Re: Linearity question, is the proffesor wrong ?

Lasse.Karagiannis@xxxxxxxxxx wrote:

Hi all, I am reading a book on control theory written by a proffessor
at
Chalmers university of Technology. His name is Bertil Thomas.

At page 116 he gives two examples of what he think is nonlinear
differential equations:
2y' + y=5*sqrt(u) and
12y''+6y=5uy+sin(u)

u is an external signal, not yet defined, and is a function of t, only.
y is the dependent variable, and is a function of t, the independent
variable.

It is not written as a system of equations, it is just according to him
two examples of nonlinear differential equations.

According to what I've learned a D.E. is nonlinear iff the dependent
variable or its derivatives has power not equal to 1, y^2, y^0.5,
(dy/dt)^3, etc.

I've taught a Mathematical Modelling course in the School of Engineering. In this course we classify ODEs using the definition of non-linear that you use, in other words it refers only to the way that y and its derivatives appear in the equations. Another element of classification is whether the coefficients are constant or functions of t. The treatment is not mathematically advanced, being limited to solving 2nd order systems by means of the characteristic equation, but it may be at a similar level to the course you're teaching.
.

Relevant Pages

  • Re: Linearity question, is the proffesor wrong ?
    ... two examples of nonlinear differential equations. ... thinks that if a D.E. has noncnstant coefficients it ... Is the proffessor correct? ...
    (sci.math)
  • Re: Linearity question, is the proffesor wrong ?
    ... according to him two examples of nonlinear differential ... and then simply say nonlinear means "not linear". ... that only works with differential equations with constant ... coefficients, then he thinks that if a D.E. has noncnstant ...
    (sci.math)
  • Leon Mark Glass
    ... perception; neural networks. ... Biology 309 - Mathematical Models in Biology ... One dimensional differential equations modelling growth and decay ... Second order linear and nonlinear differential equations ...
    (sci.nonlinear)
  • Linearity question, is the proffesor wrong ?
    ... I am reading a book on control theory written by a proffessor ... At page 116 he gives two examples of what he think is nonlinear ... two examples of nonlinear differential equations. ... thinks that if a D.E. has noncnstant coefficients it is non-linear. ...
    (sci.math)
  • second order coupled differential equations with nonlinear terms
    ... Which solver to use for second order coupled differential equations ... differential equations and some linear and some nonlinear equations ...
    (comp.soft-sys.matlab)