406-0252-AAL Mathematics II
|Semester||Autumn Semester 2016|
|Lecturers||A. Cannas da Silva|
|Periodicity||every semester recurring course|
|Language of instruction||English|
|Comment||Enrolment ONLY for MSc students with a decree declaring this course unit as an additional admission requirement.|
Any other students (e.g. incoming exchange students, doctoral students) CANNOT enrol for this course unit.
|Abstract||Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations.|
|Objective||Mathematics is of ever increasing importance to the Natural Sciences and Engineering. The key is the so-called mathematical modelling cycle, i.e. the translation of problems from outside of mathematics into mathematics, the study of the mathematical problems (often with the help of high level mathematical software packages) and the interpretation of the results in the original environment.|
The goal of Mathematics I and II is to provide the mathematical foundations relevant for this paradigm. Differential equations are by far the most important tool for modelling and are therefore a main focus of both of these courses.
|Content||- Multivariable Differential Calculus:|
functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence.
- Multivariable Integral Calculus:
multiple integrals, line and surface integrals, work and flux, Green, Gauss and Stokes theorems, applications.
- Partial Differential Equations:
separation of variables, Fourier series, heat equation, wave equation, Laplace equation, Fourier transform.
|Literature||- Thomas, G. B.: Thomas' Calculus, Parts 2 (Pearson Addison-Wesley).|
- Kreyszig, E.: Advanced Engineering Mathematics (John Wiley & Sons).
|Performance assessment information (valid until the course unit is held again)|
|Performance assessment as a semester course|
|ECTS credits||7 credits|
|Examiners||A. Cannas da Silva|
|Language of examination||English|
|Repetition||The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.|
|Mode of examination||written 90 minutes|
|Written aids||20 pages A4 (= 10 sheets of paper - front & back sides) summary. 1 English dictionary. No (pocket) calculators, no cellular phones.|
|This information can be updated until the beginning of the semester; information on the examination timetable is binding.|
|Main link||Link to course syllabus and suggested work plan in English|
|Only public learning materials are listed.|
|406-0252-AA R||Mathematics II|
Self-study course. No presence required.
|210s hrs||A. Cannas da Silva|
|No information on groups available.|
|There are no additional restrictions for the registration.|
|Environmental Sciences Master||Course Units for Additional Admission Requirements||E-|