MATHEMATICS-1

The course will furnish fundamental of calculus with particular reference to statistical and economical data. To this purpuse, the items of functions and matrix calculus will be focused on economical applications like utility and production theory.

1. Knowledge and understanding:
1.1. understanding how the concept of function can represent economic phenomena and analyzing the relative properties, for istance, considering the link between price, demand and offer even in dynamic term
1.2. understanding how the linear algebra models are useful to represent multi dimensional quantities
1.3. comprehension of basic concepts of calculus, like monotonicity and optimality, to represent, model and optimize economical phenomena

2. Applying knowledge and understanding:
2.1. ability to use the concept of function and its properties
2.2. ability to model economic quantities with particual reference to the concept of istantaneous change and properties of incresing/decreasing
2.3. apply calculus tools to solve quantitative problems, in particular but not limited to, optimization problems
2.4 to know the main operations between matrices and the matrix representation of a linear system

3. Making judgements:
3.1. interpreting concepts like average and istantaneous variation
3.2. understanding calculus and linear algebra
3.3. reflecting on limits and capabilities of quantitative analysis

A preparatory course in mathematics (Additional Learning Requirements, OFA) is organized for the course Mathematics. This preparatory course provides prerequisites that are necessary to successfully take Mathematics.

The program of the whole course (12 cfu, 60 hours) is the following:

Single variable functions. Derivatives. Single variable optimization. Integrals. Interest rates and present values. Several variable functions. Optimization with several variables. Matrix algebra and linear equations systems.

Luciano Battaia Appunti per un corso di Matematica (in italian), http://www.batmath.it/matematica/0-appunti_uni/corso-ve.pdf . Other material will be suggested during the course.

Grading is based on a final written exam, based on two consecutive proofs. The first is formed by some questions with multiple answers, and its overcoming is necessary condition to be admitted to the second. The second proof consists on the solution of some exercices.

Lectures, room exercises, tutorials.

Detailed information and study materials on the e-learning page of the course.

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