## CALCULUS

## Syllabus

EN
IT

### Prerequisites

Elementary rules of computation involving numbers fractions and polynomials, representation of points in the plane through Cartesian coordinates, basic notions concerning lines and parabolas and their representation in the plane, methods of resolution of first and second order equations and inequations, definition and basic properties of logarithms, exponentials and trigonometric functions. All the arguments in the above list are included

among the topics of the math Pre-courses so that all students can go through a quick review of those notions while attending the Pre-courses. However, a quick review may be

not enough for all students who have a weak- or even very weak -background in mathematics. In this case, students are strongly encouraged to work hard even before the beginning of Pre-courses in order to catch up with the ordinary Italian school level. Any school textbook can be used for reviewing the above mentioned topics.

among the topics of the math Pre-courses so that all students can go through a quick review of those notions while attending the Pre-courses. However, a quick review may be

not enough for all students who have a weak- or even very weak -background in mathematics. In this case, students are strongly encouraged to work hard even before the beginning of Pre-courses in order to catch up with the ordinary Italian school level. Any school textbook can be used for reviewing the above mentioned topics.

### Program

- 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

- 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

### Books

Lawrence D. Hoffmann, Gerald L. Bradley, Dave Sobecki, Michael Price: Applied Calculus for Business, Economics, and the Social and Life Sciences, Expanded Edition, ed. Mc Graw-Hill, 2012-2013.

Claudia Neheauser:_Calculus for Biology and Medicine, 3rd ed. Pearson International, 2011.

Claudia Neheauser:_Calculus for Biology and Medicine, 3rd ed. Pearson International, 2011.

### Bibliography

Further readings: Notes given by teacher on differential equations : http://www.mat.uniroma2.it/~porretta/notes-porretta2.pdf

### Teaching methods

In-classs teaching.

### Exam Rules

Two mid-term examinations are given, each make up to 30% of the final grade, provided the exam is passed in the winter session, for attending students. At the end of the lecture period, a final written examination is done, which make up to 40% of the grade.