( ECTS credits)
Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam.
reg. data record Bachelor (180 ECTS) Physik - 2020
page 37 / 120
Mathematics 1 and 2
(16 ECTS credits)
Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam. page 38 / 120
Module title Abbreviation Mathematics 1 for Students of Physics and Nanostructure Technology 10-M-PHY1-152-m01
Module coordinator Module offered by
Dean of Studies Mathematik (Mathematics) Institute of Mathematics ECTS Method of grading Only after succ. compl. of module(s)
8 numerical grade
--Duration Module level Other prerequisites 1 semester undergraduate
--Contents
Fundamentals on numbers and functions, sequences and series, differential and integral calculus in one varia-ble, vector spaces, simple differential equations.
Intended learning outcomes
The student gets acquainted with basic concepts of mathematics. He/She learns to apply these methods to sim-ple problems in natural and engineering sciences, in particular in the fields of physics and nanostructure techno-logy, and is able to interpret the results.
Courses (type, number of weekly contact hours, language — if other than German)
V (5) + Ü (2)
Module taught in: Ü: German or English
Method of assessment (type, scope, language — if other than German, examination offered — if not every semester, information on whether module is creditable for bonus)
a) written examination (approx. 90 to 120 minutes, usually chosen) or b) oral examination of one candidate each (approx. 20 minutes) or c) oral examination in groups (groups of 2, 15 minutes per candidate)
Language of assessment: German and/or English creditable for bonus
Allocation of places
--Additional information
--Referred to in LPO I (examination regulations for teaching-degree programmes)
--Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam.
reg. data record Bachelor (180 ECTS) Physik - 2020
page 39 / 120
Module title Abbreviation Mathematics 2 for Students of Physics and Nanostructure Technology 10-M-PHY2-152-m01
Module coordinator Module offered by
Dean of Studies Mathematik (Mathematics) Institute of Mathematics ECTS Method of grading Only after succ. compl. of module(s)
8 numerical grade
--Duration Module level Other prerequisites 1 semester undergraduate
--Contents
Linear maps and systems of linear equations, matrix calculus, eigenvalue theory, differential and integral calcu-lus in several variables, differential equations, Fourier analysis.
Intended learning outcomes
The student gets acquainted with fundamental concepts of advanced mathematics. He/She learns to apply the-se methods to simple problems in natural and engineering sciences, in particular in the field of physics and na-nostructure technology, and is able to interpret the results.
Courses (type, number of weekly contact hours, language — if other than German)
V (5) + Ü (2)
Module taught in: Ü: German or English
Method of assessment (type, scope, language — if other than German, examination offered — if not every semester, information on whether module is creditable for bonus)
a) written examination (approx. 90 to 120 minutes, usually chosen) or b) oral examination of one candidate each (approx. 20 minutes) or c) oral examination in groups (groups of 2, 15 minutes per candidate)
Language of assessment: German and/or English creditable for bonus
Allocation of places
--Additional information
--Referred to in LPO I (examination regulations for teaching-degree programmes)
--Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam. page 40 / 120
Mathematics 3 and 4
(16 ECTS credits)
Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam.
reg. data record Bachelor (180 ECTS) Physik - 2020
page 41 / 120
Module title Abbreviation Mathematics 3 for Students of Physics and related Disciplines (Differential
Equations)
11-M-D-152-m01
Module coordinator Module offered by
Managing Director of the Institute of Theoretical Physics and Astrophysics
Faculty of Physics and Astronomy
ECTS Method of grading Only after succ. compl. of module(s)
8 numerical grade
--Duration Module level Other prerequisites 1 semester undergraduate
--Contents
Basics of ordinary differential equations in physics.
Ordinary differential equations and systems of differential equations.
Fundamentals of function theory.
1. Ordinary differential equations 1.1 Solution methods
1.2 Existence and uniqueness theorem 1.3 Systems of differential equations
1.4 Greens function for inhomogeneous problems 1.5 Hermitsche DGL, Legendre DGL
2. Function theory 2.1 Complex functions
2.2 Differentiation, holomorphic functions 2.3 Singularities in the complex
2.4 Complex integration and the Cauchy integral theorem 2.5 Laurent series, residual theorem, Fourier transformation
2.6 Analytical continuation, meromorphic functions, whole functions
2.7 gamma, beta, hypergeometric functions, sets of Weierstrasse and Mittag-Leffler 2.8 Differential equations in the complex, Bessel differential equation
2.9 Saddle point method
3. (quasi) linear differential equations of 1st order Intended learning outcomes
The student has basic knowledge of mathematics to understand the dynamic equations and knowledge of soluti-on methods for ordinary differential equatisoluti-ons as well as the theory of the functisoluti-ons of a complex variable and is proficient in the required computing techniques.
Courses (type, number of weekly contact hours, language — if other than German)
V (4) + Ü (2)
Module taught in: Ü: German or English
Method of assessment (type, scope, language — if other than German, examination offered — if not every semester, information on whether module is creditable for bonus)
written examination (approx. 120 minutes) Language of assessment: German and/or English Allocation of places
--Additional information
--Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam. page 42 / 120
Referred to in LPO I (examination regulations for teaching-degree programmes)
--Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam.
reg. data record Bachelor (180 ECTS) Physik - 2020
page 43 / 120
Module title Abbreviation Mathematics 4 for Students of Physics and related Disciplines (Complex
Ana-lysis)
11-M-F-152-m01
Module coordinator Module offered by
Managing Director of the Institute of Theoretical Physics and Astrophysics
Faculty of Physics and Astronomy
ECTS Method of grading Only after succ. compl. of module(s)
8 numerical grade
--Duration Module level Other prerequisites 1 semester undergraduate
--Contents
Basic knowledge of functional analysis that is required in the course Quantum Mechanics I. The definition of Hil-bert space opens up understanding of quantum mechanical states as vectors. The representation-free form of quantum mechanics and the representation as a wave function generated by basic states form an important ele-ment of the formal framework of quantum mechanics with the so-called bracket formalism by Dirac.
Fundamentals of partial differential equations in physics and systems of differential equations.
Part I: functional analysis 1.1 Linear vector spaces
1.2 Metric, standardized spaces 1.3 Linear operators
1.4 Function space, completion, Lebesgue integral, Hilbert space 1.5 Linear operators on the Hilbert space
1.6 Matrix representation of operators
1.8 The Dirac delta function and its different representations
Part II: differential equations 2. Partial differential equations
2.1 Linear partial differential equations of 2nd order 2.2 1D and 3D wave equation
2.3 Helmholtz equation and potential theory 2.4 Parabolic differential equations
Intended learning outcomes
The student has basic knowledge of mathematics and basic knowledge of Hilbert space mathematics, as well as knowledge of solution methods for partial differential equations and is proficient in the necessary computing techniques.
Courses (type, number of weekly contact hours, language — if other than German)
V (4) + Ü (2)
Module taught in: Ü: German or English
Method of assessment (type, scope, language — if other than German, examination offered — if not every semester, information on whether module is creditable for bonus)
written examination (approx. 120 minutes) Language of assessment: German and/or English Allocation of places
--Additional information
--Referred to in LPO I (examination regulations for teaching-degree programmes)
--Bachelor’s with 1 major Physics (2020) JMU Würzburg • generated 09-Nov-2021 • exam. page 44 / 120