## MATHEMATICS MATEMATICA

A.Y. Credits
2016/2017 8
Lecturer Email Office hours for students
Margherita Carletti Every week, one hour before and after lessons
Teaching in foreign languages
Course with optional materials in a foreign language English
This course is entirely taught in Italian. Study materials can be provided in the foreign language and the final exam can be taken in the foreign language.

### Assigned to the Degree Course

Biotechnology (L-2)
Curriculum: PERCORSO COMUNE
Date Time Classroom / Location

### Learning Objectives

The course is meant to provide students with the fundamentals of differential and integral calculus, necessary to the biological/biotechnological disciplines, and to develop the logical-deductive abilities necessary for their future study, research and professional activities..

### Program

1 Numerical sets
1.1 Integer, rational, irrational and real numbers
1.2 Absolute value
1.3 Intervals and neighbourhoods
1.4 Internal, external, boundary, isolated and accumulation points
1.5 Infimum and supremum, minimum and maximum of a set of real numbers
1.6 Complex numbers
2 Real functions of real variable
2.1 Definition of real funcion of real variable
2.2 Symmetric functions
2.3 Increasing and decreasing functions
2.4 Periodic functions
2.5 Domain and codomain of a function; rational and irrational algebraic functions; absolute value functions; exponential and logarithmic functions. Hints of trigonometric functions.
3 Limits and continuity
3.1 Definition of limit of a function
3.2 Theorem of uniqueness of the limit , theorem sign permanence ; theorem of comparison
3.3 Weierstrass' theorem and the intermediate zero theorem
3.4 Definition of continuous function in a point and in an interval
3.5 Discontinuity points
4 Derivation
4.1 Definition of first derivative of a function in a point and its geometric interpretation
4.2 Higher order derivatives
4.3 Lagrange's and Rolle's theorems and de l'Hospital's rule
4.4 Derivatives and increasing and decreasing functions
4.5 Maximum and minimum points
4.6 Convexity and concavity
4.7 Inflection points and inflection tangents
4.8 Graphic of a function
5 Integration
5.1 Primitive of a function
5.2 Indefinite integral and its properties
5.3 Integration by decomposition, by decomposition in simple fractions, by substitution and by parts
5.4 Area of trapezoid
5.5 Definite integral and its properties
5.6 Mean value theorem
5.7 Fundamental theorem of integral calculus ( Torricelli)
5.8 Improper integrals (hints).
6 Differential equations
6.1 I and II order differential equations; Cauchy's problem
6.2 Integration by separation of variables
6.3 Linear equations
6.4 II order differential equations with costant coefficients; Cauchy's problem
7 Elements of linear algebra
7.1 Vector spaces and subspaces
7.2 Linearly independent vectors
7.3 Bases and dimensions
7.4 Matrices and matrix operations
7.5 Inverse matrices
7.6 Rank of a matrix
7.7 Eigenvalues and eigenvectors of a matrix
7.8 Linear algebraic systems; Cramer's rule, Rouché-Capelli's theorem; homogeneous systems.

None

### Learning Achievements (Dublin Descriptors)

Students will have to demonstrate:

-  Knowledge and comprehension of the treated topics

-  Capability of application of known concepts in unknown contexts

-  Ability in switching from the analytical concepts to the corresponding geometric interpretation

-  Good linguistic exposition of the treated topics

-  Capability of linking the main treated topics one another.

### Teaching Material

The teaching material prepared by the lecturer in addition to recommended textbooks (such as for instance slides, lecture notes, exercises, bibliography) and communications from the lecturer specific to the course can be found inside the Moodle platform › blended.uniurb.it

### Supporting Activities

Students are strongly recommended to attend the pre-course in Mathematics that will take place the week before the beginning of lessons.

For students who have not passed the Cisia TOLC test for the evaluation of basic mathematical knowledge, attendance of the pre-course in Mathematics consists of an OFA (Obbligo Formativo Aggiuntivo) in preparation to the additional test provided to evaluate the fullfilment of the minimum requirements in mathematical skills.

### Teaching, Attendance, Course Books and Assessment

Teaching

Frontal lessons

Attendance

Not compulsory, though strongly recommended

Course books

Erin N. Bodine, Suzanne Lenhart and Louis J. Gross, Mathematics for the Life Sciences, Princeton University Press, 2014.

Assessment

The examination consists of a written and an oral part.

The written examination is 90 minutes long.

Students are admitted to the oral examination if they have passed the written one with the minimum mark of 12/30.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

### Additional Information for Non-Attending Students

Teaching

None

Course books

Erin N. Bodine, Suzanne Lenhart and Louis J. Gross, Mathematics for the Life Sciences, Princeton Uniersity Press, 2014.

Assessment

The examination consists of a written and an oral part.

The written examination is 90 minutes long.

Students are admitted to the oral examination if they have passed the written one with the minimum mark of 12/30.

Disability and Specific Learning Disorders (SLD)

Students who have registered their disability certification or SLD certification with the Inclusion and Right to Study Office can request to use conceptual maps (for keywords) during exams.

To this end, it is necessary to send the maps, two weeks before the exam date, to the course instructor, who will verify their compliance with the university guidelines and may request modifications.

### Notes

 « back Last update: 23/01/2017

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