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
This class presents the fundamental probability and statistical concepts used in elementary data analysis. It will be taught at an introductory level for students with junior or senior college-level mathematical training including a working knowledge of calculus. A small amount of linear algebra and programming are useful for the class, but not required.
¿Por qué las grúas no se vuelcan al levantar grandes pesos? ¿por qué las mesas sólo necesitan tres patas (no alineadas) para apoyarse? Este curso te guiará paso a paso en los conocimientos básicos para entender el equilibrio de estructuras simples.
Discrete mathematics forms the mathematical foundation of computer and information science. It is also a fascinating subject in itself. Learners will become familiar with a broad range of mathematical objects like sets, functions, relations, graphs, that are omnipresent in computer science. Perhaps more importantly, they will reach a certain level of mathematical maturity - being able to understand formal statements and their proofs; coming up with rigorous proofs themselves; and coming up with interesting results.
Control of Mobile Robots is a course that focuses on the application of modern control theory to the problem of making robots move around in safe and effective ways. The structure of this class is somewhat unusual since it involves many moving parts - to do robotics right, one has to go from basic theory all the way to an actual robot moving around in the real world, which is the challenge we have set out to address through the different pieces in the course.
Enumerative combinatorics deals with finite sets and their cardinalities. In other words, a typical problem of enumerative combinatorics is to find the number of ways a certain pattern can be formed. In the first part of our course we will be dealing with elementary combinatorial objects and notions: permutations, combinations, compositions, Fibonacci and Catalan numbers etc. In the second part of the course we introduce the notion of generating functions and use it to study recurrence relations and partition numbers.
Este curso provee al estudiante con conceptos y herramientas matemáticas para modelar problemas en física, que al aplicar podrá enfrentar con éxito los cursos de física universitarios. Así pues, la filosofía de este curso consiste en cubrir temas conceptuales relativos a la Física y desarrollar tu capacidad de aprender y aplicarlos en tu vida profesional.
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.
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).