# MATHEMATICS

# MATHEMATICS

Arithmetic: natural numbers, integers, and rational numbers, and the arithmetical operations and their properties, decimal representation of a number.

Algebra: expressions with letters and simple algebraic manipulations; sum, product, and division with residue between polynomials; equations and inequalities of first and second degree. Basic elements of trigonometry. Cartesian coordinates.

Give the mathematical preparation necessary to master the tools commonly used in other disciplines, in particular Physics and Chemistry.

Real functions in real variables: Generalities. Domain and Range of a function, Domain of existence of a function, Injectivity, Surjectivity. Operations with functions. Composition of functions, inverse function. Graph of a function. Elementary functions (Polynomial functions, trigonometric functions, exponential and logarithmic functions). Graphs of elementary functions. Reading a graph. Limits and continuity of a function: Definition of limit. Theorems on limits. Some notable limits. Continuous functions. Continuity of elementary functions. Theorems on continuous functions.

Derivatives: Definition. Rules of derivation. Derivatives of elementary functions. Successive derivatives. Relative maxima and minima. Rolle’s Theorem, Cauchy’s Theorem, Lagrange’s Theorem. Study of a function. Tracing the graph of a function.

Integrals: Definition of definite integral. Properties of the definite integral. Definition of primitive. Indefinite integral. Fundamental Theorem of Calculus. Application of integral calculus to areas and volumes. Calculation of integrals, integration by parts.

Differential equations: definition of differential equation. A few examples of simple solutions. Examples of application of differential equations.

Vinicio Villani, Matematica per discpipline Bio-Mediche , McGraw- Hill

Fabio Bellissima & Carla Crociani Matematica di Base, Carocci

Letcures and working groups

written test and oral examination

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