1-1 What is a Differentiable Equations?

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Del curso dictado por Korea Advanced Institute of Science and Technology

Introduction to Ordinary Differential Equations

63 calificaciones

Korea Advanced Institute of Science and Technology

Introduction to Ordinary Differential Equations

63 calificaciones

In this introductory course on Ordinary Differential Equations, we first provide basic terminologies on the theory of differential equations and then proceed to methods of solving various types of ordinary differential equations. We handle first order differential equations and then second order linear differential equations. We also discuss some related concrete mathematical modeling problems, which can be handled by the methods introduced in this course. The lecture is self contained. However, if necessary, you may consult any introductory level text on ordinary differential equations. For example, "Elementary Differential Equations and Boundary Value Problems by W. E. Boyce and R. C. DiPrima from John Wiley & Sons" is a good source for further study on the subject. The course is mainly delivered through video lectures. At the end of each module, there will be a quiz consisting of several problems related to the lecture of the week.

De la lección

Introduction

1-1 What is a Differentiable Equations?3:49

1-2 Order and Normal Form6:29

1-3 Linear and Nonlinear Equations5:52

Conoce a los instructores

Kwon, Kil Hyun
Professor
Department of Mathematical Sciences

[MUSIC]

Hello everyone.

Let's start the course on ordinary differential equations.

Even though we can catch a very small tip of this huge iceberg

through this introductory course, I do hope that you can enjoy

some beauty and the usefulness of the theory of ordinary differential equations.

First, let me introduce some basic definitions and

terminologies related to the theory of differential equations.

There will be the common words which we are going to use throughout the course.

Are you ready?

So let's get into the chapter one introduction, okay?

First the basic definitions and terminologies, okay?

The mathematical modeling of our physical, or biological, or

the ecological phenomenon, often produces an equation, which

involves ordinary or partial derivatives of some unknown function, okay?

Such an equation is called a differential equation.

There are two types of differential equations.

First, the differential equation involving only ordinary derivative respect to

a single independent variable is called an ordinary differential equation.

On the other hand, a differential equation involving partial derivatives with respect

to more than one independent variable is called a partial differential equation.

For example, Newton's second law of motion applied

to a free falling body leads to an ordinary differential equation.

Say, m times d squared h over

d t squared is equal to m times dv over dt

is equal to negative m times g.

Where m is the mass of the object,

g the gravitational acceleration, h the height of the object,

and v which is equal to dh over dt, is the velocity.

On the other hand, modeling of vibrating strings,

under some ideal conditions, leads to a partial

differential equation called the wave equation,

which is d square u over d u squared minus c square

times d square u over dx square is equal to zero.

Where t is the time, x the location along the string,

c the wave speed, and u as a function of x, and

time is the displacement of the string.

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