# e-book Ordinary Differential Equations and Operators

Lecture 1 Play Video. Lecture 2 Play Video. Solving Differential Equations: Two Distinct Real Roots This is a video in the series for solving systems of ordinary differential equations.

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Lecture 3 Play Video. Lecture 4 Play Video. Lecture 5 Play Video. Lecture 6 Play Video. Test For Stability of the Origin This video addresses the stability of the origin on a phase portrait of a 2X2 system of ordinary differential equations. Lecture 7 Play Video. Lecture 8 Play Video. Lecture 9 Play Video. Lecture 10 Play Video. Introduction to Differential Equations This is an introduction to differential equations. Lecture 11 Play Video. Lecture 12 Play Video. Lecture 13 Play Video. Lecture 14 Play Video. Lecture 15 Play Video. Derivation a General Solution and Integrating Factor for a Linear Differential Equation This video defines total differential, exact equations and uses clairiots theorem to derive the form of the integrating factor for a First order linear ODE.

Lecture 16 Play Video.

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Linear Differental Equations: Example I This the first example of two on how to solve a linear differential equation using and integrating factor. Lecture 17 Play Video. Linear Differential Equations: Example II This the second example of two on how to solve a linear differential equation using and integrating factor.

Lecture 18 Play Video. Using Differential Operators A differential operator acts on a function.

## Differential Equations

Lecture 19 Play Video. Solving Linear DE's with Two Distinct Real Roots One way to solve homogeneous linear differential equations is by using differential operators and characteristic equations. Lecture 20 Play Video. Solving Linear DE's with Repeated Real Roots One way to solve homogeneous linear differential equations is by using differential operators and characteristic equations.

Lecture 21 Play Video. Solving Linear DE's with Complex Roots One way to solve homogeneous linear differential equations is by using differential operators and characteristic equations. Lecture 22 Play Video.

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Fundamental Solution Set for Linear DE's Three criteria for a fundamental set of solutions to a differential equation must be satisfied. Lecture 23 Play Video. Factoring Operators When dealing with differential operators with constant coefficients then the operators are factorable and do factor like polynomials.

Lecture 24 Play Video. Annihilator Method I This is the first example of using the annihilator method for solving non-homogeneous linear differential equations. Lecture 25 Play Video. Writing a Differential Equation as a System This video is about writing a differential equation as a system of differential equations.

Lecture 26 Play Video. Existence and Uniqueness Linear D. Lecture 27 Play Video. Lecture 28 Play Video. Runge-Kutta Method The video is about Runge-Kutta method for approximating solutions of a differential equation using a slope field. Lecture 29 Play Video. The Wronskian and a Test for Independence The Wronskian is a fun name to say and it is not hard to calculate.

Lecture 30 Play Video. Euler Method The video is about Euler method for approximating solutions of a differential equation using a slope field. A definiteness result for determinantal operators Pages Binding, Paul et al. On second-order left-definite boundary value problems Pages Bennewitz, C. A von Neumann factorization of some selfadjoint extensions of positive symmetric differential operators and its application to inequalities Pages Brown, Richard C. Inclusion theorems for solutions of differential equations with aid of pointwise or vector monotonicity Pages Collatz, Prof.

The liouville-green asymptotic theory for second-order differential equations: A new approach and some extensions Pages Eastham, M. Non-self-adjoint operators and their essential spectra Pages Evans, W. A concept of adjointness and symmetry of differential expressions based on the generalised Lagrange identity and Green's formula Pages Everitt, W.

On quadratic integral inequalities associated with second-order symmetric differential expressions Pages Everitt, W. Nonoscillation theorems for differential equations with general deviating arguments Pages Fink, A. Self-adjoint 4-th order boundary value problem in the limit - 4 case Pages Fulton, Charles T.

Differential equation introduction - First order differential equations - Khan Academy

Factorization and the Friedrichs extension for ordinary differential operators Pages Kauffman, Robert M. Boundedness criteria for hyperbolic characteristic initial value problems Pages Kreith, K. Matrix riccati inequality and oscillation of second order differential systems Pages Kwong, Man Kam. A new approach to second order linear oscillation theory Pages Kwong, Man Kam et al. Small amplitude limit cycles of polynomial differential equations Pages Lloyd, N.

Regular growth and zero-tending solutions Pages Macki, Jack W.

• Course summary?
• Ordinary differential equation - Wikipedia!
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