Course Mathematics 1 Kunz

Responsible: Prof. Dr. Dietmar Kunz

Course

Meets requirements of following modules(MID)

in active programs
- Ba MT2012 MA1

Course Organization

Version
created	2011-11-09
VID	1
valid from	WS 2012/13
valid to

Course identifiers
Long name	Mathematics 1 Kunz
CID	F07_MA1_Kunz
CEID (exam identifier)

Contact hours per week (SWS)
Lecture	5
Exercise (unsplit)
Exercise (split)	2
Lab
Project
Seminar
Tutorial(voluntary)	2

Total contact hours
Lecture	75
Exercise (unsplit)
Exercise (split)	30
Lab
Project
Seminar
Tutorial (voluntary)	30

Max. capacity
Exercise (unsplit)
Exercise (split)	40
Lab
Project
Seminar

Total effort (hours): 300

Instruction language

German

Study Level

undergraduate

Prerequisites

tangible school knowledge

Textbooks, Recommended Reading

Fetzer/Frankel: Mathematik
Papula: Mathematik

Instructors

Prof. Dr. Dietmar Kunz
Prof. Dr. Stefan Grünvogel

Supporting Scientific Staff

Transcipt Entry

Mathematics 1

Assessment

Type
wE	if directly following course: 30% midterm exam, 70% concluding written exam
wE	if not directly following course: 100%

Total effort [hours]
wE	10

Frequency: 2/year

Course components

Lecture/Exercise

Objectives

basics
- statements
- sets
- natural numbers
  - factorial
  - binomial theorem
  - mathematical induction
- real numbers
  - modulus
  - (in)equalities
- functions
  - monotonous
  - bounded
  - symmetry
  - linear adaption of axes
elementary functions
- algebraic functions
  - division of polynomials
  - Horner's method
  - partial fraction decomposition
- transcendental functions
  - trigonometric functions
  - exp and log
geometry
- coordinate systems
analysis
- convergence, divergence
  - sequences
  - functions
  - continuity
complex numbers
linear algebra
- vectors
  - linear (in)dependence
  - scalar product
    - angle between vectors
    - norm
    - orthogonal decomposition
  - cross product
    - iterated cross products
    - angle between planes
  - spherical angle, spherical triangles
- matrices
  - linear equation systems
  - Gaussian elimination
  - inversion
  - determinants
  - orthogonal matrices
  - homogeneous coordinates
  - eigenvalues, -vectors

Acquired Skills

solve exercises concerning
- basics
  - statements
  - sets
  - natural numbers
    - factorial
    - binomial theorem
    - mathematical induction
  - real numbers
    - modulus
    - (in)equalities
  - functions
    - monotonous
    - bounded
    - symmetry
    - linear adaption of axes
- elementary functions
  - algebraic functions
    - division of polynomials
    - Horner's method
    - partial fraction decomposition
  - transcendental functions
    - trigonometric functions
    - exp and log
- geometry
  - coordinate systems
- analysis
  - convergence, divergence
    - sequences
    - functions
    - continuity
- complex numbers
- linear algebra
  - vectors
    - linear (in)dependence
    - scalar product
      - angle between vectors
      - norm
      - orthogonal decomposition
    - cross product
      - iterated cross products
      - angle between planes
    - spherical angle, spherical triangles
  - matrices
    - linear equation systems
    - Gaussian elimination
    - inversion
    - determinants
    - orthogonal matrices
    - homogeneous coordinates
    - eigenvalues, -vectors

Operational Competences

solve application-related problems

Additional Component Assessment

Type
wE	written midterm exam about 8 weeks after start
fPS	exrcises during lecture and as home work

Contribution to course grade
wE	30% of the points of concluding assesssment
fPS	prerequisite to course exam

Frequency: 1/year

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