## MATHEMATICS

Algebra and Trigonometry acquired in high school: simplifying exponents, radicals, logarithms, fractions, factoring polynomials, solving equations and inequalities. Graph points in the plane. Read information from graphs, translating verbal information into math symbols. The Pythagorean Theorem.

The course score will be determined as the following weighted average:

Item Weight

Midterm 25%

Homework 20%

Quizzes 15%

Final 40%

Total 100%

This score will be converted to a grade in a scale of thirty with these values as cutoffs:

Cutoff Grade in Thirty

95 30

91 29

88 28

85 27

81 26

78 25

75 24

71 23

68 22

65 21

61 20

58 19

55 18

In this course the foundations of calculus are presented: the study of functions and their rates of change, how to model situations in order to solve problems. One of the major goals of college – level mathematics education is to move students from computational processes to conceptual thinking and communication. That is the biggest difference between this course and a high school course. Mathematics is more than a bag of tricks and there are not a limited number of types of problems that can be asked. The goal in class is to prepare students to do their homework and not necessarily to show them how to do it. The learning occurs when students can move themself into the unknown territory.

Understand what a function is and how it can be represented geometrically as a graph. Learn some standard function manipulations (algebraic combinations, composition, inverses, etc.) focusing on how such manipulations affect the shape of the graph. Learn algebraic and geometric properties of classic functions (polynomial, rational, exponential, logarithmic, trigonometric, etc.), emphasizing the relationship between them. Explore the basic two ideas for nearly all mathematical formulas in science: the derivative, which measures the instantaneous rate of change of a function and the definite integral, which measures the total accumulation of a function over an interval. The rules by which we can compute the derivative and the integral of any function are called calculus. The Fundamental Theorem of Calculus links the two processes of differentiation and integration in a beautiful way. Approach one of the central objects of mathematical modeling: Ordinary Differential Equations. They arise in many different contexts throughout mathematics and science when quantities are defined as the rate of change of other quantities. Since various differentials, derivatives, and functions become inevitably related to each other via equations, a differential equation governing dynamical phenomena, evolution and variation is the result. After an introduction to the Cauchy Problem, the two most popular cases are studied: the separable equations and the linear equations of first and second order.

For Italian readers: – Benedetto, Degli Esposti, Maffei. Matematica per le Scienze della Vita. Ambrosiana. This textbook promotes the idea of mathematics as the science of patterns. The authors introduce mathematical concepts through examples inspired by natural, physical and biological phenomena. The main topics of differential and integral calculus are covered. – Handouts and teacher prepared materials.

For English readers: – Serge Lang. A First Course in Calculus. Springer – Verlag. This textbook covers all the topics taught in the course in a simple but complete way.

Lecture sessions meet once a week for three sessions of 45 minutes each class period in the morning. In addition, week lectures are supported by a recitation session per week, which will meet for two sessions of 45 minutes in one afternoon. Every student is urged to participate at the recitations associated to the lectures.

A graphing calculator is encouraged for class discussion and for homework, but not allowed for exams or quizzes. No specific calculator is endorsed, if you have one already continue to use that one. In order to pursue a deeper acquaintance with the topics presented in the course, it is strongly recommended the use of the following math site: https://www.khanacademy.org/