# Online courses directory (89)

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

In this course you’ll learn various statistics topics including multiple testing problem, error rates, error rate controlling procedures, false discovery rates, q-values and exploratory data analysis. We then introduce statistical modeling and how it is applied to high-throughput data. In particular, we will discuss parametric distributions, including binomial, exponential, and gamma, and describe maximum likelihood estimation. We provide several examples of how these concepts are applied in next generation sequencing and microarray data. Finally, we will discuss hierarchical models and empirical bayes along with some examples of how these are used in practice. We provide R programming examples in a way that will help make the connection between concepts and implementation.

Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.

These courses make up 2 XSeries and are self-paced:

PH525.1x: Statistics and R for the Life Sciences

PH525.3x: Statistical Inference and Modeling for High-throughput Experiments

PH525.4x: High-Dimensional Data Analysis

PH525.5x: Introduction to Bioconductor: annotation and analysis of genomes and genomic assays

PH525.6x: High-performance computing for reproducible genomics

PH525.7x: Case studies in functional genomics

This class was supported in part by NIH grant R25GM114818.

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

We will learn the basics of statistical inference in order to understand and compute p-values and confidence intervals, all while analyzing data with R. We provide R programming examples in a way that will help make the connection between concepts and implementation. Problem sets requiring R programming will be used to test understanding and ability to implement basic data analyses. We will use visualization techniques to explore new data sets and determine the most appropriate approach. We will describe robust statistical techniques as alternatives when data do not fit assumptions required by the standard approaches. By using R scripts to analyze data, you will learn the basics of conducting reproducible research.

Given the diversity in educational background of our students we have divided the series into seven parts. You can take the entire series or individual courses that interest you. If you are a statistician you should consider skipping the first two or three courses, similarly, if you are biologists you should consider skipping some of the introductory biology lectures. Note that the statistics and programming aspects of the class ramp up in difficulty relatively quickly across the first three courses. By the third course will be teaching advanced statistical concepts such as hierarchical models and by the fourth advanced software engineering skills, such as parallel computing and reproducible research concepts.

These courses make up 2 XSeries and are self-paced:

PH525.1x: Statistics and R for the Life Sciences

PH525.3x: Statistical Inference and Modeling for High-throughput Experiments

PH525.4x: High-Dimensional Data Analysis

PH525.5x: Introduction to Bioconductor: annotation and analysis of genomes and genomic assays

PH525.6x: High-performance computing for reproducible genomics

PH525.7x: Case studies in functional genomics

This class was supported in part by NIH grant R25GM114818.

HarvardX requires individuals who enroll in its courses on edX to abide by the terms of the edX honor code. HarvardX will take appropriate corrective action in response to violations of the edX honor code, which may include dismissal from the HarvardX course; revocation of any certificates received for the HarvardX course; or other remedies as circumstances warrant. No refunds will be issued in the case of corrective action for such violations. Enrollees who are taking HarvardX courses as part of another program will also be governed by the academic policies of those programs.

HarvardX pursues the science of learning. By registering as an online learner in an HX course, you will also participate in research about learning. Read our research statement to learn more.

Harvard University and HarvardX are committed to maintaining a safe and healthy educational and work environment in which no member of the community is excluded from participation in, denied the benefits of, or subjected to discrimination or harassment in our program. All members of the HarvardX community are expected to abide by Harvard policies on nondiscrimination, including sexual harassment, and the edX Terms of Service. If you have any questions or concerns, please contact harvardx@harvard.edu and/or report your experience through the edX contact form.

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.

**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:**