Approaches intermediate mathematics from a thematic standpoint, using linear structure as a rigorous foundation for developing applications across science and engineering. The course develops a rigorous theory for finite dimensional vector spaces, including solvability and approximation theory. This theory is applied to first order differential equations and differential multivariate calculus. Applications include linear regression, modeling with first order differential equations, a brief introduction to regular perturbation theory, and both constrained and unconstrained optimization problems. Lab.