MATH 202 • Tüm Sınavlar • Differential Equations
Sabancı Üniversitesi MATH 202 (Differential Equations) Midterm sınavına hazırlık paketi.
İşlenen konular: Section 1.1-1.2: Introduction, Section 2.3: Linear First Order Equations, Section: 2.2: Separable Differential Equations, Section 2.4-2.5: Exact Equations & Integrating Factors, Section 2.6 Part I: Bernoulli Equation, Section 2.6 Part II: Homogeneous Equation, Section 2.6: Other Substitutions & Transformations, Section 3.1-3.4: Modeling with Differential Equations, Section 4.1-4.3: Homogeneous Second Order Linear Equations, Section 4.4-4.5: Method of Undetermined Coefficient, Linear Independence of Solutions (Wronskian).
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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
Section 1.1-1.2: Introduction
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Introduction: What is a Differential Equation
Section 2.3: Linear First Order Equations
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Integrating Factor Method
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Section: 2.2: Separable Differential Equations
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Separable Equations
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Section 2.4-2.5: Exact Equations & Integrating Factors
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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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Section 2.6 Part I: Bernoulli Equation
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Bernoulli Equations
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Section 2.6 Part II: Homogeneous Equation
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Homogeneous Equations
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Section 2.6: Other Substitutions & Transformations
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Other Substitutions (Case-1)
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Other Substitutions (Case-2)
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Section 3.1-3.4: Modeling with Differential Equations
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Modeling with Diff. Eqns. (Applications)
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Section 4.1-4.3: Homogeneous Second Order Linear Equations
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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
Section 4.4-4.5: Method of Undetermined Coefficient
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Undetermined Coefficients 1
Undetermined Coefficients 2
Undetermined Coefficients 3
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Method of D (Trial Solution)
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Linear Independence of Solutions (Wronskian)
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Wronskian Determinant 1
Wronskian Determinant 2
Fundamental Set of Solution 1
Fundamental Set of Solution 2
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Past Exam Problems
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Spring 2023 Exam: Applications: Modelling with DE
Summer 2020 Exam: Applications: Modelling with DE
Summer 2020 Exam: Classification of Differential Equations
Spring 2024 Exam: Bernoulli Equation
Spring 2024 Exam: Exact Equation with an Integrating Factor
Method of Undetermined Coefficients
Spring 2025 Exam
4 soru
Applications of 1st Oder ODEs (Population Growth)
Exact Equations and Integrating Factors
Reduction of Order
Method of Undetermined Coefficients
Spring 2024 Exam
4 soru
Applications: Modelling with DE
Exact Equation with an Integrating Factor
Bernoulli Equation
Homogeneous Second Order Linear Equations
4.6-4.7: 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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4.7: Reduction of Order
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Reduction of Order 1
Reduction of Order 2
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4.7: Existence and Uniqueness Theorem
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Existence and Uniqueness 1
Existence and Uniqueness 2
Existence and Uniqueness 3
Existence & Uniqueness for 2nd Order DE
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4.7: Cauchy-Euler Equations
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Cauchy - Euler Equations
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6.1-6.4: 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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7.1-7.4: 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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7.5: 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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7.6: 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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7.7: 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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8.1-8.3: 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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8.5-8.6: 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 I
Euler Equation II
Euler Equation III
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9.1-9.3: 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
9.1-9.3: 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
9.4-9.6: 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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9.4-9.6: Fundamental Matrix
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Fundamental Matrices
Solving systems with Fundamental Matrices
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9.7: 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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9.7: Non-homogeneous Systems Part II
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Variation of Parameters Method 1
Variation of Parameters Method 2
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Boundary Value Problems: Eigen-Functions
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Eigen-Functions 1
Eigen-Functions 2
Eigen-Functions 3
Matrix Exponential Function
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Definition and Properties
Finding Matrix Exponential Function: Part 1
Finding Matrix Exponential Function: Part 2
Example 1
Example 2
(NEW) Past Exam Spring 23
4 soru
Fundamental Matrix
Fundamental Matrix and Nonhomogeneous System
First Order Differential Equation
Laplace Transform
(NEW) Past Exam Summer 20
4 soru
Second Order ODE and Systems
Eigenvalues and Eigenvectors
Homogeneous System
Laplace Transform
(NEW) Past Exam Spring 24
3 soru
Laplace Transform
Higher Order HE
Second Order DE
(NEW) Past Exam Spring 25
4 soru
Solution of DEs with Laplace Transform
Homogeneous Const. Coef. Higher Order DEs
Homogeneous Solution of a System of DEs using Eigen Value Problem
Fundamental Matrix of System of DEs (Repeating Eigen Value)