# 00674 - Mathematics

## Learning outcomes

At the end of the course, the student is familiar with the basic tools of differential and integral calculus for functions of one variable and knows the most elementary methods for the solution of differential equations of first order. In particular, the student will be able to complete standard tasks related to differential and integral calculus (e.g., draw a quantitative graph of a function, calculate the area of a planar domain, etc.), solve simple first-order differential equations, compute determinants, solve linear systems, calculate eigenvalues and eigenvectors of a matrix.

## Course contents

Tentative syllabus (might be slightly changed):

Calculus I (Fall Semester)

Functions of a real variable. Limits and continuity. Derivative and related applications. Relative and absolute maxima and minima. Quantitative study of the graph of a function. Integrals.

Algebra and Geometry (Spring semester)

First order differential equations: linear and with separate variables. Vector spaces and linear maps. Matrices. Solution of linear systems. Eigenvalues and eigenvectors.

A good reference book, which however cannot replace a good set of notes from the class, is:

• M. Bramanti, C. D. Pagani, S. Salsa, "Matematica: calcolo infinitesimale e algebra lineare", 2nd ed., Zanichelli, 2004

A useful companion book for the exercises is:

• S. Salsa, A. Squellati, "Esercizi di matematica: calcolo infinitesimale e algebra lineare. VOLUME 1", Zanichelli, 2001 (ISBN: 8808088871)

## Teaching methods

Classroom lectures

## Assessment methods

Each part of the course has an independent test, with a grade from 18 through 32. The grade will be kept valid for a year. When the student has received, in each exam, a grade that they deem satisfactory, they may register on Almaesami to an "Appello di verbalizzazione". This is a virtual appointment (the student need not show up in person) whose purpose is to ask prof. Lenci to register the final grade for the course, which is given by the average of the two partial grades (averages greater than or equal to 31 result in a grade of "30 cum laude").

Descripition of written tests

Calculus I: 2-hour long written test, comprising 4-6 questions, among which 1-2 theoretical questions. The remaining questions are problems of the types discussed in class and given as homework, with at least one study of function. Different scores may be assigned to different questions, depending on the importance of the topic and the difficulty of the problem. The study of function will be the problem with the highest score. Partial scores are given for partial, or partially correct, answers.

Algebra and Geometry: 2-hour long written test, comprising 3 problems subdivided into one or more questions, some of which might be theoretical questions. The problems are of the types discussed in class and given as homework. Different scores may be assigned to different questions, depending on the importance of the topic and the difficulty of the problem. Partial scores are given for partial, or partially correct, answers.

## Teaching tools

• Class notes (to be studied together with the textbook).
• Notes written by the teachers on some topics.
• Lecture-by-lecture syllabus of the course.
• Homework problems, taken from the exercise book, from the list of sample problems written by the teacher and from the previous exams. Some of these problems are later solved and discussed in class.
• Depending upon the economic resources of the School, elective problem-solving meetings coordinated by a Teaching Assistant.

## Office hours

See the website of Marco Lenci

See the website of Andrea Zanellati