MATH 202 - Differential Equations - Midterm
Bu ders hakkında
Diferansiyel denklemler dersimize hoş geldiniz. Bu ders almış olduğunuz diğer matematik derslerinden oldukça farklı bir yapıya sahip. Fakat endişe etmenize hiç gerek yok. Bu dersten en yüksek verimi alabilmeniz için paketimizi şu şekilde kurguladık:
- Öncelikle konuları dikkatlice ayırdık ve çok detaylı bir şekilde ve herkes ilk defa öğreniyormuş gibi anlattık,
- Anlattığımız her konunun altına konuyu destekleyici örnekler çözdük ve bunu yaparken hiçbir adımı atlamadan ve yapılan işlemleri silmeden yaptık,
- Çözdüğümüz örnekleri de kolaydan zora doğru sıraladık, bu sayede öğrenme aşamasında eksik bir şey kalmadığına emin olduk,
- Soruları çözerken o soruya ait olan formülleri ve kullanılacak denklemleri sayfanın sağ üst köşesine hatırlatıcı olarak koyduk,
- Bu derste çözümlerin verilen denklemi sağlaması çok önemli, bu sebeple çözümlerin hepsinin doğruluğunu ispatladık,
- Bununla da yetinmedik, Wolfram Alpha, Mathdf, Emath gibi uygulamalar yardımıyla çözümlerimizi teyit ettik,
- Son 15 yılın sınav sorularını derledik ve farklı tarzda olanların tamamını paketimize ekledik,
- MIT gibi oldukça kaliteli sorular üreten üniversitelerin de beğendiğimiz sorularını paketimize dahil ettik,
- Ödevlerin öğrenme konusunda en büyük yardımcılar olduğunun farkındayız, bu sebeple sizlere ödevler verdik ve cevap anahtarını çok beğeneceğiniz bir formatta yayınladık.
- Son olarak paketin sonuna herşeyin olduğu "Summary" ve "Cheat Sheet" pdf dosyaları koyduk.
Ders paketimizi hiçbir şeyi atlamadan adım adım izleyerek bu dersten en yüksek verimi ve sınavlardan en yüksek notları alacağınıza eminiz. Hepinize başarılar dileriz.
Eğitmenler
Fatih Hoca
MATH 202
Herkese merhaba, ben Fatih Hoca. Üniversiteyi birincilikle tamamladıktan sonra 2008-2014 yılları arasında Koç Üniversitesi'nde Yüksek Lisans ve Doktora eğitimleri aldım ve birçok dersin asistanlığını yaptım. 22 senedir binlerce öğrenciye "General Physics I, General Physics II, Finite Mathematics, Calculus, Linear Algebra, Multivariable Calculus, Differentiable Equations" derslerinde yardımcı oldum ve bundan sonra da yanlarında olmaya devam edeceğim.
(4.9)
Önerilen Dersler
Konular
Test Yourself Before You Study First Order Differential Equations
EXAM - First Order Differential Equations
EXAM - First Order Differential Equations
Introduction to Differential Equations
What is a Differential Equation ?
Classifying Differential Equations
An Example for Classification of Differential Equations
First Order Differential Equations
Scheme of First Order Differential Equations
Vital Steps to Solve First Order Differential Equations
Linear, Non-Homogeneous Differential Equations
Integrating Factor
An Equation with the Standard Form
Verifying the Solution
Another Approach for the Previous Question
An Initial Value Problem
Verifying the Solution
Another Approach for the Previous Question
An Equation with a Non-Standard Form
Verifying the Solution
Another Approach for the Previous Question
Behavior of the Solution at Infinity
Homework 1
Homework 2
How can the Solution Remain Finite?
Homework 3
Homework 4
Linear, Homogeneous Differential Equations
Linear, Seperable Equations
Can We Solve it by Using Integrating Factor?
Verifying the Solution
An Example for Linear, Seperable Equations
Homework 5
Homework 6
Does It Have to be in Standard Form?
Homework 7
Homework 8
Non-Linear, Seperable Differential Equations
Non-Linear, Seperable Equations
Verifying the Solution
A Confusing Example
Homework 9
Non-Linear, Non-Seperable Differential Equations
Exact Differential Equations
An Example for Exact Differential Equations
Verifying the Solution
Example
Homework 10
Example
Homework 11
Non-Exact Differential Equations
Integrating Factor Depending on x
Homework 12
Integrating Factor Depending on y
Homework 13
An Example with a Different Structure
Homework 14
Special Case: Bernoulli Equation
Bernoulli Equation
An Example for Bernoulli Equation
Verifying the Solution
A Confusing Example
Homework 15
An IVP for Bernoulli Equation
Homework 16
Existence and Uniqueness Theorem Part I
Existence and Uniqueness Theorem
An Example for Existence and Uniqueness Theorem
Example
Test Yourself AGAIN After You Study First Order Differential Equations
EXAM - First Order Differential Equations
EXAM - First Order Differential Equations
Test Yourself Before You Study Second Order Differential Equations
EXAM - Second Order Differential Equations
EXAM - Second Order Differential Equations
Second Order Differential Equations
Scheme of Second Order Differential Equations
Vital Steps to Solve Second Order Differential Equations
Homogeneous Equations with Constant Coefficients
Homogeneous Equations with Constant Coefficients
1 - Distinct, Real Roots
An Example for Distinct, Real Roots
Verifying the Solution
An IVP for Distinct, Real Roots
Homework 17
What Happens If "t" Goes to Infinity ?
Homweork 18
2 - Imaginary Roots
An Example for Imaginary Roots
Homework 19
An IVP for Imaginary Roots
Verifying the Solution
3 - Repeated Roots
An Example for Repeated Roots
Homework 20
An IVP for Repeated Roots
Verifying the Solution
Wronskian
Wronskian and Fundamental Set of Solutions
An Example for Wronskian
Example
Wronskian - Integrating Factor Combined
Example
A Tricky Example for Wronskian
Abel's Theorem
Abel's Theorem
An Example for Abel's Theorem
Non-Standard Form Example for Abel's Theorem
Example
Example
Homogeneous Equations with Non-Constant Coefficients
Homogeneous Equations with Non-Constant Coefficients
Reduction of Order
Longer Solution or Shorter Solution ?
An Example for Reduction of Order
Verifying the Solution
Example
Homework 21
An IVP for Reduction of Order
Homework 22
Special Case: Euler Equation
Euler Equation
1 - Distinct, Real Roots
An Example for Distinct, Real Roots
Homework 23
2 - Imaginary Roots
An Example for Imaginary Roots
Homework 24
3 - Repeated Roots
An Example for Repeated Roots
Homework 25
Non-Homogeneous Equations with Constant Coefficiens
Non-Homogeneous Equations with Constant Coefficients
Variation of Parameters
An Example for Variation of Parameters
Second Method for Variation of Parameters
Homework 26
Non-Homogeneous Equations with Non-Constant Coefficients
Non-Homogeneous Equations with Non-Constant Coefficients
Variation of Parameters
An Example for Variation of Parameters
Verifying the Solution
Reduction of Order - Variation of Parameters Combined
Homework 27
Euler - Variation of Parameters Combined
Homework 28
Existence and Uniqueness Theorem Part II
Existence and Uniqueness Theorem
An Example for Existence and Uniqueness Theorem
Series Solutions of Second Order Differential Equations
Ücretsiz İçerikler
Remember These Tests !
Example 1
Series Solutions Near an Ordinary Point
Vital Steps for Series Solutions
Important Maclaurin Series Need to Know
Example 3 (Do You Remember Previous Subjects ?)
Example 4
Example 5
Example 6
Example 7
Example 8
Convergence of Power Series
Ücretsiz
Review of Power Series
Ücretsiz
Example 2
Ücretsiz
Test Yourself AGAIN After You Study Second Order Differential Equations
EXAM - Second Order Differential Equations
EXAM - Second Order Differential Equations
Cheat Sheet
Summary
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Konular
Test Yourself Before You Study First Order Differential Equations
EXAM - First Order Differential Equations
EXAM - First Order Differential Equations
Introduction to Differential Equations
What is a Differential Equation ?
Classifying Differential Equations
An Example for Classification of Differential Equations
First Order Differential Equations
Scheme of First Order Differential Equations
Vital Steps to Solve First Order Differential Equations
Linear, Non-Homogeneous Differential Equations
Integrating Factor
An Equation with the Standard Form
Verifying the Solution
Another Approach for the Previous Question
An Initial Value Problem
Verifying the Solution
Another Approach for the Previous Question
An Equation with a Non-Standard Form
Verifying the Solution
Another Approach for the Previous Question
Behavior of the Solution at Infinity
Homework 1
Homework 2
How can the Solution Remain Finite?
Homework 3
Homework 4
Linear, Homogeneous Differential Equations
Linear, Seperable Equations
Can We Solve it by Using Integrating Factor?
Verifying the Solution
An Example for Linear, Seperable Equations
Homework 5
Homework 6
Does It Have to be in Standard Form?
Homework 7
Homework 8
Non-Linear, Seperable Differential Equations
Non-Linear, Seperable Equations
Verifying the Solution
A Confusing Example
Homework 9
Non-Linear, Non-Seperable Differential Equations
Exact Differential Equations
An Example for Exact Differential Equations
Verifying the Solution
Example
Homework 10
Example
Homework 11
Non-Exact Differential Equations
Integrating Factor Depending on x
Homework 12
Integrating Factor Depending on y
Homework 13
An Example with a Different Structure
Homework 14
Special Case: Bernoulli Equation
Bernoulli Equation
An Example for Bernoulli Equation
Verifying the Solution
A Confusing Example
Homework 15
An IVP for Bernoulli Equation
Homework 16
Existence and Uniqueness Theorem Part I
Existence and Uniqueness Theorem
An Example for Existence and Uniqueness Theorem
Example
Test Yourself AGAIN After You Study First Order Differential Equations
EXAM - First Order Differential Equations
EXAM - First Order Differential Equations
Test Yourself Before You Study Second Order Differential Equations
EXAM - Second Order Differential Equations
EXAM - Second Order Differential Equations
Second Order Differential Equations
Scheme of Second Order Differential Equations
Vital Steps to Solve Second Order Differential Equations
Homogeneous Equations with Constant Coefficients
Homogeneous Equations with Constant Coefficients
1 - Distinct, Real Roots
An Example for Distinct, Real Roots
Verifying the Solution
An IVP for Distinct, Real Roots
Homework 17
What Happens If "t" Goes to Infinity ?
Homweork 18
2 - Imaginary Roots
An Example for Imaginary Roots
Homework 19
An IVP for Imaginary Roots
Verifying the Solution
3 - Repeated Roots
An Example for Repeated Roots
Homework 20
An IVP for Repeated Roots
Verifying the Solution
Wronskian
Wronskian and Fundamental Set of Solutions
An Example for Wronskian
Example
Wronskian - Integrating Factor Combined
Example
A Tricky Example for Wronskian
Abel's Theorem
Abel's Theorem
An Example for Abel's Theorem
Non-Standard Form Example for Abel's Theorem
Example
Example
Homogeneous Equations with Non-Constant Coefficients
Homogeneous Equations with Non-Constant Coefficients
Reduction of Order
Longer Solution or Shorter Solution ?
An Example for Reduction of Order
Verifying the Solution
Example
Homework 21
An IVP for Reduction of Order
Homework 22
Special Case: Euler Equation
Euler Equation
1 - Distinct, Real Roots
An Example for Distinct, Real Roots
Homework 23
2 - Imaginary Roots
An Example for Imaginary Roots
Homework 24
3 - Repeated Roots
An Example for Repeated Roots
Homework 25
Non-Homogeneous Equations with Constant Coefficiens
Non-Homogeneous Equations with Constant Coefficients
Variation of Parameters
An Example for Variation of Parameters
Second Method for Variation of Parameters
Homework 26
Non-Homogeneous Equations with Non-Constant Coefficients
Non-Homogeneous Equations with Non-Constant Coefficients
Variation of Parameters
An Example for Variation of Parameters
Verifying the Solution
Reduction of Order - Variation of Parameters Combined
Homework 27
Euler - Variation of Parameters Combined
Homework 28
Existence and Uniqueness Theorem Part II
Existence and Uniqueness Theorem
An Example for Existence and Uniqueness Theorem
Series Solutions of Second Order Differential Equations
Ücretsiz İçerikler
Remember These Tests !
Example 1
Series Solutions Near an Ordinary Point
Vital Steps for Series Solutions
Important Maclaurin Series Need to Know
Example 3 (Do You Remember Previous Subjects ?)
Example 4
Example 5
Example 6
Example 7
Example 8
Convergence of Power Series
Ücretsiz
Review of Power Series
Ücretsiz
Example 2
Ücretsiz
Test Yourself AGAIN After You Study Second Order Differential Equations
EXAM - Second Order Differential Equations
EXAM - Second Order Differential Equations
Cheat Sheet
Summary
