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## Program

### Updated A.Y. 2019-2020

Course Description
One of the things we learned from 20th century is that complex phenomena arising from social and life sciences cannot be deeply analyzed and understood unless we make use of the universal language of mathematics. This goes back to Galileo's intuition that universe be written in mathematical symbols, a principle nowadays applied to human sciences as well as to natural ones. The purpose of this course is to introduce students to those basic notions in mathematics which are essential to describe, understand and analyze possibly different models of quantitative phenomena. Main concepts and tools of differential and integral calculus are taught in order that students become familiar with functions of real variables, notions of growth, limits, rate of change, optimization, time evolution, all of them being necessary to approach mathematical models in applied sciences as well as to pursue further studies in probability and statistics. Students are expected to learn the main concepts, to practice with basic tools of calculus and to understand the use of mathematical language in applied models of real life.

Teaching Method
The course is essentially taught in the traditional way through classroom lectures; this is necessary since the mathematical language needs to be presented in action on the blackboard, where theory and practice become intrinsically linked. Additional tutorials will be devoted to those students who need extra practice as well as specific care because they lack of background. At the beginning of the year, this group of students is identified from an evaluation test at the end of the Math pre-courses. During the semester, as the program goes further, periodic evaluations are scheduled to monitor the group of students who need to follow the additional tutorials.

Schedule of Topics

Topic 1 Real numbers, elementary functions and graphs
Topic 2 Sequences and limits
Topic 3 Recurrence, discrete time models: exponentials and logarithms, log scales
Topic 4 Derivatives: rules and applications, rate of change in applied models
Topic 5 Optimization: maxima and minima, convexity, curve sketching
Topic 6 Integration: areas, antiderivatives, Fundamental Theorem of Calculus
Topic 7 Differential equations and growth models: equilibrium points, stability
Topic 8 Multivariable calculus: partial derivatives, optimization, integration