Opmerkingen:
In het vak wordt per week 4 uur colstructie gegeven en is er 1 vragenuur.
Van de colstructie-uren wordt minimaal de helft besteed aan zelf werken.

Leerdoelen:

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

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

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

• 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

• 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

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

• 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)

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

• 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)