This book is designed for undergraduate students. It is complete in itself and can be used for self-study or as a text for a formal course. Moreover, it could with advantage be used as a supplement to courses in mathematical methodsand vector field theory. Little prior knowledge is assumed. The reader should get Foundation Mathematica by the same author which should be a sufficient prerequisite. The aim of this book is to make study of undergraduate mathematics easier.Each chapter begins with an introduction, Each main idea appears in a section of its own, is motivated, is explained in great detail, and is made concrete by endless solved problems.Topics treated include (i) Differential Equation (ii) Partial Differentiation (iii) Linear Algebra (iv) Vector Analysis (vi) Vector Field Theory (vi) Complex Analysis (vii) Gamma and Beta Function (viii) Power Series Method of Solving Differentiation Equations (ix) Hypergeometric Function (x) Bessel Differential Equation (x) Hermite Polynomials and Differential Equation (xi) Legendre's Polynomials and Differential Equation (xii) Fourier Series and many more.