### Completeness of Root Functions of Regular Differential Operators

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Sufficient conditions are obtained for which this system is a Riesz basis. Similar results are obtained for the operator generated by the multipoint problem for an ordinary differential equation of even order with coefficients containing the involution operator.

Baranetskij, Boundary value problems with irregular conditions for differential-operator equations, Bukov. Baranetskij, A. Basha, Nonlocal multipoint problem for differential-operator equations of order 2n, J. Baranetskij, P. Kalenyuk, L. Kolyasa, Boundary-value for abstract second-order differential equations with operators involution, Bukov.

Kolyasa, M. Kopach, The nonlocal problem for the differentialoperator equation of the even order with the involution, Carpathian Math. Baranetskij, L. Kolyasa, Boundary-value problem for abstract second-order differential equation with involution, Journal Visnyk of Lviv Polytechnic National University. Physical and mathematical sciences, , 20— Birkhoff, On the asymptotic character of the solutions of certain linear differential equations containing a parameter, Trans.

Birkhoff, Boundary value and expansion problems of ordinary linear differential equations, Trans. Cabada, F.

Gokhberg, M. Ionkin, Solution of a boundary-value problem in heat conduction with a nonclassical boundary condition, Differ. Kalenyuk, Ya. This system of odes can be written in matrix form, and we explain how to convert these equations into a standard matrix algebra eigenvalue problem. We then discuss the important application of coupled harmonic oscillators and the calculation of normal modes. The normal modes are those motions for which the individual masses that make up the system oscillate with the same frequency.

Next, to prepare for a discussion of partial differential equations, we define the Fourier series of a function. Then we derive the well-known one-dimensional diffusion equation, which is a partial differential equation for the time-evolution of the concentration of a dye over one spatial dimension.

### Spectral properties of ordinary differential operators with involuton

We proceed to solve this equation for a dye diffusing length-wise within a finite pipe. It was a great journey to go through this course. Jeffery explains the concepts very well. I hope this course will help me greatly in my other courses. Thank you Prof. The lectures are really impressive and explain derivations throughly. I cannot enjoy more on a math course than this one.

### Introduction

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## Sasun Yakubov (Author of Completeness of Root Functions of Regular Differential Operators)

Visit the Learner Help Center. Browse Chevron Right. Math and Logic Chevron Right. Math and Logic. Differential Equations for Engineers. Offered By. About this Course 32, recent views. Flexible deadlines. Flexible deadlines Reset deadlines in accordance to your schedule. Beginner Level.

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Beginner Level Knowledge of single variable calculus. Hours to complete. Available languages. English Subtitles: English. What you will learn Check First-order differential equations. Check Second-order differential equations.

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Check The Laplace transform and series solution methods. Check Systems of differential equations and partial differential equations. Chevron Left. Syllabus - What you will learn from this course. Video 12 videos. Course Trailer 4m. Course Overview 2m. Introduction to Differential Equations 9m. Week 1 Introduction 47s.

Euler Method 9m. Separable First-order Equations 8m. Separable First-order Equation: Example 6m. Linear First-order Equations 13m.

## Second-order differential operators with interior singularity

Linear First-order Equation: Example 5m. Application: Compound Interest 13m. Application: Terminal Velocity 11m. Application: RC Circuit 11m. Reading 11 readings. Welcome and Course Information 2m. Get to Know Your Classmates 10m. Practice: Runge-Kutta Methods 10m.

Practice: Separable First-order Equations 10m. Practice: Separable First-order Equation Examples 10m. Practice: Linear First-order Equations 5m. Practice: Linear First-order Equation: Examples 10m. Practice: Compound Interest 10m. Practice: Terminal Velocity 10m. Practice: RC Circuit 10m.

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Quiz 6 practice exercises. Diagnostic Quiz 15m. Classify Differential Equations 10m. Separable First-order ODEs 15m. Linear First-order ODEs 15m. Applications 20m. Week One 1h. Video 22 videos. Week 2 Introduction 1m. The Principle of Superposition 6m.