1 Introduction 2 One-variable calculus: foundations 3 One-variable calculus: applications 4 One-variable calculus: chain rule 5 Exponents and logarithms 6 Introduction to linear algebra 7 Systems of linear equations 8 Matrix algebra 9 Determinants: and overview 10 Euclidean spaces 11 Linear independence 12 Limits and open sets 13 Functions of several variables 14 Calculus of several variables 15 Implicit functions and their derivatives 16 Quadratic forms and definite matrices 17 Unconstrained optimization 18 Constrained optimization I: first order conditions 19 Constrained optimization II 20 Homogeneous and homothetic functions 21 Concave and quasiconcave functions 22 Economic applications 23 Eigenvalues and eigenvectors 24 Ordinary differential equations: scalar equations 25 Ordinary differential equations: systems of equations 26 Determinants: the details 27 Sunspaces attached to a matrix 28 Applications of linear independence 29 Limits and compact sets 30 Calculus of several variables II.