Guide Nonlinear Differential Equations

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Contents:


  1. 1st Edition
  2. Nonlinear differential equations - MATLAB Answers - MATLAB Central
  3. Generate Nonlinear Differential Equations and Applications NoDEA citations for Film / Online Videos
  4. 625.718 - Advanced Differential Equations: Nonlinear Differential Equations and Dynamical Systems
  5. Description

1st Edition

Learning Outcomes After completed course, the students are expected to be able to: Give account for existence and uniqueness of the solutions of ordinary differential equations solutions. Make use of the phase plane to analyse two-dimensional systems with emphasis on equilibrium, existence of limit cycles and linearisation. Summarise theorems that related to the existence of periodical solutions, and apply them to simple systems. Explain important terms in asymptotic theory, such as, order symbols, asymptotic sequences and asymptotic series, and give account for truncation and convergence of asymptotic series.

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Nonlinear differential equations - MATLAB Answers - MATLAB Central

Describe asymptotic perturbation methods for approximate solutions of differential equations, and be able to discuss the characteristics of the different methods. Apply singular perturbation methods, coordinate stretching, multiscales and boundary layers to simple problems.


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Explain harmonic and sub-harmonic response and stability to driven oscillations, and perform simple analyses of the Duffings and van der Pol equations. Define Poincare and Liapunov stability. Non-linear equations can usually not be solved exactly and are the subject of much on-going research.

Generate Nonlinear Differential Equations and Applications NoDEA citations for Film / Online Videos

Here is a brief description of how to recognize a linear equation. In a differential equation, when the variables and their derivatives are only multiplied by constants, then the equation is linear. The variables and their derivatives must always appear as a simple first power. Here are some examples. Note, however, that an exception is made for the time variable t the variable that we are differentiating by. We can have any crazy non-linear function of t appear in the equation, but still have an equation that is linear in x. See the Wikipedia article on linear differential equations for more details.

625.718 - Advanced Differential Equations: Nonlinear Differential Equations and Dynamical Systems

This is another way of classifying differential equations. These fancy terms amount to the following: whether there is a term involving only time, t shown on the right hand side in equations below. The non-homogeneous part of the equation is the term that involves only time. Share full text access.

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Citing Literature. Volume 42 , Issue 4 15 March Pages Related Information.

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