Analyse 1

Bewerkingen uitvoeren met complexe getallen, oplossen kwadratische vergelijkingen, lineariseren, integreren en eenvoudige differentiaalvergelijkingen oplossen

Analysis1 – L1

Know complex numbers, perform their standard operations (addition, subtraction, multiplication, division) and convert to polar form (r[cos phi + i sin phi])

Analysis1 – L2

Solve the quadratic equation ax^2 + bx + c for real and complex roots

Analysis1 – L3

Reproduce the characteristic properties of the elementary functions arcsin, arccos, arctan.

Analysis1 – L4

Determine the tangent to an implicitly defined 2D-curve (e.g. x^2 + xy + y^2 - 2y = 0)

Analysis1 – L5

Calculate the linearisation of a function (f: R -> R) in a given point and interpret its meaning

Analysis1 – L6

Reproduce and explain the construction of the Riemann integral

Analysis1 – L7

Determine primitive functions by means of the substitution rule and the method of partial integration

Analysis1 – L8

Determine primitive functions by means of a Computer Alegbra system

Analysis1 – L9

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

Analysis1 – L10

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

Analysis1 – L11

Classify a differential equation according to order, linearity and separability

Analysis1 – L12

Infer characteristics of the solution to a differential equation from its direction field

Analysis1 – L13

Formulate a differential equation for simple dynamic phenomena, such as proportional growth

Analysis1 – L14

Calculate the analytic solution for the following types of diferential equations: 1) separable diff equation  p(y) y' + q(x) =0  ; 2) 1st order linear diff equation  y' + a(x)y = g(x) ; 3) 2nd order, linear, constant coefficient differential equation   a y'' + b y' + cy = g(x)