Course catalogue | University of Parma

Learning objectives

To supply the basic tools of infinitesimal calculus. To introduce the student to the concepts of Mathematical Analysis.

Prerequisites

- - -

Course unit content

Sets, subsets, power set. Principle of induction and applications. Equivalence and order relations: raising operators, lowering operators, narrowness. Functions and their opposites. Injectivity, surjectivity. Images and counter images. Sequences. Monotone functions. Composition of functions and invertibility. Digression on numbers: rational numbers and real numbers and their properties. Ordered fields and absolute value: first properties. Powers with real exponent. Graphs of f(x), kf(x), f(x+h), f(x)+h, |f(x)|. Graphs of elementary functions: power, root, exponential, logarithmic function. Revision of trigonometry. Functions of a real variable. Limits, continuity, derivatives, differentials. Monotone functions. Fermat, Rolle, Cauchy, Lagrange theorems (with demonstrations). De l'Hospital's rule. Function graphs. Infinitesimals and infinites. Taylor-MacLaurin polynomials with Peano remainder. Definite and indefinite integrals. Integration methods. Fundamental theorem of integral calculus. Integral function. Geometric applications. Improper integrals. Convergence criteria. Length of arches of plane curves. <br />

Full programme

- - -

Bibliography

Stoka, M: Corso di Matematica, CEDAM. Stoka-Pipitone, Esercizi e problemi di matematica, CEDAM

Teaching methods

Theoretical lectures and exercises<br />
written examination

Assessment methods and criteria

- - -

PRINCIPLES OF MATHEMATICS
cod. 13137

Learning objectives

Prerequisites

Course unit content

Full programme

Bibliography

Teaching methods

Assessment methods and criteria

Other information

PRINCIPLES OF MATHEMATICS cod. 13137

Learning objectives

Prerequisites

Course unit content

Full programme

Bibliography

Teaching methods

Assessment methods and criteria

Other information

PRINCIPLES OF MATHEMATICS
cod. 13137