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7. SETTING UP DIFFERENTIAL EQUATIONS

In kinetics the differential equations are derived from models.

Examples:

1. Direct (first order)

2. Sequential

3. Parallel

= =

= =

SUMMARY OF MATHEMATICAL RULES

Rules of Logarithms

log ab = log a + log b

= log a - log b

log 1 = 0 since 10n = 1

= log 1 - log a = -log a

log a² = log a + log a = 2log a

= log a1/2 = 1/2 log a

log a^-2 = -2log a =

Rules of Differentiation

Function	Derivative
y = k	dy/dx = 0
y = kx	dy/dx = k
y = kxn	dy/dx = knxn-1
y = k ln x	dy/dx = k/x
y = u + v + w	dy/dx = du/dx + dv/dx + dw/dx
y = uv	dy/dx = u(dv/dx) + v(du/dx)
y = u/v	dy/dx =

SUMMARY OF SEVERAL IMPORTANT DERIVATIVES AND INTEGRALS

Function	Derivative	Integral
y=xn	dy/dx = nxn-1	=
y = ex	= ex	= ex+C
y = ln x	dy/dx = 1/x	= x(ln x - 1) + C
y = 1/x	dy/dx = 1/x2	= ln x + C

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