These Lecture Notes contain the basic ideas and fundamental concepts needed for a deeper understanding and study on numerical resolution of ordinary differential equations. Rigorous exposition of the material (not taken to any extreme)  can be found. Most of the chapters include simple mathematical models of problems in biology or medicine. They have been chosen in these fields due to the recent fascination of the authors on the subject. In the contents, one can find the concepts of consistency, convergence, and stability, definitions of local and global truncation errors, and order of accuracy of a numerical method. Among the single step methods exposed, stand the Euler and Runge-Kutta Methods. Mathematical models employed to show their use include the diabetes diagnosis, the time evolution of tumors, and the respiratory mechanics. Many biographical notes of famous mathematicians and suggested literature are spread all over the text. The MATLAB programs employed can be found in the appendices.
 

Roma, A.M.; Bevilacqua, J.S.: Resolução numérica de equações diferenciais ordinárias com condições iniciais: uma introdução ilustrada com modelos em biomedicina, Notas do Minicurso do XX Congresso Nacional de Matematica Aplicada e Computacional, Gramado, RS, Brasil, 08-12/09, 1997. Português.