# Teaching

## Table of Contents

## Academic Term (Anno Accademico) 2023/2024: Financial Economics

## Academic Term (Anno Accademico) 2023/2024: Mathematical Methods II

The aim of the course is to provide a deepest introduction to the basic tools and theorems of mathematical calculus. Standard courses for students in economics are oriented to provide a specific set of computational procedures to be applied to the solution of specific problems. The present course might constitute a good complement as it is more concerned with the definition and study of general notions and it is characterized by a theorem-proving approach.

- Teaching load: 40 hours
- Lecturer : BOTTAZZI Giulio
- Teaching Assistant: TBD
- Semester: Fall
- Textbook: Advanced Calculus for Economics and Finance
- Further references and Optional readings: Principles of Mathematical Analysis, W.A. Rudin, chapters 3, 6 and 9
- Prerequisites: Basics of topology, linear algebra, metric spaces, and sequences and series.

List of topics covered by the lectures (not necessarily in this order)

Normed Spaces:

- Definition and Basic Properties
- Euclidean Norm in Rn
- p-Norm in Rn
- Operator Norm
- Finite-Dimensional Normed Spaces
- Equivalence of Norms in Rn

Differential calculus of real functions:

- Properties of derivatives.
- Continuity and differential.
- Lagrange theorem.
- de L'Hopital rule and application.
- Derivatives of fundamental functions.

Differential calculus of functions of many variables:

- Limits and Continuity in Rn
- Differential Analysis in Rn
- Mean Value Theorems
- Higher-Order Derivatives and Taylor Polynomial
- Local Maxima and Minima
- Inverse Function Theorem
- Implicit Function Theorem
- Constrained Optimisation

Constrained optimisation:

- Theorems of alternatives
- First-order conditions and Lagrangian function
- Weak and strong duality
- Second-order conditions