How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions. How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus. Changing Perspectives Parametric Equations Polar Coordinates Series and Polynomial Approximations Series and Convergence Taylor Series and Power Series The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules. This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum. Learn more about our High School and AP* Exam Preparation Courses This course was funded in part by the Wertheimer Fund. *Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
An excellent online course offered by edX: how it works
edX courses consist of weekly learning sequences. Each learning sequence is composed of short videos interspersed with interactive learning exercises, where students can immediately practise the concepts from the videos. The courses often include tutorial videos that are similar to small on-campus discussion groups, an online textbook, and an online discussion forum where students can post and review questions and comments to each other and teaching assistants. Where applicable, online laboratories are incorporated into the course.
edX offers certificates of successful completion and some courses are credit-eligible. Whether or not a college or university offers credit for an online course is within the sole discretion of the school. edX offers a variety of ways to take courses, including verified courses where students have the option to audit the course (no cost) or to work toward an edX Verified Certificate (fees vary by course). edX also offers XSeries Certificates for completion of a bundled set of two to seven verified courses in a single subject (cost varies depending on the courses).
An edX learning programme under Other Experiences
