Course code: wi2252wb

Course name: Analyse module 3

also see BLACKBOARD

ECTS creditpoints: 3

Faculty of Information Technology and Systems

Lecturer(s): Koelink, dr. H.T.

Tel.:  015-27 83639

Catalog data:

Multi variable functions or vector functions, partial derivatives, multiple integrals

Course year:

BSc 2nd year

Semester:

1B

Hours p/w:

4

Other hours:

Assessment:

Written

Assessm.period(s):

1B, 2A

(see acedemic calender) 

Prerequisites: VWO-wiskunde

Follow up: wi3105wb

Detailed description of topics:

Euclidean space, inner product, outer product, lines and planes in 3-space, multi variable functions or vector functions, limits, continuity, partial derivatives, tangent planes, linear approximation, chain rule, directional derivatives, gradient, extremal values, multiple integrals, Fubini's theorem, change of variables, surface integrals, applications: moments, expectation

Course material:

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

References from literature:

Remarks (specific information about assesment, entry requirements, etc.):

Learning goals:

The student must be able to:

1. Apply vector operations (addition, inner product, outer product)

2. Calculate and apply the equations of lines and planes

3. Apply & interpret the graphical notion of topographical map & graph for functions of two variables

4. Recognize & interpret the notions of limits & continuity for functions from Rn -> R

5. Apply partial differentiation, both implicit & explicit (e.g. the partial derivative dV/dT from PV/T = c)

6. Calculate the gradient of a function in a particular point and know its applications such as the normal vector for an implicitly defined surface

7. Apply the chain rule to determine the derivative for functions of multiple variables which themselves are functions of other multiple variables (i.e. for functions z=f(x1, x2,…,xn) with xi=xi(u1,u2,….,um) determine the partial derivative dz/dui)

8. Calculate equations of tangentplanes both for explicit and implicit defined surfaces

9. Calculate first-order & second-order approximations of a function by means of Taylor polynomials

10. Calculate maxima and minima for (simple) functions on (simple) domains

11. Calculate maxima and minima subject to constraints using Lagrange multipliers

12. Calculate double integrals, by employing repeated integrals with x, y (,z) coordinates & by coordinate transformations through the use of polar, cylindrical & spherical coordinate systems

13. Apply double & triple integrals for the calculation of volume, mass, center of gravity and inertial moments (2D & 3D)

Computer use:

Laboratory project(s):

Design content:

Percentage of design:  0 %