This book describes the main methods used to analytically solve first order ordinary differential equations (ODE). First order ODE equations are introduced including details of their classification by order and degree. The main analytical, techniques are then presented with a number of worked examples to help simplify and help the student understand complex ideas. Techniques such as using the separation of variables, exact equations, applying substitutions and solving Bernoulli type differential equations are explained both in theory and by means of numerous and fully worked examples. Some of these examples include solving first order ODE in the context of real world examples that describe for instance the radioactive decay of nuclear isotopes; this then gives the reader a perspective to their use in the real world.
57 Pages | 7,852 WordsJohn Rampton, M.Sc. (#107934)