The book of famous American mathematicians Richard Bellman and Edward Angel is devoted to one of the most important tasks of modern computational mathematics - the creation of stable numerical methods for solving equations in private derivatives. The authors convincingly show that known methods of dynamic programming and invariant immersion lead to effective methods for solving equations of elliptic and parabolic types in regular and, which is very valuable for practice, irregular areas. Successfully selected examples and exercises allow you to use the book as a teaching aid. The results presented are of great interest to specialists in the field of numerical methods and open up tempting prospects for further research. The book is also interesting for a wide range of people working in the field of applied mathematics, who, in addition to clear and clear methods, will find in it the programs of some algorithms in the FORTRAN language. The book is quite accessible to graduate students and senior students of relevant specialties.