铁砧
发表于 2025-3-23 09:58:36
Ali Ümit KeskinContains numerous problems with complete solutions.Covers a large number of real-life applications.Presents the topic in an accessible way without requiring much prior knowledge in mathematics
匍匐前进
发表于 2025-3-23 16:32:46
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averse
发表于 2025-3-23 19:31:05
First Order Ordinary Differential Equations,A first order ODE has the form
CAMP
发表于 2025-3-24 00:21:02
Second and Higher Order Ordinary Differential Equations,Second-order ODEs explicitly contain a second derivative term, but no higher derivatives. These equations are of the form . The quantities . may not appear explicitly in a second-order ODE, such as in the equation,
性冷淡
发表于 2025-3-24 02:57:38
Series Solutions of Second-Order Ordinary Differential Equations,When a second-order ODE has constant coefficients, a systematic procedure for determining fundamental solutions has been given in the previous chapter. However, a larger class of equations have variable coefficients. Therefore, we have to find solutions of ODEs using methods other than the familiar elementary functions.
Concomitant
发表于 2025-3-24 07:25:54
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踉跄
发表于 2025-3-24 11:17:16
Nonlinear Ordinary Differential Equations,Why should we be interested in nonlinear ODEs? The main reason is that many real-life systems are nonlinear in nature.
Defense
发表于 2025-3-24 17:37:21
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cylinder
发表于 2025-3-24 21:27:07
978-3-030-06999-5Springer Nature Switzerland AG 2019
Insul岛
发表于 2025-3-25 00:02:52
Special Differential Equations, Functions, and Polynomials,problem of describing planetary motion, and provide another orthogonal set of basis functions. The Legendre polynomials are one of a set of classical orthogonal polynomials, which satisfy a second-order linear ODE, so-called Legendre ODE occurring naturally in the solution of initial value problems having spherical symmetry.