Introduction

This document is intended to help you getting ready for a Master’s Degree in Medical Engineering at the University of Applied Sciences in Upper Austria. If you come from another institution, your background is probably somewhat different from those students who have already obtained their Bachelor’s Degree in Linz.
In order to minimize the frictions with getting started, the list below should allow you to check your existing background knowledge.
If you find that your knowledge of some of the material is already a bit faded, please use your available learning materials, as well as the references provided below, to brush up your knowledge before you start your Master’s degree in Linz. This will allow you pick up new knowledge smoothly.
For each of the points below, you find some recommendations for free information on the internet, recommended literature, as well as an exercise to check your current knowledge.
We are looking forward to seeing you on our campus in Linz!

Math

Topics

• Differentiation
  product rule
  quotient Rule
  chain Rule
• Integration
  definite integral
  indefinite integral
  initial conditions
• Differentiation and integration of polynomials
• Differentiation and integration of trigonometric functions
• Definition and application of trigonometric functions (e.g. projection of a vector)
• Basic linear algebra
  scalar product (calculation + interpretation)
  vector product (calculation + interpretation)
  matrix multiplication
  vector addition and subtraction
  unit vectors
• Complex numbers
  Euler equation
  conversion between Cartesian and polar coordinates

References

• Gilbert Strang: Introduction to Linear Algebra, 6th ed
• Gilbert Strang: Calculus [free: Online and PDF]
• Anthony Croft: Mathematics for engineers (5th ed, hardcopy)
• geeksforgeeks.org/maths/maths/(free)

Computers

Topics

• File structure on the computer
• Basic file operations (generate new files and folders, zip and unzip files, ...)
• Editing TXT-files with a TXT-editor (e.g. notepad++)
• Using the command line / a terminal (cd, dir/ls, ...)
• Running programms from the command line
• Modifying environment variables (e.g. PATH)
• Showing/hiding file extensions

References

• howtogeek.com/learning-the-windows-command-line-heres-where-to-start

Python

Topics

• Basic data types, and how to work with them
  tuples
  lists
  dictionaries
  Panda DataFrames
  Numpy arrays
• Slicing data (i.e. extracting a certain range of data from e.g. an array)
• Defining and using functions
  input parameters
  return parameters
  docstrings
• Installation of new packages (from the command line)
• Using a debugger (e.g. setting and using a breakpoint)
• Concept of workspace
• Basic plotting
  to a graphics window
  to a file
  inline (in Jupyterlab or in Jupyter QtConsole)
  saving a plot
• Smoothing and differentiating data
• Finding minima/maxima of signals
• Matrix multiplication with NumPy arrays
• Saving data to a computer

References

• Python Crash Course, 3rd Edition
• learnpython.org (free)
• 7 steps to Python, and references therein (free)

Signal Analysis

Topics

• Smoothing and differentiating data: FIR- and IIR-Filters
• FFT

References

• Hands-on Signal Analysis with Python (2021)
• Short: Signal Smoothing with scipy (free)
• Detailed: Introduction to Digital Filters, by Julius O. Smith III (free, very good. Implementations with
  Matlab, not with Python)

Electronics

Topics

• Calculation of real and complex resistances, for
  serial circuits
  parallel circuits
• Use of an oscilloscope
• Basic mechanism of transistors
• Basic OPA-Circuits
• Basic Transistor-Circuits

References

• Electronics-Tutorials
• Virtual Oscilloscope

Mechanics

Topics

• Newton’s law
• Calculation of center of gravity
• Calculation of torque
• Calculation of moment of inertia
• Force projection

References

• An Introduction to Mechanics (2nd Edition), by Daniel Kleppner and Robert Kolenkow
• Wikibook: General Mechanics (free)