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:

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