Autumn Semester 2020 takes place in a mixed form of online and classroom teaching.
Please read the published information on the individual courses carefully.

406-0252-AAL  Mathematics II

SemesterSpring Semester 2019
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.

AbstractContinuation of the topics of Mathematics I. Main focus: multivariable calculus and partial 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.
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 flow, 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, Part 2, Pearson Addison-Wesley.
- Kreyszig, E.: Advanced Engineering Mathematics, John Wiley & Sons.