This course offers a comprehensive exploration of the practical applications of Calculus in addressing constrained optimization problems within the domain of Economics.

Commencing with a crash course on the essential linear algebra concepts, which includes rank of matrices, determinant, eigenvalues, eigenvectors, and definiteness, the curriculum progresses to the core principles of optimization.

Students will engage in the systematic resolution of optimization problems characterized by both equality and inequality constraints, with an introduction to the Kuhn-Tucker formulation for optimization problems with a complete set of non-negativity constraints . The economic interpretation of Lagrange multipliers as shadow prices is thoroughly examined, accompanied by a rigorous presentation and proof of the envelope theorem. To finish off, we will state the second-order conditions for both constrained and unconstrained optimisation problems, providing insights into the nature of critical points in such setting.

Throughout the lectures, emphasis is placed on precise definitions and the derivation of pivotal theorems, fostering the development of logical deduction and analytical acumen. Practical illustrations elucidate the real-world relevance of optimization problems in Economics, establishing a pragmatic understanding. Supplementary to the lectures, tutorial sessions led by TAs are designed to facilitate a nuanced comprehension of calculus calculations, ensuring participants adeptly navigate theoretical concepts.

This course aims to integrate Calculus and its pragmatic application in addressing optimization problems within the field of Economics.

The tentative syllabus can be found below :

1. Linear algebra (I) : Basis and dimensions
2. Linear algebra (II) : Ranks
3. Linear algebra (III) : Definiteness
4. Optimization (I) : FOC and NDCQ
5. Optimization (II) : Kuhn-Tucker formulation
6. Optimization (III) : Envelope theorems
7. Optimization (IV) : Second order conditions