onlara özel anlama yolları geliştirmenin önemini çok iyi biliyorum. Öğretmenin aslında bir "sanat" olduğunu biliyorum ve bu sanatı sizlere gösterebilmek için buradayım.
Ömer Faruk Altun
Co-founder & Head of Education
2011 yılında Endüstri Mühendisliği okumak için başladığım Sabancı Üniversitesi'nden 2018 yılında Bilgisayar Mühendisi olarak mezun oldum. 13 yıldır Altun ismiyle başta Sabancı Üniversitesi olmak üzere çeşitli okullarda Endüstri ve Bilgisayar Mühendisliği alanlarında ders vermekteyim. Unicourse'ta sunduğum derslerin yanında eğitim departmanının da sorumluluğunu üstlenmekteyim.
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
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Bernoulli Equations
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Homogeneous Differential Equations
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Homogeneous Equations
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Other Substitution Techniques
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Case 1: Given Substitution
Case 2: Equations of the form F(ax + by + c)
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Applications: Modeling with Differential Equations
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Modeling with Diff. Eqns. (Applications)
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Exact Differential Equations
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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
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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
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Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
Wronskian and Linear Independence
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Reduction of Order Method
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Reduction of Order 1
Reduction of Order 2
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Variation of Parameters
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Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
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Method of Undetermined Coefficients
4 konu anlatımı · 6 soru
Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
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D metodu - Konu Anlatımı
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High Order Linear Equations
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General Theory of nth Order DEs (Wronskian)
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Homogeneous DEs with Constant Coefficients
The Method of Undetermined Coefficients
The Method of Variation of Parameters
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Systems of First Order Differential Equations
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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
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(NEW) FALL 2024 Exam Problems
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Homogeneous Equations
Bernoulli Equations
Numerical Solution of a 1st Oder ODE with Euler and Heun's Method
2nd Order Const. Coef. Homogeneous Equations
(NEW) FALL 2025 Exam Problems
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Applications
Method of Undetermined Coefficients
Constant Coef. Differential Equations, Wronskian
Method of Variation of Parameters
Existence and Uniqueness Theorem
Exact Equations
Substitutions
Cauchy-Euler Equation
Power Series Solution of Second Order Equations
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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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The Laplace Transform
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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
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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
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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
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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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Linear Algebra Review (Hiç hatırlamayanlar)
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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
Linear Algebra Review (Temelim sağlam diyenler)
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Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
A Matrix with Irrational Eigenvalues
Complex Eigenvalues
Complex Eigenvalues-2
Fundamental Matrix
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Fundamental Matrices
Solving systems with Fundamental Matrices
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Non-homogeneous Systems Part I
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Linear Algebra: Nonhomogeneous Systems
Non-hom. Systems: Given Particular Solution
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Review of Diagonalization
Method of Diagonalization I
Method of Diagonalization II
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Non-homogeneous Systems Part II
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Variation of Parameters Method 1
Variation of Parameters Method 2
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(NEW) FALL 2024 Exam Problems
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Solution with Substitutions
Method of Undetermined Coefficients
Solution of ODEs with Laplace Transform
Solution of a System of ODEs with Laplace Transform
Power Series Solution around an Ordinary Point
(NEW) FALL 2025 Exam Problems
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Substitutions
Power Series Solution around Ordinary Points
Solution of Diff. Eqns. with Laplace Transform
General Solution of a 2nd Order Const. Coef. Diff. Eqn. (with boundary values)
Linear Equations
Method of Undetermined Coefficients
Solution with Laplace Transform including Convolution Integral
Past Exam Problems
4 soru
Applications, Substitutions
Solution of Diff. Eqns. with Laplace Transform
Laplace Transform of a Piecewise Function
Cauchy-Euler Equation