MATH 204 • Tüm Sınavlar • Differential Equations
Eski öğrencilerimizin yorumları her şeyi özetlese de bizde bir şeyler söylemek istiyoruz: Unicourse'un kurulduğu ilk dönemde, öğrencilerimize sunduğumuz ilk dersimizdi Math 204.
Tüm kayıtları Koç'un kampüsünde alınmıştır. Kısacası ilk göz ağrımızdır ve bizim için sembolik bir önemi vardır bu dersin. Diferansiyel Denklemler dersi bundan önce aldığın Calculus (MATH 106), Multivariable Calculus (MATH 203), Linear Algebra (MATH 107) derslerinden birer parça barındırıyor; Bu dersimizde sunduğumuz tüm konular, sırasıyla: 1) First Order Differential Equations with Integrating Factor 2) Separable Equations 3) Bernoulli Equations 4) Exact Equations 5) Exact Equations and Integrating Factors 6) Existence and Uniqueness Theorem 7) Second Order Homogeneous Equations 8) Reduction of Order Method 9) Wronskian Determinant 10) Abel’s Theorem 11) Existence and Uniqueness for Second Order Equations 12) Method of Undetermined Coefficient 13) Method of Variation of Parameters
Ayda 1899 TL, peşin fiyatına 3 taksit
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 2.1: 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
Section 2.2: 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
Section 2.4 Part I: Bernoulli Equations
1 konu anlatımı · 3 soru
Bernoulli Equations
Exam like Question 1
Exam like Question 2
Exam like Question 3
Section 2.4 Part II: Homogeneous Equations
1 konu anlatımı · 4 soru
Homogeneous Equations
Exam like Question 1
Exam Like Question 2
Exam Like Question 3
Exam like Question 4
Section 2.6: Exact Differential Equations
7 konu anlatımı · 4 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
Section 2.5: Autonomous DE & Population Models
3 konu anlatımı
Modeling with DE & Population Models I
Modeling with DE & Population Models II
Autonomous Differential Equations
Existence and Uniqueness Theorem
3 konu anlatımı
Existence and Uniqueness Theorem I
Existence and Uniqueness Theorem II
Existence and Uniqueness Theorem III
Section 3.1-3.3: Second Order Differential Equations
7 konu anlatımı · 5 soru
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
Exam like Question 1-2-3
Exam like Question 4-5-6
Exam like Question 7-8-9
Exam like Question 10-11-12
Exam like Question 13
Section 3.2: The Wronskian Determinant
6 konu anlatımı · 3 soru
Wronskian Determinant 1
Wronskian Determinant 2
Wronskian Determinant 3
Fundamental Set of Solution 1
Fundamental Set of Solution 2
Wronskian and Linear Independence
Exam like Question 1
Exam like Question 2
Exam like Question 3
Section 3.2: Abel's Theorem
2 konu anlatımı · 2 soru
Abel’s Theorem 1
Abel’s Theorem 2
Exam-like Question 1
Exam-like Question 2
Existence & Uniqueness for Second Order DE
1 konu anlatımı · 2 soru
Existence & Uniqueness for 2nd Order DE
Exam like Question 1
Exam like Question 2
Section 3.4: Reduction of Order
3 konu anlatımı · 2 soru
Reduction of Order I
Reduction of Order II
Reduction of Order III
Exam like Question 1
Exam like Question 2
Section 3.5: The Method of Undetermined Coefficient
3 konu anlatımı · 4 soru
Undetermined Coefficients I
Undetermined Coefficients II
Undetermined Coefficients III
Exam like Question 1-2-3-4-5
Exam like Question 6
Exam like Question 7
Exam like Question 8
Section 3.6: Variation of Parameters
1 konu anlatımı · 4 soru
Variation of Parameter
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Past Exams & Sample Midterm Problems
49 soru
Integrating Factor 1
Integrating Factor 2
Integrating Factor 3
Integrating Factor 4
Integrating Factor 5
Separable Equations 1
Separable Equations 2
Separable Equations 3
Separable Equations 4
Bernoulli Equation 1
Bernoulli Equation 2
Bernoulli Equation 3
Exact Equations
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Second Order Eq. with Constant Coefficients
Second Order Eq. with Constant Coefficients
Second Order Eq. with Constant Coefficients
Second Order Eq. with Constant Coefficients
Fundamental Set of Solutions 1
Fundamental Set of Solutions 2
Fundamental Set of Solutions 3
Fundamental Set of Solutions 4
From Wronskian to Equation 1
From Wronskian to Equation 2
Abel's Theorem 1
Abel's Theorem 2
Abel's Theorem 3
Abel's Theorem 4
Reduction of Order 1
Reduction of Order 2
Reduction of Order 3
Reduction of Order 4
Method of Undetermined Coefficients
Method of Undetermined Coefficients
Method of Undetermined Coefficients
Method of Undetermined Coefficients
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
Challenging Past Exam Problem I
Challenging Past Exam Problem II
Challenging Past Exam Problem III
Challenging Past Exam Problem IV
Challenging Past Exam Problem V
Sample Midterm 1 Questions 1
8 soru
Problem 1 Part A: Separable Equations
Problem 1 Part B: Bernoulli Equations
Problem 2: Exact Equations
Problem 3 Part A: Second ODE with Two Complex Roots
Problem 3 Part B: Finding Equation from Solution
Problem 3 Part C: Theory of Second ODE & Wronskian
Problem 4 Part A-B: Abel's Theorem
Problem 5: Variation of Parameters
Sample Midterm 1 Questions 2
9 soru
Separable Differential Equations
Bernoulli Differential Equation
Exact Differential Equations
(Fall 2024 Final) Exact Differential Equations
Second Order ODE with Constant Coefficients
Existence and Uniqueness Theorem
Second Order ODE with Constant Coefficients
Fundamental Set of Solutions
Abel’s Theorem
Variation of Parameters
1 konu anlatımı · 4 soru
Variation of Parameter
Exam like Question 1
Exam like Question 2
Exam like Question 3
Exam like Question 4
Power Series Solution of Second Order Equations
5 konu anlatımı · 2 soru
Power Series Review
Power Series Solutions I
Power Series Solutions II
Power Series Solutions III
Power Series Solutions IV
Exam-like Question 1
Exam-like Question 2
The Laplace Transform
6 konu anlatımı · 3 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
Exam-like Question 2
Exam-like Question 3
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
Exam-like Question 1
Exam-like Question 2
Exam-like Question 3
Step Functions and IVP
6 konu anlatımı · 4 soru
Step Functions 1
Step Functions 2
Step Functions 3
Exam-like Question 1
Exam-like Question 2
Initial Value Problems with Step Functions 1
Initial Value Problems with Step Functions 2
Initial Value Problems with Step Functions 3
Exam-like Question 3
Exam-like Question 4
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
Exam-like Question 1
Exam-like Question 2
Review of Math 107
4 konu anlatımı
Eigenvalues & Eigenvectors: 3 Vital Steps
Eigenvalues & Eigenvectors: A Special Tip
Complex Eigenvalues
Complex Eigenvalues-2
Systems of First Order Linear Equations
5 konu anlatımı · 2 soru
Introduction
Homogeneous Systems: Distinct Real Eigenvalues 1
Homogeneous Systems: Distinct Real Eigenvalues 2
Homogeneous Systems: Complex Eigenvalues 1
Homogeneous Systems: Complex Eigenvalues 2
Exam-like Question 1
Exam-like Question 2
Non-homogeneous Systems Part I
3 konu anlatımı · 3 soru
Review of Diagonalization
Method of Diagonalization I
Method of Diagonalization II
Exam like Question 1
Exam like Question 2
Exam like Question 3
Non-homogeneous Systems Part II
3 konu anlatımı · 2 soru
Fundamental Matrices
Variation of Parameters Method 1
Variation of Parameters Method 2
Exam-like Question
Fall 2024 Final Exam Problem
Past Exams & Sample Midterm Problems
31 soru
Variation of Parameter 1
Variation of Parameter 2
Variation of Parameter 3
Variation of Parameter 4
Power Series Solution 1
Power Series Solution 2
Power Series Solution 3
Power Series Solution 4
Power Series Solution 5
Laplace Transform 1
Laplace Transform 2
Laplace Transform 3
Laplace Transform & Step Function
Laplace Transform & Step Function 2
Laplace Transform & Step Function 3
Laplace Transform & Step Function 4
Laplace Transform & Step Function 5
The Convolution Integral 1
The Convolution Integral 2
The Convolution Integral 3
The Convolution Integral 4
Systems of Differential Equations 1
Systems of Differential Equations 2
Systems of Differential Equations 3
Systems of Differential Equations 4
Systems of Differential Equations 5
Systems of Differential Equations 6
Systems of Differential Equations 7
Systems of Differential Equations 8
Systems of Differential Equations 9
Systems of Differential Equations 10
(Bonus): Extra Exam Practice
17 soru
Variation of Parameters
Variation of Parameters
Variation of Parameters Method
Power Series Solution
Power Series Solution
Power Series Solution
Solving Equations with Laplace Transform
Solving Equations with Laplace Transform
Solving Equations with Laplace Transform
Laplace Transform: Step Function
Laplace Transform: Step Function
Laplace Transform: Step Function
Laplace Transform: Convolution Integral
Laplace Transform: Convolution Integral
System of DE: Distinct Real Eigenvalues
System of DE: Distinct Real Eigenvalues
System of DE: Complex Eigenvalues
Sınav Provası: Fall 2024 Exam
7 soru
Variation of Parameters Method
Homogeneous and Constant Coef. Diff. Equations
Power Series Solution with Taylor's Expansion
Power Series Solution around Ordinary Point
Laplace Transform with Convolution Integral
Inverse Laplace Transform
Solution of Diff. Eqns. with Laplace Transform
Sınav Provası: Spring 2025 Exam
4 soru
Power Series Solution
Convolution Integral and Laplace Transform
Solution of D.Es. with Laplace Transform
System of Equations (using Eigen Value Solution)
Numerical Methods: Euler's Method
4 konu anlatımı · 2 soru
Euler’s Method I
Euler’s Method II
Exam like Question 1
Exam like Question 2
Improved Euler’s Method (Heun's Method)
Improved Euler’s Method (Heun's Method)
Boundary Value Problems: EigenFunctions
1 konu anlatımı · 3 soru
Eigen-Functions
Exam like Question 1
Exam like Question 2
Exam like Question 3
Fourier Series
4 konu anlatımı · 3 soru
Fourier Series I
Fourier Series II
Fourier Series III
Fourier Series IV
Exam like Question 1
Exam like Question 2
Exam like Question 3
Separation of Variables: Heat Conduction in a Rod
1 konu anlatımı · 3 soru
Heat Equations
Exam like Question 1
Exam like Question 2
Exam like Question 3
The Wave Equation
1 konu anlatımı · 2 soru
Wave Equation
Exam like Question 1
Exam like Question 2
(NEW) Extra Final Practice Part I
12 soru
Euler's Method
Eigenfunction and Boundary Value Problems
Eigenfunction and Boundary Value Problems
Fourier Series Expansion
Fourier Series Expansion
Fourier Series Expansion
Heat Equation
Heat Equation
Heat Equation
Heat Equation
Heat Equation
Heat Equation
(NEW) Extra Final Practice Part II
8 soru
Euler Method
Euler Method
Boundary Value Problems
Boundary Value Problems
EigenFunctions: Boundary Value Problems
EigenFunctions: Boundary Value Problems
Fourrier Series Expansion
Fourrier Series Expansion
Sample Final Problems
15 soru
Systems of Differential Equations 1
Systems of Differential Equations 2
Systems of Differential Equations 3
Systems of Differential Equations 4
Systems of Differential Equations 5
Systems of Differential Equations 6
Systems of Differential Equations 7
Systems of Differential Equations 8
Systems of Differential Equations 9
Systems of Differential Equations 10
Systems of Differential Equations 11
Non-homogeneous Systems 1
Non-homogeneous Systems 2
Challenging Past Final Problem 1
Challenging Past Exam Problem 2
Sample Final Questions 1
10 soru
Linear Equations
Exact Equations
Reduction of Order Method
Power Series Solution of DEs.
Variation of Parameters Method for System of Diff. Equations
Exponent of a Matrix (Eigen Val. Prob. and Fundamental Matrix)
Fourier Series
Heat Equation (Part-1)
Heat Equation (Part-2)
Wave Equation (d'Alembert's Formula)
Bonus Part: Midterm Subjects
22 soru
Linear Equations
Linear Equations
Separable Equation
Separable Equation
Separable Equation
Bernoulli Equation
Bernoulli Equation
Exact Equation
Exact Equation (with Integrating Factor)
Exact Equation (with Integrating Factor)
Reduction of Order Method
Reduction of Order Method
Variation of Parameters Method
Variation of Parameters Method
Variation of Parameters Method
Power Series Solution
Power Series Solution
Solving DE with Laplace Tr.
Solving DE with Laplace Tr.
Solving DE with Laplace Tr.
Solving DE with Laplace Tr.
Solving DE with Laplace Tr.