MATH 152 • Midterm + Final • Differential Equations
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Gürkan Hoca
Öğr. Üy.
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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