MTH306Y - MAPLE figures


  Phase Portraits for Linear Systems with Real Eigenvalues (Section 3.3)
(a) A "simple" sink
    dx/dt=-x                                   
    dy/dt=-4y

eigenvalue: -1   straight-line solutions on y=0
eigenvalue: -4   straight-line solutions on x=0

phae portrait for a "simple" sink


(b) A more general sink
    dx/dt=-5x-2y
    dy/dt=-x-4y

eigenvalue: -3   straight-line solutions on y=-x
eigenvalue: -6   straight-line solutions on y=x/2

A more general sink

(c) A "simple" source
    dx/dt=x
    dy/dt=4y

eigenvalue: 1   straight-line solutions on y=0
eigenvalue: 4   straight-line solutions on x=0

A "simple" source


(d) A more general source
    dx/dt=5x+2y
    dy/dt=x+4y
 
eigenvalue: 3   straight-line solutions on y=-x
eigenvalue: 6   straight-line solutions on y=x/2

A more general source
 

(e) A "simple" saddle
    dx/dt=-2x
    dy/dt=4y

eigenvalue: -2   straight-line solutions on y=0
eigenvalue:  4   straight-line solutions on x=0

A "simple" saddle


(f) A more general saddle
    dx/dt=5x+4y
    dy/dt=9x

eigenvalue: -4   straight-line solutions on y=-9x/4
eigenvalue:  9   straight-line solutions on y=x

A more general saddle



  Vector Fields (Section 2.2)
(a) Vector field for
      dy/dt=v  
      dv/dt=-y

harmonic oscillator with k/m=1


(b) Vector field for
      dy/dt=v  
      dv/dt=-3y

harmonic oscillator with k/m=3


(c) Vector field for
      dx/dt=-x 
      dy/dt=-y

decoupled system

(d) Vector field for
      dR/dt=2R-1.2RF 
      dF/dt=-F+0.9RF

predator-prey model



Slope Fields (Section 1.3)
(a) Slope field for y'=y-t

slope field for y'=y-t




(b) Slope field for y'=t2

slpoe field for y'=t^2


(c) Slope field for y'=y(1-y)

slope field for y'=y(1-y)

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