This book addresses the need for mathematical techniques to be introduced early on in the undergraduate program. Topics that are unique to the undergraduate curriculum, i.e. series, complex analysis, variational calculus, and integral transforms, do overlap in the advanced undergraduate-graduate curriculum and need to be introduced early on in the undergraduate program at the appropriate level. Throughout this book, these topics are crafted anew and tailored to both the needs and level of the intended audience. Topical coverage includes functional analysis; vector analysis; general coordinates and tensors; determinants and matrices; linear algebra; infinite series; complex numbers and functions; complex integrals and series; ordinary differential equations; second-order differential equations and special functions; Bessel's equation and Bessel's functions; partial differential equations and special functions; other useful functions of mathematical physics; Fourier series; integral transforms; variational analysis; probability theory; and information theory. This book equips students with the necessary mathematical skills that are required by a majority of the physics and engineering undergraduate programs, and it also establishes the background needed to understand and appreciate more advanced topics.