406-0253-AAL  Mathematics I & II

Lehrveranstaltungen

Katalogdaten

Kurzbeschreibung	Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations. The main focus of Mathematics II is multivariable calculus.
Lernziel	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.
Inhalt	1. 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. 4. Multivariable Differential Calculus: functions of several variables, partial differentiation, curves and surfaces in space, scalar and vector fields, gradient, curl and divergence. 5. Multivariable Integral Calculus: multiple integrals, line and surface integrals, work and flow, Green, Gauss and Stokes theorems, applications. 6. Introduction to Partial Differential Equations: separation of variables, heat equation, wave equation, Laplace equation.
Skript	See literature
Literatur	- Bretscher, O.: Linear Algebra with Applications, Pearson Prentice Hall. - Thomas, G. B.: Thomas' Calculus, Part 1, Pearson Addison-Wesley. - Thomas, G. B.: Thomas' Calculus, Part 2, Pearson Addison-Wesley. - Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.
Voraussetzungen / Besonderes	Prerequisites: familiarity with the basic notions from Calculus, in particular those of function, derivative and integral. Schedule and location of the assistance hours (Mathe-Lab) may be found on the Moodle webpages for the parallel courses in German: - 401-0251-00L Mathematik I in the Fall semester and - 401-0252-00L Mathematik II in the Spring semester.
Kompetenzen	Fachspezifische Kompetenzen Konzepte und Theorien geprüft Methodenspezifische Kompetenzen Analytische Kompetenzen geprüft

Leistungskontrolle

Information zur Leistungskontrolle (gültig bis die Lerneinheit neu gelesen wird)
Leistungskontrolle als Semesterkurs
ECTS Kreditpunkte	13 KP
Prüfende	A. Cannas da Silva, S. Kalisnik Hintz
Form	Sessionsprüfung
Prüfungssprache	Englisch
Repetition	Die Leistungskontrolle wird in jeder Session angeboten. Die Repetition ist ohne erneute Belegung der Lerneinheit möglich.
Prüfungsmodus	schriftlich 180 Minuten
Hilfsmittel schriftlich	Summary with up to 40 A4 pages (= 20 double-sided sheets of paper). 1 English dictionary. No calculators, no laptops, no cellular phones.
Diese Angaben können noch zu Semesterbeginn aktualisiert werden; verbindlich sind die Angaben auf dem Prüfungsplan.

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Studiengang	Bereich	Typ
Gesundheitswissenschaften und Technologie Master	Auflagen-Lerneinheiten	E-
Umweltnaturwissenschaften Master	Auflagen-Lerneinheiten	E-