406-0251-AAL  Mathematics I

SemesterSpring Semester 2020
LecturersA. Cannas da Silva
Periodicityevery semester recurring course
Language of instructionEnglish
CommentEnrolment 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.



Courses

NumberTitleHoursLecturers
406-0251-AA RMathematics I
Self-study course. No presence required.
180s hrsA. Cannas da Silva

Catalogue data

AbstractThis course covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.
ObjectiveMathematics 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.
Content1. Linear Algebra and Complex Numbers:
systems of linear equations, Gauss-Jordan elimination, matrices, determinants, eigenvalues and eigenvectors, cartesian and polar forms for complex numbers, complex powers, complex roots, fundamental theorem of algebra.

2. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, fundamental theorem of calculus, antiderivative, integration methods, improper integrals.

3. Ordinary Differential Equations:
variation of parameters, separable equations, integration by substitution, systems of linear equations with constant coefficients, 1st and higher order equations, introduction to dynamical systems.
Literature- Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall.
- Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
ECTS credits6 credits
ExaminersA. Cannas da Silva
Typesession examination
Language of examinationEnglish
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 90 minutes
Written aidsSummary with up to 20 A4 pages (= 10 double-sided sheets of paper). 1 English dictionary. No calculators, no laptops, no cellular phones.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
Main linkLink to course syllabus and suggested work plan in English
Additional linksLink to course syllabus and suggested work plan in English
Only public learning materials are listed.

Groups

No information on groups available.

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Spatial Development and Infrastructure Systems MasterCourse Units for Additional Admission RequirementsE-Information
Environmental Sciences MasterCourse Units for Additional Admission RequirementsE-Information