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Medical Photonics / Semester information / Winter term 2018/2019 / 1st semester / Module A0.1 - PreCourse "Mathematics"

Module A0.1 - PreCourse "Mathematics"

Coordinator

Prof. Dr. Herbert Gross

Lecturer

Dr. Holger Babovsky, Andreas Stark

Schedule

  • Lectures: daily from October 2nd to October 12th, 9:00 a.m. - 12:00 a.m.
    Location: SR 013a August-Bebel-Str. 4.
  • Exercises: daily from October 2nd to October 12th, 2.00 p.m. - 3.30 p.m.
    Location: SR 013a August-Bebel-Str. 4.
  • Course materials: Will be distributed during the course

Contents

Lecture Topics Exercises

1
02.10.2018

The exponential function

  • Definition and characteristics
  • Growth and decay
  • Hyperbolic Functions
  

2
04.10.2018

Complex numbers

  • Definitions and rules for calculation
  • The complex plane, polar coordinates

 

3
05.10.2018

Complex numbers II

  • Eulers Formula and de Moivre's Formula

 

4
08.10.2018

Dot and cross product

  • Repitition: Vectors, scalar Product, vector product
  • Geometrical applications
  • Physical Significance

 

 

5
09.10.2018

Differential calculus in one variable 

  • The derivation: Terms, definition and geometric meaning
  • Important limits and derivatives
  • Rules of differentiation and further derivatives
  • Implicit differentiation

 

 

6
10.10.2018

Differential calculus in two and three variables

  • Functions with two Variables
  • Partial Derivation
  • Geometrical Interpretation: Tangent plane and perpendicular vector of a plane
  • Directional derivative and gradient, Examples
  • The gradient in three dimensions

 

 

7
11.10.2018

Calculations with small sizes

  • Examples
  • Taylor series
  • Differences and differentials
  • Linear approximation and error propagation

 

 

8
12.10.2018

Integral calculus

  • the indefinite integral
  • the definite integral
  • integration techniques I: the substitution method
  • integration techniques II: partial integration