Analyse 2

Analytisch limieten bepalen en (numeriek) met reeksontwikkeling benaderen

Analysis2 – L1

Distinguish between the two types of improper integrals: discontinuous integrand or infinite integration interval

Analysis2 – L2

Determine the convergence or divergence of an improper integral by means of comparison tests

Analysis2 – L3

Recognize the various types of sequences: explicit and recursive sequences (e.g. Fibonacci sequence)

Analysis2 – L4

Explain in own words convergence and limit of a sequence. Reproduce simple properties of these two aspects (a.o. sum law, constant multiple law, product law, squeeze theorem). Reproduce standard limiting cases, e.g. LIM (1 + x/n) = e^x ; LIM n-th ROOT of n = 1

Analysis2 – L5

Recognize an infinite series and explain in own words the meaning of convergence and divergence. Know the convergence and divergence of some important examples such as SUM 1/n ; SUM 1/n^2 ; SUM r^n

Analysis2 – L6

Reproduce and apply a number of simple convergence criteria to infinite series (test for divergence, sum law, product law, integral test)

Analysis2 – L7

Determine the convergence radius of power series and determine the Taylor power series expansion of elementary functions (such as sin x ; e^x ; ln x)

Analysis2 – L8

Approximate functions by means of Taylor polynomials and determine estimates of the errors

Analysis2 – L9

Reproduce and interpret basic vector geometry in two- and three-dimensional space (length, perpendicularity, inner product, outer product, determinant, formulation of the equations for lines and planes)