# Online courses directory (258)

The course consists of a sampling of topics from algebraic combinatorics. The topics include the matrix-tree theorem and other applications of linear algebra, applications of commutative and exterior algebra to counting faces of simplicial complexes, and applications of algebra to tilings.

This course provides an introduction to algebraic number theory. Topics covered include dedekind domains, unique factorization of prime ideals, number fields, splitting of primes, class group, lattice methods, finiteness of the class number, Dirichlet's units theorem, local fields, ramification, discriminants.

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**Course Summary**

In this first part of Vehicle Dynamics, we illuminate the longitudinal dynamic aspects of vehicles.

**Clear and brief:** acceleration and braking.

**In Detail:** After an introduction, we will look at driving resistances and slip, explain the demand of power and limits of a car, then clarify the needs for a clutch and gears and look at the rear and front weights during acceleration and braking. The course will be finished by two applications from automotive mechatronics.

**What will I learn?**

By the end of the course you will …

- understand basic principles of accelerating and braking a car.
- know the driving resistances and their influences on vehicle dynamics.
- understand the discrepancy between demands and limits of powertrain.
- understand the necessity of gears and clutch.
- understand the correlation between braking, wheel load and recovery of energy.
- be able to calculate simple properties of a car.

**What do I have to know?**

Some basic understanding of the following subjects will help you successfully participate in this course: Algebra; Trigonometric Functions; Differential Calculus; Linear Algebra; Vectors; Coordinate Systems; Force, Torque, Equilibrium; Mass, Center of Gravity, Moment of Inertia; Method of Sections, Friction, Newton's Law, (Lagrange's Equation)

**Course structure**

**This course has a total of 12 chapters, and the topics for each chapter are the following:**

#### Chapter 1: Preliminaries

#### Chapter 2: Introduction and Rolling Resistance

#### Chapter 3: Resistances: Grading, Acceleration, Aerodynamic Drag

#### Chapter 4: Real and ideal characteristic maps

#### Chapter 5: Approximation of the ideal map: Clutch and transmission

#### Chapter 6: Driving performance and axle loads

#### Chapter 7: ABS: Anti-lock Braking System

#### Chapter 8: ACC

#### Chapter 9: Homework Solutions Chapters 1 -3

#### Chapter 10: Homework Solutions Chapter 4 - 5

#### Chapter 11: Homework Solutions Chapter 6 - 8

#### Chapter 12: Solution of the exam

**Course Summary**

In this second part of Vehicle Dynamics, we will illuminate the lateral dynamic aspects of vehicles.

**Clear and brief:** the cornering of a car.

**In Detail:** We will start with a simple single-track model and then describe the slip angle of a wheel. The slip angle results in cornering forces, which are essential for understanding lateral dynamics. After that, we will look at the dependency between longitudinal and lateral forces using Kamm’s circle and Krempel’s diagram. Then we will investigate steady state cornering, stability and the influence of different weight distributions between inner and outer side wheels of the car. The course will finish with two applications from automotive mechatronics.

**What will I learn?**

At the end of the course you will …

- understand basic principles of cornering of a car.
- know slip angle and cornering forces.
- understand the single track model.
- understand the steady state cornering, stability and the influence of different weight distribution between inner and outer side of the car.
- be able to calculate simple properties of a car.

**What do I have to know?**

Some basic understanding of the following subjects will help you successfully participate in this course:

Algebra; Trigonometric Functions; Differential Calculus; Linear Algebra; Vectors; Coordinate Systems; Force, Torque, Equilibrium; Mass, Center of Gravity, Moment of Inertia; Method of Sections, Friction, Newton's Law, (Lagrange's Equation)

**Course structure**

**This course has a total of 10 chapters, and the topics for each chapter are the following:**

#### Chapter 1: Preliminaries

#### Chapter 2: Single-Track Model

#### Chapter 3: Tyre side slip

#### Chapter 4: Steady state cornering

#### Chapter 5: Solution of linear single track model

#### Chapter 6: Stability and step steer

#### Chapter 7: Wheelload transfer

#### Chapter 8: Suspension systems

#### Chapter 9: Active lateral systems

#### Chapter 10: Solutions Homework: Part 1

#### Chapter 11: Solutions Homework: Part 2

**Course Summary**

In this third part of Vehicle Dynamics, we will illuminate the vertical dynamic aspects of vehicles. In short, we will describe the elements involved when a car drives on a bumpy or rough street.

We will start with a survey of suspensions and springs and dampers. After this, we will explain the description of rough streets and give an introduction to Fourier integrals. Next, we will take a closer look at vertical models. In the last fundamental part of the course, we will describe the conflict between driving safety and comfort. The course will be finished with two applications from automotive mechatronics.

**What will I learn?**

At the end of the course you will …

- know different kinds of suspensions, springs and dampers.
- know the description of rough and bumpy streets.
- understand the Fourier integral.
- understand the conflict between driving safety and comfort.
- be able to calculate simple properties of a car.

**What do I have to know?**

Some basic understanding of the following subjects will help you successfully participate in this course:

Algebra; Trigonometric Functions; Differential Calculus; Linear Algebra; Vectors; Coordinate Systems; Force, Torque, Equilibrium; Mass, Center of Gravity, Moment of Inertia; Method of Sections, Friction, Newton's Law, (Lagrange's Equation)

**Course structure**

**This course has a total of 11 chapters, and the topics for each chapter are the following:**