Calculus 1C: Coordinate Systems & Infinite Series

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Обучение бесплатное
Certificate
Сертификация платная
Duration
3 месяца
О курсе

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.

    Программа
    Calculus 1C: Coordinate Systems & Infinite Series
    Master the calculus of curves and coordinate systems; approximate functions with polynomials and infinite series. Part 3 of 3.
    Что Вы изучите?
    • To compute arc length
    • Methods for parameterizing curves
    • To do calculus in polar coordinates
    • How to approximate functions with Taylor polynomials
    • To determine convergence properties of infinite series
    Лекторы
    David Jerison
    David Jerison
    Professor of Mathematics Massachusetts Institute of Technology

    David Jerison received his Ph.D. from Princeton University in 1980, and joined the mathematics faculty at MIT in 1981. In 1985, he received an A.P. Sloan Foundation Fellowship and a Presidential Young Investigator Award. In 1999 he was elected to the American Academy of Arts and Sciences. In 2004, he was selected for a Margaret MacVicar Faculty Fellowship in recognition of his teaching. In 2012, the American Mathematical Society awarded him and his collaborator Jack Lee the Bergman Prize in Complex Analysis.

    Professor Jerison's research focuses on PDEs and Fourier Analysis. He has taught single variable calculus, multivariable calculus, and differential equations at MIT several times each.

    Gigliola Staffilani
    Gigliola Staffilani
    Abby Rockefeller Mauzé Professor of Mathematics Massachusetts Institute of Technology
    Gigliola Staffilani is the Abby Rockefeller Mauzé Professor of Mathematics since 2007. She received her Ph.D. from the University of Chicago in 1995. Following faculty appointments at Stanford, Princeton, and Brown, she joined the MIT mathematics faculty in 2002. She received both a teaching award and a research fellowship while at Stanford. She received a Sloan Foundation Fellowship in 2000. In 2014 she was elected to the American Academy of Arts and Sciences. Professor Staffilani is an analyst, with a concentration on dispersive nonlinear PDEs. She has taught multivariable calculus several times at MIT, as well as differential equations.
    Jennifer French
    Jennifer French
    Lecturer & Digital Learning Scientist Massachusetts Institute of Technology
    Jen French is an MITx Digital Learning Scientist and Lecturer in the MIT math department. She earned her PhD in mathematics from MIT in 2010, with specialization in Algebraic Topology. For the last two years, she has developed videos, visual interactives, and problems providing immediate feedback using the edX platform residentially in the MIT math department to aid student learning.
    Karene Chu
    Karene Chu
    Lecturer and Research Scientist Massachusetts Institute of Technology
    Karene Chu received her Ph.D. in mathematics from the University of Toronto in 2012. Since then she has been a postdoctoral fellow first at the University of Toronto/Fields Institute, and then at MIT, with research focus on knot theory. She has taught single and multi-variable calculus, and linear algebra at the University of Toronto where she received a teaching award.
    Платформа
    EdX
    Эта платформа предоставляет все курсы бесплатно. Авторами выступают топовые университеты и корпорации, которые стараются удерживать стандарты качества. За несоблюдение дедлайнов, невыполнение домашнего задания студенты теряют баллы. Как и в других платформах, лекционные видео чередуются с практическими заданиями. Обучение проводится на английском, китайском, испанском, французском и хинди.