Coursecode: wi104th
Coursename: Analysis [for graduates of TH-WbMT]
DUT creditpoints: 8
ECTS creditpoints: 12 |
Faculty
of Technical Mathematics and Informatics |
Lecturer(s):
Corstens, ir. H.F.M. |
Tel.: 015-2783898 |
Catalog data:
Basic concepts, complex numbers, limits, continuity, differential calculus, integral
calculus, vector valued functions of several variables, multiple integrals, vector
calculus, sequences and series. |
Courseyear:
1
Semester: 5/5/2/0
Hours p/w: 5/5/2/0
Other hours: -
Assessment: written
Assessm.period(s): see Remarks
(see academic calendar) |
Prerequisites:
- |
Follow
up: - |
Detailed
description of topics:
1.1 Basic concepts, concept of a function, inverse
function, inverse circular functions, hyperbolic functions.
1.2 Complex numbers, modulus, argument, roots of
algebraic equations, -exponential equations.
1.3 Functions of one real variable, limiting values,
continuity, properties of continuous functions, intermediate value theorem.
2.1 Differential calculus, definition and rules of
differentiation, chain rule, mean value theorem, extrema, Taylors theorem, Landau
O-symbol, interpolation, numerical solution of equations.
2.2 Integral calculus, properties of integrals,
fundamental theorem, techniques of integration, improper integrals, numerical methods.
3.1 Vector valued functions of several variables,
partial derivatives, tangent plane, Taylors formula, gradient, divergence, curl, change of
variables, inverse- and implicit function theorems, extrema.
3.2 Multiple integrals, Fubini's theorem, change of
variables, polar-, cilindrical and spherical coordinates, applications.
4.1 Line- and surface integrals, integral theorems of
Gauss and Stokes.
4.2 Infinite series, convergence and divergence,
tests, absolute- and relative convergence, power series, radius of convergence, summation
of power series.
|
Course
material:
Almering, J.H.J., e.a., "Analyse"; Delft,
Delftse Universitaire Pers [remark: at Delft obtainable from VSSD] ISBN 90-407-1260-3. |
References
from literature:
Meulenbeld, B., A.W. Grootendorst,
"Analyse", deel 1, 2, 3; Delft, Delftse Universitaire Pers
Courant R., F. John, "Introduction to
calculus" vol. I, II, Interscience Publishers (John Wiley & Sons)
|
Remarks
(specific information about assesment, entry requirements, etc.):
1.1, 1.2 and 1.3 are treated in first quarter
(5/0/0/0) followed by preliminary examination;
2.1 and 2.2 in second quarter (0/5/0/0) followed by preliminary examination;
3.1 and 3.2 in third quarter (0/0/4/0) followed by preliminary examination;
4.1 and 4.2 in fourth quarter (0/0/0/4) followed by preliminary examination;
re-examination see academic calendar;
part 1, 2, 3 and 4 each counts for 2 DUT credits;
final mark for student Wb is established taking the
arithmetic mean of the parts as agreed upon your curriculum provided the mark for every
part separately >= 5;
final mark for student MT is established taking the
arithmetic mean of the 4 parts provided the mark for every part separately >= 5.
|
Goals:
To provide students with:
1. A comprehension of mathematical concepts as used
in engineering applications
2. A skill to handle these concepts to perform
calculations
3. A preparation for more advanced courses
|
Computer
use: |
Laboratory
project(s): |
Design
content: |
Percentage
of design: 0% |