Medical Photonics / Semester information / Winter term 2022/2023 / 1st semester / Module A0.1 - PreCourse "Mathematics"

# Module A0.1 - PreCourse "Mathematics"

**Coordinator**

Prof. Dr. Christian Franke

**Lecturer**

Dr. Holger Babovsky

**Schedule**

- Lectures: online videos that can be found on this page
- Exercises: daily from October 10th to October 14th
**Start: October 11th, at 09:00 a.m.**(August-Bebel-Straße 4 - SR 117)

Please note: The part in presence of the pre-course in Mathematics starts on Tuesday October 11th. In the meantime, please watch the videos on the exponential function and on complex numbers and try to solve both the excercises.

## Contents

## The Exponential Function

In this section, you will learn

- the
*Definition*and some*Characteristics*of the Exponential Function, - how
*Growth*and*Decay*can be represented mathematically and - what the
*Hyperbolic Functions*are. - In every chapter, you will also see various
*examples*helping you to apply the methods taught in that section.

Videos - To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:

Series 1

Please note that you will be forwarded to an external page that might collect some data (there the corresponding privacy statement of the provider will be valid).

## Complex Numbers

- In the second chapter, you will learn some
*Definitions*and*Rules for Calculation*with Complex Numbers, - to use a
*Graphic Representation*of Complex Numbers and in that context you will learn to know the widely used term*Polar Coordinates*and see how we can apply this with Complex Numbers and - you will learn the definitions of
*Eulers Formula*and of*de Moivre's Formula* - As in the previous chapter, you will also see various examples helping you to apply the methods taught in that section

Videos - To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:

Series 2

Please note that you will be forwarded to an external page that might collect some data (there the corresponding privacy statement of the provider will be valid).

## Vectors

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

- To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:

Series 3

## Differentiation in One Variable

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

- To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:

Series 4

## Differentiation in Two or 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

- To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:

Series 5

## Calculations with small Numbers

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

- To give you the possibility to apply the content learned in the videos, you should try to solve the following series of exercices:

Series 6