# Online courses directory (5)

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

This physics course introduces the concept of tensor product states to discuss entanglement and Bell inequalities. You will learn about angular momentum and its representations. This is used to understand the spectrum of central potentials and to introduce hidden symmetries. Lastly, you will learn about the addition of angular momentum and an algebraic approach to the hydrogen atom spectrum.

This is the last of three courses offering a sophisticated view of quantum mechanics and its proper mathematical foundation.

- Part 1: Wave Mechanics
- Part 2: Quantum Dynamics
- Part 3: Entanglement and Angular Momentum

To follow this course you should have taken Part 1: Wave Mechanics, and Part 2: Quantum Dynamics.

Completing the 3-part Quantum Mechanics series will give you the necessary foundation to pursue advanced study or research at the graduate level in areas related to quantum mechanics

The series will follow MIT’s on campus 8.05, the second semester of the three-course sequence on undergraduate quantum mechanics, and will be equally rigorous. 8.05 is a signature course in MIT's physics program and a keystone in the education of physics majors.

Learner Testimonials

“*I’ve thought long and hard to come up with a better MOOC than this one (I’ve completed 25 of these things over the past 2 years) and can’t do it. 8.05x is #1 and I suspect will stay that way for some time to come.*”

“*Being an engineering student from India trying to shift to Physics, I am often faced with the requirement to study topics on my own. Very often this has led me to feel inadequate. 8.05x was the perfect opportunity for me to both gain knowledge and evaluate my understanding on a high quality international platform. It has really exceeded my expectations. Now, at the end of fifteen weeks, I feel more confident and hopefully I am more knowledgeable.*”

**FAQ**

Who can register for this course?

Unfortunately, learners from Iran, Cuba, Sudan and the Crimea region of Ukraine will not be able to register for this course at the present time. While edX has received a license from the U.S. Office of Foreign Assets Control (OFAC) to offer courses to learners from Iran and Sudan our license does not cover this course.

Separately, EdX has applied for a license to offer courses to learners in the Crimea region of Ukraine, but we are awaiting a determination from OFAC on that application. We are deeply sorry the U.S. government has determined that we have to block these learners, and we are working diligently to rectify this situation as soon as possible.

**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:**