Lecture

Introduction to Linear Differential Equations

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Description

This lecture provides an introduction to linear differential equations, explaining the implicit relationship between a function and its derivatives. It covers first-order linear differential equations, with examples and solutions. The lecture also discusses homogeneous and inhomogeneous cases, along with methods to find particular solutions. Various techniques such as 'Ansatz' and 'Variation of Constants' are presented, with practical examples and applications.

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Related concepts (32)

Homogeneous differential equation

A differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.

Ink wash painting

Ink wash painting (; is a type of Chinese ink brush painting which uses washes of black ink, such as that used in East Asian calligraphy, in different concentrations. It emerged during the Tang dynasty of China (618–907), and overturned earlier, more realistic techniques. It is typically monochrome, using only shades of black, with a great emphasis on virtuoso brushwork and conveying the perceived "spirit" or "essence" of a subject over direct imitation.

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Japanese calligraphy

Japanese calligraphy, also called 習字, is a form of calligraphy, or artistic writing, of the Japanese language. Written Japanese was originally based on Chinese characters only, but the advent of the hiragana and katakana Japanese syllabaries resulted in intrinsically Japanese calligraphy styles. The term shodō (書道, "way of writing") is of Chinese origin and is widely used to describe the art of Chinese calligraphy during the medieval Tang dynasty. Early Japanese calligraphy was originated from Chinese calligraphy.

Painting

Painting is the practice of applying paint, pigment, color or other medium to a solid surface (called the "matrix" or "support"). The medium is commonly applied to the base with a brush, but other implements, such as knives, sponges, and airbrushes, can be used. In art, the term "painting" describes both the act and the result of the action (the final work is called "a painting").

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