This book combines the classical analysis and modern applications of applied mathematics for chemical engineers. The book introduces traditional techniques for solving ordinary differential equations (ODEs), adding new material on approximate solution methods such as perturbation techniques and elementary numerical solutions. It also includes analytical methods to deal with important classes of finite-difference equations. The last half discusses numerical solution techniques and partial differential equations (PDEs). The reader will then have the good sense to apply mathematics in the formulation of problems in Chemical Engineering. New to the second edition is a chapter on Linear Algebra: Vectors and Matrices, and as well, includes new homework problems on modern topics like Biological Engineering. The revised chapter provides strong motivation for learning why vectors and matrix methods are important, particularly for solving large arrays of linear algebraic and differential equations. Like the first edition there are many examples provided as homework and worked examples.