Students preparing for upper-division physics and engineering classes need to become adept practitioners of mathematical methods, developing an understanding of the most used methods, skill in their theoretical and computational application, and competence in selecting the mathematical and computational methods appropriate to each challenge. In this class students are introduced to a core toolset of mathematical methods employed by professional physicists, including techniques from linear algebra (optimization, eigenvalue problems, solutions in terms of sets of special functions) and calculus (differentiation in applications up to partial differential equations, single- and multi-variable calculus and complex calculus, Fourier and Laplace transforms). Students will apply these methods to representative physics problems including previews of future coursework using spreadsheets, a computer algebra system (such as Mathematica or MATLAB), and will sample the use of computational libraries such as BLAS.