Content: Topics in linear algebra: Review of basic linear algebra -- Linear independence -- The rank of a matrix -- Main results on linear systems -- Eigenvalues -- Diagonalization -- Quadratic forms -- Quadratic forms with linear constraints -- Partitioned matrices and their inverses -- Multivariable calculus: Gradients and directional derivatives -- Convex sets -- Concave and convex functions I -- Concave and convex functions II -- Quasiconcave and quasiconvex functions -- Taylor's formula -- Implicit and inverse function theorems -- Degrees of freedom and functional dependence -- Differentiability -- Existence and uniqueness of solutions of systems of equations -- Static optimization: Extreme points -- Local extreme points -- Equality constraints: The lagrange problem -- Local second-order conditions -- Inequality constraints: Nonlinear programming -- Sufficient conditions -- Comparative statics -- Nonnegativity constraints -- Concave programming -- Precise comparative statics results -- Existence of language multipliers -- Topics in integration: Review of one-variable integration -- Leibniz's formula -- The gamma function -- Multiple integrals over product domains -- Double integrals over general domains -- The Multiple Riemann integral -- Change of variables -- Generalized double integrals -- Differential equations I: First-order equations in one variable -- Introduction -- The direction is given: Find the path! -- Separable equations -- First-order linear equations -- Exact equations and integrating factors -- Transformation of variables -- Qualitative theory and stability -- Existence and uniqueness -- Differential equations II: Second-order equations and systems in the plane -- Introduction -- Linear differential equations constant coefficients -- Stability for linear equations -- Simultaneous equations in the plane -- Equilibrium points for linear systems -- Phase plane analysis -- Stability for nonlinear systems -- Saddle points -- Differential equations III: Higher-order equations -- Calculus of variations -- Control theory: basic techniques -- Control theory with many variables -- Difference equations -- Discrete time optimization -- Topology and separation -- Correspondences and fixed points -- Appendix A: Sets, completeness, and convergence -- Appendix B: Trigonometric functions.