406-0252-AAL Mathematics II
| Semester | Spring Semester 2016 |
| Lecturers | A. Cannas da Silva |
| Periodicity | every semester recurring course |
| Language of instruction | English |
| Comment | Enrolment 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. |
| Abstract | Continuation of the topics of Mathematics I. Main focus: multivariable calculus and partial differential equations. |
| Learning objective | 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. |
| 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. |