By Michael C. Makoid, Ph.D., Phillip J. Vuchetich, Pharm.D., M.S., Umesh V. Banakar, Ph.D.
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Extra info for Basic Pharmacokinetics
The LaPlace transform is used to quickly solve (integrate) ordinary, linear differential equations. 1 is available for working with the LaPlace transform for problems throughout the book. 1. O. com Basic Pharmacokinetics REV. 25 Copyright © 1996-1999 Michael C. 1 ZERO AND INFINITY Any number multiplied by zero equals zero. Any number multiplied by infinity ( ∞ ) equals infinity. Any number divided by zero is mathematically undefined. Any number divided by infinity is mathematically undefined. 2 EXPRESSING LARGE AND SMALL NUMBERS Large or small numbers can be expressed in a more compact way using indices.
Basic Pharmacokinetics REV. 25 Copyright © 1996-1999 Michael C. edu/pkinbook/ 2-15 Mathematics Review Calculus deals with infinitesimally small changes. When the value of ∆x is infinitesimally small it is written dx and is known as the derivative of x. Hence, dy ------ = f ( x ) dx Where dy/dx is the derivative of y with respect to x and f ( x ) indicates some function of x. 5 DIFFERENTIATION FROM FIRST PRINCIPLES Differentiation is the process whereby the derivative of y with respect to x is found.
The integrated expression for this particular case is: 3 y = x + A , therefore 3 0 = 0 + A , thus A = 0 In some examples, such as first-order reaction rate kinetics, the value of A is not zero. 10 (b). 13 A USEFUL INTEGRAL Accept that if, Ax dy ------ = Be dx Basic Pharmacokinetics REV. 25 Copyright © 1996-1999 Michael C. edu/pkinbook/ 2-20 Mathematics Review then, Ax Be + A y = ----------A This integral will be useful for equations which define the bioavailability of a drug product. 14 EXAMPLE CALCULATIONS (a) Consider, 2 c = 3t ( t – 2 ) + 5 Where c is the drug concentration in a dissolution fluid at time t .
Basic Pharmacokinetics by Michael C. Makoid, Ph.D., Phillip J. Vuchetich, Pharm.D., M.S., Umesh V. Banakar, Ph.D.