MATH 215 • Midterm + Final • Differential Equations
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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.
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Konular
Introduction
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Introduction (Don't Skip this Video ;)
Atılım MATH276 Introduction Podcast
Preliminaries
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Fast Calculus Review
Classification of Differential Equations
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Existence Uniqueness Theorem for 1st Order DEs
Separable Equations
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Separable Equations
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Linear Equations
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Linear Equations
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Bernoulli Equations
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Bernoulli Equations
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Homogeneous Equations
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Homogeneous Equations
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Exact Equations and Integrating Factors
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Exact Equations
Integrating Factors for Exact Equations
Different Types of Integrating Factors
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Substitutions
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Substitutions
Substitutions for F(ax + by + c)
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Applications
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Applications
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1st Order ODEs: Review
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Overview of 1st Order Differential Equations
Higher Order Linear ODEs Basic Theory
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The Wronskian and Linear Independence
Higher Order Linear Ordinary Differential Equations: Basic Theory of Higher Order Linear ODEs
Reduction of Order Method
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Reduction of Order Method
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Homogeneous Constant Coefficient Equations
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Homogeneous Constant Coefficient Equations
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Undetermined Coefficients Method
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Undetermined Coefficients Method
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Variations of Parameters Method
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Variation of Parameters Method (Non-Wronskian Method)
Variation of Parameters Method (Wronskian Method)
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Cauchy-Euler Equations
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Caucy Euler Equation
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Power Series Solutions
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Power Series Solutions (Ordinary Point)
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Power Series Solutions (Regular Singular Points)
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Laplace Transforms
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Laplace Transform (Introduction)
Laplace Transform as an Integral
Laplace of Basic Functions (without using table)
Laplace Tables and Properties of Laplace Transform-1
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Unit Impulse, Step and Ramp Functions
Laplace of Time Delayed and Periodic Functions
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Convolution and Complex Shift
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Initial and Final Value Theorems
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Inverse Laplace with Partial Fractions
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Solution of Differential Equations by the Laplace Transforms
Formula Sheet for Laplace Transforms
System of Linear ODEs
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System of Linear Ordinary Differential Equations
Partial Differential Equations
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Partial Differential Equations: Separation of Variables and Heat Equation
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Fourier Analysis and Solution of Heat Equation through the Fourier Series
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Fourier Analysis
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Past Exam Questions 1
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Substitutions
Laplace Transform of a Discontinuous Function
Verifying the Solutions, Linear Independence
Convolution Integral
Heat Equation
Fourier Transfrom
Classification of Singular Points
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Classification of Differential Equations
Bernoulli Equation
Separable Equation
Complementary and Particular Solutions (Wronskian and Linear Indep.)
Reduction of Order Method
Applications of Differential Equations
Exact Equation Integrating Factor
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Homogeneous Equations
Substitutions
Exact Equations and Integrating Factors
Reduction of Order Method
Homogeneous, Const. Coef. Higher Order DEs
Homogeneous, Const. Coef. Higher Order DEs
Applications
Past Exam Questions 4
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Partial Differential Equations: Heat Equation
Fourier Series Expansion
Bernoulli Equations
Solution of System of ODEs with Elimination
Power Series Solution Around Regular Singular Points
Solution of Higher Order ODEs: General Theory
Laplace Transform (with Convolution Integral)
Solution of ODEs with Laplace Transform (Piecewise Functions)
Formula Sheet for All Chapters
Formula Sheet for All Chapters