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Go to class

Single Variable Calculus

University of Pennsylvania

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.

Go to class
  • Provider: University of Pennsylvania
  • Cost: FREE (7 days trail)
  • Effort: Approx. 19 hours to complete
  • Duration: 6-8 hours/week
  • Language: English

Syllabus

  • 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 u003Ciu003Ediscreteu003C/iu003E input. These are u003Ciu003Esequencesu003C/iu003E, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for u003Cbu003Ediscrete calculusu003C/bu003E.
  • 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 u003Cbu003Enumerical analysisu003C/bu003E, answering such questions as u003Ciu003E
  • Series and Convergence Tests
  • In
  • 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 sense of what we've been doing when we Talyor-expand. This module will cover power series in general, from we which specify to our beloved Taylor series.
  • 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.