Inhalt

Abstract:

Mathematics is a challenge for first-year students in physics, chemistry, biology, computer science and all engineering sciences. On the one hand, freshmen at the university are not as familiar (as they should be) with school mathematics, on the other hand, they are confronted with a kind of "new" mathematics, university mathematics, which has its own way of thinking. New concepts emerge, a new (symbolic) language needs to be learned, and there are new problems and situations that go beyond the content covered in school. Many students are therefore overwhelmed and may even abandon their studies for this reason. This course repeats important mathematical concepts of school mathematics and introduces the basic concepts of university initial mathematics. The aim is to enable students to solve typical scientific and engineering problems with mathematics. This course is not just a "calculus or formula course", but aims to develop a basic understanding of the most important concepts of analysis - numbers, sequences, functions, equations, derivative, integral, differential equation - in simple application situations. For this purpose, the understanding of the mathematical concepts is developed on an intuitive and often visual level, also with the help of dynamic and interactive computer presentations. The course has been developed by the Universities of Würzburg and Erlangen-Nuremberg as well as by the University of Applied Sciences Würzburg-Schweinfurt on the German side, and by the Universities Aalto Universtiy Helsinki, Metroplian University of Applied Sciences and Vaasa University on the Finnish side.

Gliederung:

The contents of this course are central to first-year-students in physics, chemistry, biology, computer science and all engineering sciences. It contents the following chapters

1. functions (from linear to trigonometric and exponential functions, insight into functions of several variables)

2. sequences and limits (properties of sequences, limits of sequences and functions, continuity)

3. equations (linear, quadratic, polynomial, trigonometric, exponential equations)

4. Derivation (derivations of basic functions, extreme value problems)

5. integral (main theorem of differential and integral calculus, integrals of elementary functions, integration techniques)

6. differential equations (ordinary differential equations of first and second order)

Detaillierter Inhalt:

In Chapter 1, "functions" and their central properties from school mathematics are repeated: linear and quadratic functions, power, exponential and trigonometric functions. Their basic properties are presented, explained by examples and illustrated by various interactive presentations. Chapter 2 deals with the topic "sequences and limits". Important properties of sequences are worked out and explained. The concept of limits of sequences then forms the basis for central concepts of analysis such as limits of functions, derivative and integral. Chapter 3 repeats the concept of equations of school mathematics and develops an access to methods of university mathematics based on this. A variety of types of equations are presented, but all of them can be traced back to prototypes. For polynomial equations there is - in school - at least for quadratic equations a solution formula. Higher degree polynomial equations, exponential equations and trigonometric equations can only be solved iteratively, approximately or graphically. Chapter 4 deals with the differential calculus. It deals with the definition and basic properties of derivatives. The different rules of differentiation are used, but not all of them are proved in detail. Furthermore, the emphasis is on application problems which can be solved with differential calculus, e.g. traffic problems, packaging problems and a variety of extreme value problems. Chapter 5 deals with integral calculus. Starting with the definition of the Riemann integral, various methods of integration are discussed: partial integration, method of substitution and integration using partial fraction decompositions. Many application problems of engineering mathematics are discussed. The focus is on practical methods of calculation and the geometrical illustration of integrals. More attention is given to motivational examples and illustrations of the main ideas than to strict proofs. Chapter 6 deals with methods for solving the most important cases of the 1st and 2nd order differential equations: separable and linear 1st order equations, linear 2nd order equations with constant coefficients, characteristic polynomial, homogeneous and inhomogeneous cases, basic applications like exponential decay and harmonic oscillation. Differential equations are solved mathematically, but emphasis is also placed on developing the mathematical thinking and problem-solving skills of the students. Most basic types of ordinary differential equations are discussed along with elementary solution methods. Several application-oriented examples from classical scientific problems are discussed.

Schwierigkeitsgrad:

Einsteiger

Lehr-/Lernform:

Virtuelle Vorlesung

Interaktionsformen mit dem System/Betreuer:

E-Mail, Übungsaufgaben für Selbstlernbetrieb, Chat

Interaktionsformen mit Mitlernenden:

Chat

Kursdemo:

zur Kursdemo

Schlagworte:

Mathematics

Nutzung

Zielgruppe:

Gesundheitswissenschaften für Uni-Studierende, Naturwissenschaften für Uni-Studierende, Ing.-Wissenschaften für FH-Studierende, Naturwissenschaften für FH-Studierende

Nutzbar im Studiengang:

First-year students in all fields with a scientific basis, i.e. physics, chemistry, biology, computer science, but also business informatics, functional materials, aerospace,...

First-year students at the universities of applied sciences with a scientific-technical basis: electronics, mechanical engineering, …

Geeignet für Berufsfeld:

-

Formale Zugangsvoraussetzungen:

-

Erforderliche Vorkenntnisse:

The course is presented in MOODLE. The used program Geogebra (www.geogebra.com) is today an open source program used in almost all schools and in didactic university lectures. Knowledge of the use of both programs is one of the standard competencies of students. No other special technical requirements are necessary.

Erforderliche Vorkenntnisse bzgl. Handhabung der Lernplattform:

-

Verantwortlich

Trägerhochschule:

Uni Würzburg

Anbieter:

Prof. Dr. Hans-Stefan Siller

Autoren:

Hans-Georg Weigand, Wigand Rathmann, Boris Bittner

Betreuer:

Prof. Dr. Hans-Stefan Siller

Prüfung

1. Online-Test

Art der Prüfung:

Online-Testat

Prüfer:

Prof. Dr. Hans-Stefan Siller

Anmeldeverfahren:

–

Prüfungsanmeldefrist:

–

Prüfungsabmeldefrist:

–

Kapazität:

–

Prüfungsdatum:

–

Prüfungszeitraum:

–

Prüfungsdauer:

–

Prüfungsort:

Online

Zustündiges Prüfungsamt:

Universität Würzburg, Universität Erlangen-Nürnberg, HAW Würzburg-Schweinfurt; ggfs. Heimathochschule

Zugelassene Hilfsmittel:

–

Formale Voraussetzungen für die Prüfungsteilnahme:

–

Inhaltliche Voraussetzungen für die Prüfungsteilnahme:

–

Zertifikat:

Ja (ungraded certificate)

Anerkennung an folgenden Hochschulen:

Uni Erlangen-Nürnberg (FAU), Uni Würzburg, FH Würzburg-Schweinfurt

Sonstige Anerkennung:

not yet known

Online-Prüfungsan-/-abmeldung:

Nein

Bemerkung:

Date will be announced in the course

2. Written exam

Art der Prüfung:

schriftlicher Leistungsnachweis (Klausur)

Prüfer:

Prof. Dr. Boris Bittner

Anmeldeverfahren:

Information will be given in the course.

Prüfungsanmeldefrist:

–

Prüfungsabmeldefrist:

–

Kapazität:

–

Prüfungsdatum:

–

Prüfungszeitraum:

–

Prüfungsdauer:

90 Minuten

Prüfungsort:

–

Zustündiges Prüfungsamt:

University of Applied Sciences Würzburg-Schweinfurt

Zugelassene Hilfsmittel:

–

Formale Voraussetzungen für die Prüfungsteilnahme:

Mathematics Basics for International BA Logistics & International BA Business and Engineering.

Inhaltliche Voraussetzungen für die Prüfungsteilnahme:

–

Zertifikat:

Ja (Graded certificate)

Anerkennung an folgenden Hochschulen:

FH Würzburg-Schweinfurt

Sonstige Anerkennung:

not yet known

Online-Prüfungsan-/-abmeldung:

Nein

Bemerkung:

Date will be announced in the course.

Erforderliche Technik

Betriebssystem:

Nutzungsbedingungen

Gebühren:

Nein

Nutzungsentgelte:

für andere Personen als (reguläre) Studenten der vhb Trägerhochschulen nach Maßgabe der Benutzungs- und Entgeltordnung der vhb

Copyright:

-

Hinweise zur Nutzung:

The course is offered via Moodle at the University of Würzburg. The course offers exercises, students had to solve in a time frame of two to three weeks. The solutions will be sent in by the participants and they will be corrected by tutors. At the end of the course an exam will be written. This can be written live on site or as an online exam. This will be decided in due course.