First order ordinary differential equations, second order ordinary differential equations with constant coefficients, 2x2 linear systems with constant coefficients, stability of equilibrium solutions, Laplace transform, Fourier series, partial differential equations which include the heat equation and the wave equation.
Systems of linear equations and Gauss-Jordan elimination, matrix algebra and linear transformations, vector spaces and subspaces, eigenvalues and eigenvectors, diagonalization, orthogonality, singular value decomposition.
Derivatives and applications to rates of change, related rates, linearization, optimization and graphing techniques. The Fundamental Theorem of Calculus, relating differential and integral calculus, the beginning of Integral Calculus.
Topics include visualizing and graphing data, evaluating the average rate of change, solving linear equations and inequalities, solving linear absolute value equations and inequalities, modeling with linear functions and discussion of interpolation, solving quadratic equations using different solution methods, solving quadratic inequalities, modeling with quadratic functions.