401-0251-00L  Mathematics I

SemesterAutumn Semester 2022
LecturersA. Cannas da Silva
Periodicityyearly recurring course
Language of instructionGerman



Courses

NumberTitleHoursLecturers
401-0251-00 VMathematik I: Analysis I und Lineare Algebra4 hrs
Mon08:15-10:00HG G 3 »
Thu08:15-10:00HG G 3 »
01.12.08:15-10:00HG G 3 »
15.12.08:15-10:00HG G 3 »
A. Cannas da Silva
401-0251-00 UMathematik I: Analysis I und Lineare Algebra
Groups are selected in myStudies.
Die Übungen beginnen in der zweiten Semesterwoche.
Mo 14-16 für Studiengänge Erd- und Klimawissenschaften bzw. Umweltnaturwissenschaften.
Di 14-16 für Studiengänge Agrarwissenschaften bzw. Lebensmittelwissenschaften.

Zusätzlich wird das Mathe-Lab (Präsenzstunden) angeboten: Mo 12-14, Di 16-18 und Mi 16-18, jeweils im HG E 41.
2 hrs
Mon14:15-16:00CHN D 44 »
14:15-16:00CHN F 42 »
14:15-16:00ETZ E 9 »
14:15-16:00ETZ G 91 »
14:15-16:00ETZ H 91 »
14:15-16:00ETZ K 91 »
14:15-16:00HG F 26.5 »
14:15-16:00LFW C 4 »
Tue14:15-16:00CAB G 56 »
14:15-16:00CLA E 4 »
14:15-16:00LFO C 13 »
14:15-16:00LFW C 5 »
14:15-16:00RZ F 21 »
A. 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. Single-Variable Calculus:
review of differentiation, linearisation, Taylor polynomials, maxima and minima, antiderivative, fundamental theorem of calculus, integration methods, improper integrals.

2. 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.

3. Ordinary Differential Equations:
separable ordinary differential equations (ODEs), integration by substitution, 1st and 2nd order linear ODEs, homogeneous systems of linear ODEs with constant coefficients, introduction to 2-dimensional dynamical systems.
Literature- Thomas, G. B.: Thomas' Calculus, Part 1 (Pearson Addison-Wesley).
- Bretscher, O.: Linear Algebra with Applications (Pearson Prentice Hall).
Prerequisites / NoticePrerequisites: familiarity with the basic notions from Calculus, in particular those of function and derivative.

Performance assessment

Performance assessment information (valid until the course unit is held again)
Performance assessment as a two-semester course together with 401-0252-00L Mathematics II (next semester)
For programme regulations
(Examination block)
Bachelor's Degree Programme in Agricultural Sciences 2015; Version 01.03.2019 (Examination Block)
Bachelor's Degree Programme in Earth and Climate Sciences 2016; Version 25.02.2020 (Examination Block)
Bachelor's Degree Programme in Environmental Sciences 2011; Version 12.01.2016 (Examination Block)
Bachelor's Degree Programme in Environmental Sciences 2016; Version 27.09.2019 (Examination Block)
Bachelor's Degree Programme in Food Science 2016; Version 06.03.2019 (Examination Block)
ECTS credits13 credits
Performance assessment as a semester course (other programmes)
ECTS credits6 credits
ExaminersA. Cannas da Silva
Typesession examination
Language of examinationGerman
RepetitionThe performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examinationwritten 90 minutes
Additional information on mode of examinationACHTUNG: Die folgenden Angaben betreffen den JAHRESKURS Mathematik I und II, wo Lernelemente in Form von wöchentlichen Quizzes angeboten werden: Es werden zwölf Quizzes pro Semester angeboten. Jedes Quiz wird benotet mit 0 oder 1 Punkt. Insgesamt können maximal 12 Punkte pro Semester gesammelt werden. Die erreichte Punktzahl für jedes Semester P ergibt einen Notenzuschlag von Min(0.125, 0.0125 P) zur ungerundeten Endnote in der Basisprüfung. Für die beiden Semester zusammen gibt es also einen maximalen Bonus von 0.25 Notenpunkten, der erreicht wird, wenn mindestens 10 Quizzes pro Semester erfolgreich gelöst werden. Weitere Details werden auf der Vorlesungshomepage gelistet.
Written aids20 A4-Seiten (= 10 doppelseitige Blätter) Notizen. 1 Wörterbuch für fremdsprachige Studierende. Keine (Taschen)Rechner, keine Mobiltelefone.
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block.
This information can be updated until the beginning of the semester; information on the examination timetable is binding.

Learning materials

 
LiteratureHauptliteratur: "Analysis 1" von Thomas, Weir und Hass - nicht online!
Hauptliteratur: "Lineare Algebra - Eine Einführung" von Gramlich - online an der ETH
Only public learning materials are listed.

Groups

401-0251-00 UMathematik I: Analysis I und Lineare Algebra
GroupsG-01A
Mon14:15-16:00ETZ G 91 »
G-01B
Tue14:15-16:00CAB G 56 »
G-02A
Mon14:15-16:00ETZ K 91 »
G-02B
Tue14:15-16:00RZ F 21 »
G-03A
Mon14:15-16:00CHN F 42 »
G-03B
Tue14:15-16:00CLA E 4 »
G-04A
Mon14:15-16:00HG F 26.5 »
G-04B
Tue14:15-16:00LFO C 13 »
G-05A
Mon14:15-16:00ETZ H 91 »
G-05B
Tue14:15-16:00LFW C 5 »
G-06
Mon14:15-16:00CHN D 44 »
G-07
Mon14:15-16:00LFW C 4 »
G-08
Mon14:15-16:00ETZ E 9 »

Restrictions

There are no additional restrictions for the registration.

Offered in

ProgrammeSectionType
Agricultural Sciences BachelorFirst Year ExaminationsOInformation
Earth and Climate Sciences BachelorFirst Year ExaminationsOInformation
Food Science BachelorFirst Year ExaminationsOInformation
Environmental Sciences BachelorFirst Year ExaminationsOInformation