Single Variable Calculus
date_range Starts on January 28, 2019
event_note End date March 11, 2019
list 5 sequences
assignment Level : Introductive
chat_bubble_outline Language : English
card_giftcard 240 points
Want to share this course in your company?
My Mooc
For Business
Users' reviews
-
starstarstarstarstar

Key informations

credit_card Free access
verified_user Fee-based Certificate
timer 30 hours in total

About the content

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: 1) the introduction and use of Taylor series and approximations from the beginning; 2) a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4) a clear, dynamic, unified approach. In this fifth part--part five of five--we cover a calculus for sequences, numerical methods, series and convergence tests, power and Taylor series, and conclude the course with a final exam. Learners in this course can earn a certificate in the series by signing up for Coursera's verified certificate program and passing the series' final exam.

more_horiz Read more
more_horiz Read less
dns

Syllabus

  • Week 1 - A Calculus for Sequences
    It's time to redo calculus! Previously, all the calculus we have done is meant for functions with a continuous input and a continuous output. This time, we are going to retool calculus for functions with a discrete input. These are sequences, and...
  • Week 2 - Introduction to Numerical Methods
    That first module might have seemed a little...strange. It was! In this module, however, we will put that strangeness to good use, by giving a very brief introduction to the vast subjects of numerical analysis, answering such questions as "how do we ...
  • Week 3 - Series and Convergence Tests
    In "ordinary" calculus, we have seen the importance (and challenge!) of improper integrals over unbounded domains. Within discrete calculus, this converts to the problem of infinite sums, or series. The determination of convergence for such will occupy ...
  • Week 4 - Power and Taylor Series
    This course began with an exploration of Taylor series -- an exploration that was, sadly, not as rigorous as one would like. Now that we have at our disposal all the tests and tools of discrete and continuous calculus, we can finally close the loop and make se...
  • Week 5 - Concluding Single Variable Calculus
    Are we at the end? Yes, yes, we are. Standing on top of a high peak, looking back down on all that we have climbed together. Let's take one last look down and prepare for what lies above.
record_voice_over

Intructors

Robert Ghrist
Professor
Mathematics and Electrical & Systems Engineering

store

Content designer

The University of Pennsylvania (commonly referred to as Penn) is a private university, located in Philadelphia, Pennsylvania, United States. A member of the Ivy League, Penn is the fourth-oldest institution of higher education in the United States, and considers itself to be the first university in the United States with both undergraduate and graduate studies.
assistant

Platform

Coursera is a digital company offering massive open online course founded by computer teachers Andrew Ng and Daphne Koller Stanford University, located in Mountain View, California. 

Coursera works with top universities and organizations to make some of their courses available online, and offers courses in many subjects, including: physics, engineering, humanities, medicine, biology, social sciences, mathematics, business, computer science, digital marketing, data science, and other subjects.

You are the designer of this MOOC?
What is your opinion on this resource ?
Content
0/5
Platform
0/5
Animation
0/5