Academic Year 2020/2021 - 1° Year

12 CFU - 1° Semester

**Mathematics and Computer Science: applications in biotechnology**To show basic mathematical concepts and how they can be used in the elaboration of simple models useful for the understanding of the biological phenomena; develop the ability to calculate and manipulate the most common mathematical objects; present with sufficient accuracy some simple but significant methods of proof of mathematics to refine the logical abilities; teach to communicate clearly the rigorous concepts. Knowing the fundamentals of computer science and possible applications in biology.

**FISICA APPLICATA ALLE BIOTECNOLOGIE**The course aims to provide students with the basic elements of Physics needed for applications of specific interest in the field of Biotechnology.

The course also aims to enhance:

- physical quantities and dimensional analysis;
- vector calculation and applications;
- static and dynamic of the material point and of the rigid body;
- fluidostatic and fluid dynamics;
- thermodynamics

**Mathematics and Computer Science: applications in biotechnology**Through lessons and practical sessions at the end of each learning unit (when planned).

If the lessons are given in a mixed or remote way, the necessary changes with respect to what was previously stated may be introduced, in order to meet the program envisaged and reported in the syllabus.

**FISICA APPLICATA ALLE BIOTECNOLOGIE**Lectures with application examples.

If the lessons are given in a mixed or remote way, the necessary changes with respect to what was previously stated may be introduced, in order to meet the program envisaged and reported in the syllabus.

**Mathematics and Computer Science: applications in biotechnology****Mathematics Section**Recalls on numerical sets and on arithmetic calculation, properties of real numbers and their consequences.

Elementary theory of sets

Elementary functions: n-th power and roots functions, exponential functions and logarithm functions: definitions, properties, graphs, applications.

Use of exponentials and logarithms in the life sciences: models for the evolution of a population.

Functions of a real variable: overview of definition domain, growth, decrescence, maximum and minimum (absolute), composition of elementary functions and their graph.

Limits: definitions, properties, rules of calculation, order of infinity and infinitesimal, graphic aspects, oblique asymptotes.

Continuous functions: definition, properties, zero theorem, approximation of the zeroes of a function (for example of the roots of a polynomial) with the bisection method.

Continuous functions: existence of maximum and minimum over a closed and limited interval. Composition of elementary functions and their graph, considering definition domain, limits at the ends of the definition domain, crescenza and decrescence, maximums and minima.

Derivatives.

Integrals: definition, properties, area calculation, approximation with the trapezoidal method.

Differential equations, notes on numerical methods of resolution. Enzymatic and molecular kinetics.**Computer Section****Basic concepts.**Fundamental concepts of information theory; General concepts: Hardware, Software; Information technology; Types of computers; Main components of a PC; Performance of a computer. Hardware: Central processing unit; Memory; Input Devices; Output peripherals; Input / output devices; Memory devices. Software: Types of software; System software; Application software; Graphical User Interface; System development.

**Introduction to algorithms.**Algorithms; Properties of the Algorithms; Description; Constants and Variables; Propositions and Predicates; Block diagrams

**Introduction to computational biomedicine.**Bioinformatics and computational modeling in biomedicine.

**Applications Section**Usage and access of the most important genomic, proteinomic and bibliographic databases

Practical examples of classical bioinformatics: assembly of genomic fragments, analysis and alignment of biosequences

Protege and ontologies: outline

COPASI: molecular modeling

Agent models: netlogo and customs systems**FISICA APPLICATA ALLE BIOTECNOLOGIE****1) Physics quantities**Quantities in physics--International system-Dimensions and dimensional calculation-Measurement uncertainties

**2) Vectors**Reference frame and euclidean axes; Geometrical meaning of vectors; Vectors in physics and their role in describing 2D and 3D space; Vector and scalar quantities; Vectors in the plane and their decomposition; Versors; Operation with vectors: sum, difference product

**3) Kinematics**Position and displacement vector; Velocity and accelerations vectors; ; One dimensional motion with constant velocity; One dimensional motion with constant acceleration; Freely falling objects; Projectile motion; Uniform Circular motion; Centripetal acceleration

**4) Dinamics**The concept of force; Newton's laws of motion; The force as a vector; Gravitational force; Forces of friction; The concept of work; Equilibrium condition and the inclined plane (with and without friction forces); Work done by a constant and a varying force; Conservative forces; Elastic forces and Hooke's law; The simple pendulum; Mass-spring system; Kinetic Energy and the wrok-kinetic energy theorem: Gravitaional force and gravitaional law; Conservation of energy; Potential energy; The isolated systems: conservation of mechanical energy; Linear momentum and its conservation; Impulse and momentum; Angular position, veolicity and acceleration; Rotational kinematics; Rigid body; Angular momentum and torque; Energy in rotational motion; Angular momentum conservation;

**5) Fluid mechanics**Pressure; Variation of pressure with depth; Stevin's law; Pressure measurements; Pascal's law; Buoyant forces and Archimede's principle; Fluid dynamics; Bernoulli's equation

**6) Thermodinamics**Temperature and the zeroth law of thermodynamics; Thermic contact; Thermometers; Absolute scale of temperatures; Thermic equilibrium; The heat; Thermal expansion of solids and liquids; Specific heat and calorimetry; Temperature of equiibrium; Latenet heat; The first law of thermodynamics; Work, heat and internal energy in thermodynamics; Transformation; Peferct gases; Transformations with constant temperature or volume or pressure; Molar specifi heat; The Mayer relation; Adiabatic transformations; The Carnot Cycle; The Carnot principle; The second law of thermodynamics; Entropy;

**6) Electromagnetism**Point-like charges; The Coulomb law; Electric field and its sources; the Gauss law; Electric potential and energy; Capacity and Capacitors; Current, resistance and Ohm's laws; Magnetic field and its sources; Time-dependent magnetic fields; Introduction to the Maxwell equations; Electromagnetic waves and properties; Applications

**Mathematics and Computer Science: applications in biotechnology**Teacher's slides

**FISICA APPLICATA ALLE BIOTECNOLOGIE**1. D. Halliday, R. Resnick, J. Walker "Fondamenti di Fisica" (2015) Casa Ed. Ambrosiana;

For other texts please ask the lecturer.