The goal of this course is to employ tools from Calculus and develop mathematical theory to tackle important problems, specifically constrained optimization problems, in Economics. We shall begin with a crash course in linear algebra. We will define the rank, determinant, eigenvalues, eigenvectors, and definiteness of matrices. These concepts will be used to
solve optimization problems with equality or inequality constraints (or a mix of both). Then we proceed to discuss the Kuhn-Tucker formulation, the economic interpretation of Lagrange multipliers as shadow prices, the envelope theorem and the second order test under constraints which determine the nature of a critical point.
Definitions are discussed and the most important theorems are derived in the lectures with a view to help students to develop their abilities in logical deduction and analysis. Practical applications of optimization problems in Economics are illustrated in order to promote a more organic interaction between the theory of Calculus and students' own fields of study. This course also provides discussion sessions in which students are able to make their skills in handling calculations in Calculus more proficient under the guidance of our teaching assistants.