This part of engineering fundamentals is going to introduce you to Systems Engineering. I’m going to explain the basic concepts of how to describe a system in the time domain using examples to make things clearer. This story is not about modeling.

1. Abstract
2. The basic elements: P, I and D
3. Variations of basic elements
4. Summary

Abstract

To be very abstract, a system is something that gets an input and has an output. The numbers of inputs and outputs can vary so we will differentiate between a Single Input Single Output System (SISO-System) and a Multiple-Inputs Multiple-Output Systems (MIMO-System). The input is…

In this part of the engineering fundamentals series, I’m going to cover why engineers need to know their basic algorithms and why this helps to improve CAE. Three different algorithms from three different fields of application are covered with mathematical descriptions, code, pictures and examples.

1. Why engineers should know their algorithms
2. Jacobi Method
3. Heun’s Method
4. Gradient Descent
5. Summary

Why engineers should know their algorithms

Computer-Aided Engineering (CAE) is getting more and more important in modern engineering. FEM-programs, simulation tools and huge libraries are offered to the engineer who has to decide what suits his problem best he’s facing. But to make a good decision you have…

There are hundreds of different tools, apps and programs available to us when it comes to creativity and productivity tools. I’m going to present to you my Top 6 tools I currently use in university and I think are best for students. If your university provides you with a version of Microsoft Office 365 it is free to use, like the rest of the tools I’m going to present (there might be Pro-Versions of some of the tools that cost a bit).

This story starts a new series called productivity fundamentals where I’m going to present different topics wit regards…

This story will give you an introduction to how to model technical systems. It covers why modeling is so important for engineers, some basic techniques, and an example of a technical system describes via an ODE.

1. Why modeling is so important as an engineer
2. Basic techniques & math
3. A common example
4. Summary

This story starts a series called engineering fundamentals where I’m going to cover different topics from the world of engineering.

Why modeling is so important as an engineer

Just to make this clear right away: Not every engineer is modeling technical systems at his job, by far. However, in my opinion, it is a more and…

Math & Nature | An introduction to Metaheuristics

This story will cover the fundamentals of Metaheuristics and will give you an introduction to the basic concept of the Particle Swarm Optimization (PSO) algorithm.

1. What are Metaheuristics?
2. Particle Swarm Optimization
3. What is this useful for?
4. Summary

What are Metaheuristics?¹

A metaheuristic is a high-level abstraction of established sets of mathematical rules with some randomness that leads a search process to find (near)-optimal solutions to a problem.¹

Metaheuristics are used to solve optimization problems as an alternative to exact methods like Newton’s Method or Gradient Descent. Their advantage over such exact methods is their low…

This story will show you an alternative Random Search algorithm that might be useful for your Hyperparameter Tuning. I will cover the main concept behind it and give a detailed example of the algorithm.

1. What is a greedy algorithm?
2. The concept of Deep Random Search
3. Discussion

What is a greedy algorithm?

In informatics, an algorithm is used to solve problems systematically. There are many concepts on how to design an algorithm. A greedy concept is one of the most basic ones. A solution is defined stepwise and the greedy algorithm makes his decision (to solve the problem at a certain step) based on the current…

This story will give you a brief introduction to the basics of numerical integration and how it is used to solve Ordinary Differential Equations. I will cover the explicit Euler and implicit Euler method as well as Heun’s method in this story.

1. How to solve ODEs numerically
2. Explicit Euler
3. Implicit Euler
4. The combination of both Euler methods (aka Heun’s method)

How to solve ODEs numerically

Ordinary Differential Equations are not only a special set of equations in mathematics. From the perspective of an ongoing engineer, ODEs can be used to describe dynamic systems in our real world. So let’s go with an example.