MATHEMATICS THAT WORKS

From ancient times, mathematics has developed side-by-side with physics; only in the last two hundred years they came apart as different branches of science. Extensive use of mathematics in other sciences, such as biology, chemistry, economics, pharm
acology, environmental and social sciences is even more recent. Nowadays, knowledge of mathematical techniques is indispensable also for students and researchers in these fields.

The series of textbooks "Mathematics that Works" presents math
ematical methods with a sharp focus on applicability. There is an ample supply of worded-out examples and instructive exercises. The techniques are illustrated in applications from various branches of science; here, the connection between the mathema
tical method and the application is equally important as the mathematics itself. Thus the way the students digest the matter is aimed at practical usability within their own field, and skills take priority over the mathematical abstraction level. By
connecting mathematics to its applications the usage of mathematics in the applied sciences is facilitated.

This volume treats time-dependent processes that can be modelled with ordinary differential equations. This text is intended as a sec
ond course; the reader is assumed to be familiar with the basic concepts from calculus and linear algebra. The level of difficulty is somewhat higher than in the previous volumes; the applications are more advanced, and the mathematical modelling has
more emphasis. Thus the technical and computational skills shift to the second place. It is assumed that modern engineers and scientists supplement their conceptual abilities on the computational level with computer packages as MatlabTM, MapleTM or
MathematicaTM.