Introduction to Numerical Methods in Differential Equations

This is a textbook for upper division undergraduates and beginning graduatestudents. Its objective is that students learn to derive test and analyzenumerical me... » 

This is a textbook for upper division undergraduates and beginning graduatestudents. Its objective is that students learn to derive test and analyzenumerical methods for solving differential equations and this includes bothordinary and partial differential equations. In this sense the book isconstructive rather than theoretical with the intention that the studentslearn to solve differential equations numerically and understand themathematical and computational issues that arise when this is done. Anessential component of this is the exercises which develop both the analyticaland computational aspects of the material. The importance of the subject of thebook is that most laws of physics involve differential equations as do themodern theories on financial assets. Moreover many computer animation methodsare now based on physics based rules and are heavily invested in differentialequations. Consequently numerical methods for differential equations areimportant for multiple areas. The author currently teaches at RensselaerPolytechnic Institute and is an expert in his field. He has previouslypublished a book with Springer Introduction to Perturbation Methods. «