This course provides a brisk, entertaining treatment of differential and integral calculus, with an emphasis on conceptual understanding and applications to the engineering, physical, and social sciences.
Calculus is one of the grandest achievements of human thought, explaining everything from planetary orbits to the optimal size of a city to the periodicity of a heartbeat. This brisk course covers the core ideas of single-variable Calculus with emphases on conceptual understanding and applications. The course is ideal for students beginning in the engineering, physical, and social sciences.Distinguishing features of the course include:
- the introduction and use of Taylor series and approximations from the beginning;
- a novel synthesis of discrete and continuous forms of Calculus;
- an emphasis on the conceptual over the computational; and
Learn the mathematical theory of linear differential equations and their application to systems such as the mass-spring system and other linear oscillations. Phenomena as diverse as the motion of the planets, the spread of a disease, and the oscillations of a suspension bridge are governed by differential equations. This course is an introduction to the mathematical theory of ordinary differential equations and follows a modern dynamical systems approach.
Analytic Combinatorics teaches a calculus that enables precise quantitative predictions of large combinatorial structures. This course introduces the symbolic method to derive functional relations among ordinary, exponential, and multivariate generating functions, and methods in complex analysis for deriving accurate asymptotics from the GF equations.
This course is an introduction to the finite element method as applicable to a range of problems in physics and engineering sciences. The treatment is mathematical, but only for the purpose of clarifying the formulation. The emphasis is on coding up the formulations in a modern, open-source environment that can be expanded to other applications, subsequently.
In this course, you will learn the science behind how digital images and video are made, altered, stored, and used. We will look at the vast world of digital imaging, from how computers and digital cameras form images to how digital special effects are used in Hollywood movies to how the Mars Rover was able to send photographs across millions of miles of space.
Learn how to think the way mathematicians do - a powerful cognitive process developed over thousands of years. Mathematical thinking is not the same as doing mathematics – at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself.
The purpose of this course is to review the material covered in the Fundamentals of Engineering (FE) exam to enable the student to pass it. It will be presented in modules corresponding to the FE topics, particularly those in Civil and Mechanical Engineering.
Une fonction discontinue peut-elle être solution d'une équation différentielle? Comment définir rigoureusement la masse de Dirac (une "fonction" d'intégrale un, nulle partout sauf en un point) et ses dérivées? Peut-on définir une notion de "dérivée d'ordre fractionnaire"? Cette initiation aux distributions répond à ces questions - et à bien d'autres.
Data science courses contain math—no avoiding that! This course is designed to teach learners the basic math you will need in order to be successful in almost any data science math course and was created for learners who have basic math skills but may not have taken algebra or pre-calculus. Data Science Math Skills introduces the core math that data science is built upon, with no extra complexity, introducing unfamiliar ideas and math symbols one-at-a-time.
In this course you will learn a whole lot of modern physics (classical and quantum) from basic computer programs that you will download, generalize, or write from scratch, discuss, and then hand in. Join in if you are curious (but not necessarily knowledgeable) about algorithms, and about the deep insights into science that you can obtain by the algorithmic approach.
MOOCs – Massive Open Online Courses – enable students around the world to take university courses online. This guide, by the instructors of edX’s most successful MOOC in 2013-2014, Principles of Written English (based on both enrollments and rate of completion), advises current and future students how to get the most out of their online study, covering areas such as what types of courses are offered and who offers them, what resources students need, how to register, how to work effectively with other students, how to interact with professors and staff, and how to handle assignments. This second edition offers a new chapter on how to stay motivated. This book is suitable for both native and non-native speakers of English, and is applicable to MOOC classes on any subject (and indeed, for just about any type of online study).