MATHEMATICAL ANALYSIS A

PREREQUISITES: elementary algebra, trigonometry, analytic geometry, rational powers, exponentials and logarithms; elementary functions.

PROGRAM
LOGIC: propositions and predicates, sets, functions, order relations and equivalence.

NUMERICAL SETS: natural numbers and the principle of induction, integers, rational, real numbers.
REAL FUNCTIONS: extrema of real functions, monotone functions, even and odd functions, powers, absolute value, trigonometric functions, hyperbolic functions, graphs of real functions.
SEQUENCES: overview of topology, sequences and their limits; comparison theorems and algebraic theorems, continuity, monotone sequences, key examples, the number of Napier; recursively defined sequences (overview).
CONTINUOUS FUNCTIONS: limits of functions, continuity, first properties of continuous functions, continuous functions on an interval (zeros, intermediate values​​); Weierstrass theorem, infinitesimals.
DERIVATIVES: definition of the derivative, the first properties; algebraic operations on derivatives, derivatives and local properties of functions; theorems of Rolle, Lagrange, Cauchy; indeterminate forms, de l'Hôpital theorem, Taylor's formula and various remains, asymptotic developments; functions convex qualitative study of functions.
INTEGRATION: construction and first properties of the integral, primitive, fundamental theorem of integral calculus, methods of integration.