# Mathematical analysis 1 (2007/2008)

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Course code
4S00030
Credits
6
Coordinator
Mauro Spera
Teaching is organised as follows:
Modulo I 3 MAT/05-MATHEMATICAL ANALYSIS 1° Q - solo 1° anno Marco Squassina
Modulo II 3 MAT/05-MATHEMATICAL ANALYSIS 2° Q Mauro Spera

#### Learning outcomes

Module: Modulo I
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Module: Modulo II
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The course provides an introduction to differential and integral calculus for functions of one real variable; geometric and physical motivations and applications thereof will be stressed throughout.

#### Syllabus

Module: Modulo I
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Module: Modulo II
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Mathematical Analysis (advanced module): Syllabus (tentative) The course provides an introduction to differential and integral calculus for functions of one real variable; geometric and physical motivations and applications thereof will be stressed throughout.
Historical introduction. The notion of derivative and its geometrical and physical meaning.
Derivatives of higher order. Derivatives of elementary functions. Rules of differentiation.
Critical points. The theorems of Fermat, Rolle, Lagrange, Cauchy. de l'Hopital's rule. Convexity and second derivative. Taylor's formula. Applications to function plotting.
The definite (Riemann) integral. Integrability of continuous functions. The integral function. The mean value theorem for definite integrals. Indefinite integrals. The fundamental theorem of calculus. Integration techniques. Applications to areas and volumes. Cavalieri's principle. Numerical series. Improper integrals. Introduction to first order differential equations; geometrical meaning; elementary methods of integration (separation of variables, variation of parameters).

NOTES: 1. Some complementary lecture notes to the text below will be made available.
2. The programme is tentative and subject to slight changes.

Reference text (with exercises):

M.CONTI, D.L. FERRARIO, S.TERRACINI, G.VERZINI, Analisi Matematica -
Dal calcolo all'analisi, vol.1 Apogeo, Milano, 2006.

#### Assessment methods and criteria

Module: Modulo I
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Final written and oral exams.

Module: Modulo II
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Assessment : written exam (with some "qualifying" questions therein, among others), followed by an oral exam (optional).

 Author Title Publisher Year ISBN Note M. Conti, D. L. Ferrario, S. Terracini, G. Verzini Analisi matematica. Dal calcolo all'analisi, Vol. 1 (Edizione 1) Apogeo 2006 88-503-221 testo adottato