This course covers numerical techniques for solving problems in applied mathematics, including error analysis, roots of equations, interpolation, numerical differentiation and integration, ordinary differential equations, matrix methods and selected topics from among: eigenvalues, approximation theory, non-linear systems, boundary-value problems, numerical solution of partial differential equations.

Sequences and induction; convergence of sequences and series; limits, continuity, and differentiability; Riemann integrals; sequences of functions and an introduction to topology.

First-order differential equations, linear differential equations, Laplace transforms, systems of differential equations, non-linear systems, series solutions, introduction to partial differential equations. Special emphasis is placed on applications to physics and engineering.

Functions of a complex variable, differentiation, analytic and elementary functions, Cauchy's theorem and contour integration, Taylor and Laurent series, residues and poles, and conformal mapping. Emphasis is placed on physical applications.

Introduction to principles of real analysis. Topics include rational numbers, completeness, sequences, limits, continuity, and implications to Calculus.

First-order differential equations, linear differential equations, Laplace transforms, systems of differential equations, non-linear systems, series solutions, applications in the physical, biological, social, and engineering sciences.

The mathematics of inferential statistics. Topics include probability distributions and densities, expectation, moment-generating functions, functions of random variables, limiting distributions, and the theory behind statistical methods such as estimation, hypothesis testing, regression and correlation.

Examines mathematical techniques for understanding place-based environmental issues, analyzing situations, and taking appropriate action. Students will apply methods for collecting, understanding, and displaying data effectively, including gathering environmental data outdoors, then make conclusions using basic inferential statistics. Students will also examine the use of stock-flow systems and other mathematical tools to model interacting populations, energy, pollution spread, recycling, and financial networks.

Systems of linear equations, matrices, determinants, vector spaces, linear transformations, eigenvalues and eigenvectors, diagonalization applications, and linear programming.

Multivariate calculus. Topics include vectors, vector functions and derivatives; curves; partial and directional derivatives; Lagrange multipliers; double and triple integrals; spherical and cylindrical co-ordinates; vector integrals, Green's Theorem, and surface integrals.