Derived from
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14618 Matematica ed elementi di Fisica in Agricultural and Environmental Sciences L-25 0 Nobili Paolo
(syllabus)
MATHEMATICS
COMBINATORIAL CALCULUS Provisions, permutations and combinations with and without repetition, binominal coefficients, definitions and properties. MATRICES AND DETERMINANTS Definitions and properties of matrices, triangular and diagonal matrices, transposed and opposite matrices, inverse matrices. Product associated with a matrix, determinant, Laplace theorems, rule Sarrus, general properties of determinants, and lesser rank or characteristic of a matrix. Eigenvalues and eigenvectors of a square matrix. SYSTEMS OF LINEAR EQUATIONS General information on systems of linear equations, theorem Rouchè-Capelli, Cramer theorem, systems of m equations in n unknowns, homogeneous systems. FUNCTION OF REAL VARIABLE Relations, applications or functions, definition domain, codomain or target set of a function, image. Graph of a function. Injective function or injection, surjective or a surjection, or bijection bijective function or one-to-one correspondence, invertibility of functions. Rational functions, composite functions, inverse functions, extremes of a function. Limits of a function, theorems about limits, uniqueness theorem of the limit theorem of the permanence of the sign, comparison theorem, the limit of the sum, product, quotient etc .. functions, special limits. CONTINUOUS FUNCTIONS Definitions and properties, continuity of a function, Napier's constant, maximum and minimum of a function. DERIVATIVES Definition of the derivative, geometrical meaning, derivation rules, derivation of trigonometric functions, derivation of composite functions and inverse, the derivative of the sum of functions, derivative of the product of two or more functions, the derivative of the quotient of two functions, etc. derivability and continuity of a function, differential, higher order derivatives, maxima and minima of a function, asymptotes, concavity and convexity, flexed, graphs of functions. Rolle's theorem, Cauchy, Lagrange, De L'Hopital, undetermined forms. Logarithm function, exponential function, hyperbolic functions. INTEGRATION Indefinite integral, primitive, property, integration by decomposition, integration by parts and by substitution, integration of rational functions, definite integral, the relationship between integration and derivability, calculating areas, Torricelli's theorem.
ELEMENTS OF PHYSICS
Models, theories, measures. The international system. Scalar and vector quantities; sum and difference of vectors; decomposition of vectors along directions assigned; scalar product, vector product, mixed product. KINEMATICS Motion of a particle. Coordinate systems. Speed and acceleration linear. Uniform circular motion, angular velocity, angular acceleration. DYNAMIC Newton's laws (I, II and III) and their applications. Friction forces. Work and kinetic energy. Conservative forces. Potential energy; conservation of energy. Power. Dissipative forces. Momentum and its conservation; shocks and their classification. Motion of rigid systems and equilibrium conditions. Moment of inertia and angular momentum for rotation about a fixed axis; moment of forces; second law of mechanical systems. Kinetic energy; Rolling and role of friction. Work and power. FLUIDS Fluid statics and applications. Fluid dynamics: flow rate, the law of conservation of reach. Bernoulli's theorem and applications. Real fluids: surface tension and capillary action.
(reference books)
"Lezioni di matematica generale" - Alvaro Marucci - Edizioni Sette Città, Viterbo
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