Knowledges and comprehension: knowledges of the main theoretical results in single variable calculus.
Skills and abilities: employing theoretical results to solve problems and exercises, and applying mathematical knowledges to other courses.
Elementary algebra, basic equations and inequalities, logic.
Course contents summary
Differential and integral calculus.
NUMERICAL SETS: natural numbers and induction, integer numbers, rational numbers and real numbers.
REAL FUNCTIONS: special functions, power functions, absolute value, trigonometric functions, graphs of real functions.
SEQUENCES: definition of topology, sequences and their limits, comparison theorems, algebra of sequences, special sequences.
CONTINUOUS FUNCTIONS: limits of functions, continuity, properties of continuous functions, Weierstrass Theorem and consequences, infinitesimal.
DERIVATIVES: definition and main properties, algebra of derivatives, Rolle, Lagrange and Cauchy Theorems, De l'Hopital Theorem, Taylor series, study of functions.
RIEMANN INTEGRAL: definition and main properties, fundamental theorem of calculus, computations of integrals.
"Analisi Matematica 1", Bramanti, Pagani,Salsa.
"Analisi Matematica 1", Languasco.
"Analisi Matematica Uno", Marcellini, Sbordone.
Assessment methods and criteria
Both written and oral exam. In the written part the student will solve mathematical exercises, in the oral part the student will discuss the statements, the proofs and the meanings of the main theoretical results of the course.