Enrollment year
2017/2018
Academic discipline
MAT/05 (MATHEMATICAL ANALYSIS)
Department
DEPARTMENT OF BIOLOGY AND BIOTECHNOLOGY "LAZZARO SPALLANZANI"
Course
BIOLOGICAL SCIENCES
Curriculum
PERCORSO COMUNE
Period
(01/10/2017 - 14/01/2018)
Lesson hours
48 lesson hours
Prerequisites
Algebraic equations and inequalities of the first and second degree. Planar analytic geometry. Trigonometry. Exponential and logarithmic functions.
Learning outcomes
The course is aimed at presenting the bases of differential and integral calculus for functions of one real variable.
Course contents
Analytic geometry in the plane: lines, conics. Set theory: natural, integer, real numbers. Growth rate; arithmetic and geometric progressions, sequences. Mean and median values. Use of percentages. Concept of function: domain, image space, sign. Elementary functions: powers, polynomials, trigonometric functions, logarithms and exponentials. Logarithmic scales. Limits of sequences and of functions. Continuous functions and their basic properties. Discontinuities. Concept of derivative; geometrical and physical interpretation. Tangent line. Monotone, concave, convex functions. Minima, maxima and inflection points. Fundamental theorems of differential calculus. Study of a function of one real variable. Taylor polynomials. De L'Hopital's rule. Integrals. Integration by parts and by substitution.
Teaching methods
Lessons, partly devoted to the resolution of exercises. A tutoring course complements the morning lessons.
Reccomended or required readings
V. Villani, G. Gentili, Matematica - Comprendere e interpretare fenomeni delle scienze della vita, Mc Graw-Hill
Assessment methods
Written and oral exam. The written test will be devoted to the resolution of exercises involving
applications of the main mathematical tools introduced during the course. The oral exam will
be aimed at verifying the comprehension of the basic definitions of the theory and the capacity
to illiustrate them by means of concrete examples.
Further information is available at the website
http://www-dimat.unipv.it/giulio/linkedmaterial/bio/faqbio2017.html
Further information
Further information at the web address:
http://www-dimat.unipv.it/giulio/istmat17.html
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