laatst gewijzigd: 26/08/2003

Vakcode: wi1250wb

Vaknaam: Analyse 1

ZIE OOK BLACKBOARD

Het betreft een colstructie

ECTS studiepunten: 3

Faculteit der Informatietechnologie en Systemen

Docent(en): Koelink, dr. H.T.

Tel.:  015-27 83639

Trefwoorden:

Differential equations, implicit differentiation, integration, complex numbers

Cursusjaar:

BSc 1st year

Semester:

1A

Coll.uren p/w:

4

Andere uren p/w:

1 (vragenuur)

Toetsvorm:

Written

Tentamenperiode:

1A, 1B

(zie jaarindeling)

 

Voorkennis: VWO wiskunde

Wordt vervolgd door: wi1251wb

Uitgebreide beschrijving van het onderwerp:

Complex numbers, differentiation, mean value theorem, implicit differentiation,linear approximation, improper integrals, substitution rule, integration by parts, differential equations, modeling, Euler's solution method, direction fields, separable differential equations, linear differential equations, applications to the logistic equation, predator-prey model, Hooke's law for vibrating springs

College materiaal:

J.Stewart, “Calculus: early transcendentals”, 5th ed. ISBN 0-534-39321-7

Referenties vanuit de literatuur:

Opmerkingen (specifieke informatie over tentaminering, toelatingseisen, etc.):

Bonus exercise using a computer algebra package

Leerdoelen:

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)

 

Computer gebruik:

Computer algebra package is needed for some exercises.

Practicum:

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