Learning objectives
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Mathematical models of various types
Prerequisites
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Course unit content
<br />INTEGRAL CALCULUS AND DIFFERENTIAL EQUATIONS <br />
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1. ORDINARY DIFFERENTIAL EQUATIONS. CAUCHY PROBLEM. EXISTENCE THEOREM AND LOCAL UNIQUENESS; MENTION OF DEMONSTRATION. DIFFERENTIAL EQUATIONS WITH SEPARABLE VARIABLES, HOMOGENEOUS DIFFERENTIAL EQUATIONS, FIRST ORDER LINEAR HOMOGENEOUS DIFFERENTIAL EQUATIONS, CONSTANT COEFFICIENT LINEAR DIFFERENTIAL EQUATIONS. METHOD OF VARIATION OF CONSTANTS. SOME DIFFERENTIAL EQUATIONS OF PARTICULAR FORM. 2. MATHEMATICAL MODELS: EXPONENTIAL GROWTH, LOGISTIC GROWTH, LOGISTIC GROWTH WITH CONSTANT SAMPLING. LOTKA-VOLTERRA MODEL. MODELS OF EPIDEMICS. <br />
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LINEAR ALGEBRA <br />
1. VECTOR SPACES ON VECTOR R AND LINEAR INDEPENDENCE. BASIS OF A VECTOR SPACE. 2. LINEAR APPLICATIONS BETWEEN VECTOR SPACES AND MATRICES. RANK OF A MATRIX. DETERMINANT OF A SQUARE MATRIX AND METHODS FOR CALCULATION. 3. EIGENSPACES, EIGENVALUES AND EIGENVECTORS OF LINEAR APPLICATIONS. 4. METHOD OF LEAST SQUARES AND MENTION OF THE SOLUTION OF LINEAR SYSTEMS. <br />
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DIFFERENTIAL CALCULUS FOR FUNCTIONS OF SEVERAL VARIABLES <br />
1. CONTINUITY AND DIFFERENTIABILITY OF FUNCTIONS IN SEVERAL VARIABLES. PARTIAL, DIFFERENTIAL AND GRADIENT DERIVATIVES. SCHWARZ THEOREM, HESSIAN MATRIX. STATIONARY POINTS, EXTREME POINTS AND SADDLE POINTS. NECESSARY CONDITIONS FOR EXTREME POINTS. 2. MENTION OF THE LAGRANGE MULTIPLIER METHOD.
Full programme
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Bibliography
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[1] Antonio C. Capelo, Modelli Matematici in Biologia, Decibel. <br />
[2] Franco Conti, Calcolo, McGraw-Hill. <br />
[3] Franco Conti, Paolo Acquistapace, Anna Savojni, Analisi Matematica, McGraw-Hill. <br />
[4] Giovanni Prodi, Istituzioni di Matematica, McGraw-Hill. <br />
[5] Giovanni Prodi, Metodi Matematici e Statistici, McGraw-Hill. <br />
[6] Walter Rudin, Principi di Analisi Matematica, McGraw-Hill.
Teaching methods
A written exercise and a short oral exam on the part not covered by the written exam
Assessment methods and criteria
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Other information
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