 basic topological terms (metric spaces, connectedness, compactness),
 differentiation (in the multidimensional case)  in particular: Taylor expansion, curves, implicit functions theorem, inverse function theorem, extremes under constraints,
 integration (multidimensional)  in particular: Fubini's theorem, variable transformation,
 geometry of Euclidean space (especially: orthogonal transformations, projections),
 eigenvalues, diagonalisability, principal axis transformation, calculation of the Jordan normal form,
 dual space.
Module MAT1012PM2
Fundamentals of Mathematics II (for Students of Physics) (M, 13.0 LP)
Module Identification
Module Number  Module Name  CP (Effort) 

MAT1012PM2  Fundamentals of Mathematics II (for Students of Physics)  13.0 CP (390 h) 
Basedata
CP, Effort  13.0 CP = 390 h 

Position of the semester  1 Sem. in WiSe/SuSe 
Level  [2] Bachelor (Fundamentals) 
Language  [DE] German 
Module Manager  
Lecturers 
Lecturers of the department Mathematics

Area of study  [MATService] Mathematics for other Departments 
Reference course of study  [PHY82.128SG] B.Sc. Physics 
LivecycleState  [NORM] Active 
Courses
Type/SWS  Course Number  Title  Choice in ModulePart  PresenceTime / SelfStudy  SL  SL is required for exa.  PL  CP  Sem.  

6V+2U+1T  MAT1012K2  Fundamentals of Mathematics II
 P  126 h  264 h 
qUSchein
   PL1  13.0  WiSe/SuSe 
 About [MAT1012K2]: Title: "Fundamentals of Mathematics II"; PresenceTime: 126 h; SelfStudy: 264 h
 About [MAT1012K2]: The study achievement [qUSchein] proof of successful participation in the exercise classes (incl. written examination) must be obtained.
Examination achievement PL1
 Form of examination: oral examination (2030 Min.)
 Examination Frequency: each semester
Evaluation of grades
The grade of the module examination is also the module grade.
Contents
Competencies / intended learning achievements
Upon successful completion of this module, the students
 know and understand the basic concepts, propositions and methods of Linear Algebra and multidimensional Analysis; through the exercises and the tutorials they have acquired a confident, precise and independent handling of the terms, statements and methods dealt with in the lectures;
 recognise the connections between the areas of Linear Algebra and Analysis;
 are trained in analytical thinking; they are able to recognise abstract structures and to work on mathematical problems imaginatively;
 have learned, on the basis of a proof and structureoriented approach, to comprehend mathematical proofs and to independently prove or disprove mathematical statements in simple examples;
 are able to convey elementary mathematical facts; their teamwork and communication skills have been trained through exercises and tutorials.
Literature
 O. Forster: Analysis 2,
 H. Heuser: Lehrbuch der Analysis, Teil 2,
 M. Barner, F. Flohr: Analysis II,
 K. Königsberger: Analysis 2,
 G. Fischer: Lineare Algebra,
 K. Jänich: Lineare Algebra,
 H.J. Kowalsky, G.O. Michler: Lineare Algebra,
 S. Bosch: Lineare Algebra.
Materials
Further literature will be announced in the lecture(s); exercise material is provided.
Registration
Registration for the exercise classes and tutorials via the online administration system URM (https://urm.mathematik.unikl.de).
Requirements for attendance (informal)
Modules:
Requirements for attendance (formal)
Proof of successful participation in the exercise classes of "Fundamentals of Mathematics I" is prerequisite for participation in the module examination.
References to Module / Module Number [MAT1012PM2]
Course of Study  Section  Choice/Obligation 

[PHY82.128SG] B.Sc. Physics  Mathematikmodule  [P] Compulsory 