4.8
123 ratings
26 reviews

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 18 hours to complete

Suggested: 6-8 hours/week...

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 18 hours to complete

Suggested: 6-8 hours/week...

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
2 hours to complete

## 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 <i>discrete</i> input. These are <i>sequences</i>, and they will occupy our attention for this last segment of the course. This first module will introduce the tools and terminologies for <b>discrete calculus</b>....
4 videos (Total 53 min), 2 readings, 5 quizzes
4 videos
BONUS!5m
Differences17m
Discrete Calculus16m
Your Guide to Getting Started in this Course10m
5 practice exercises
Core Homework: Sequences14m
Core Homework: Differences12m
Challenge Homework: Differences8m
Core Homework: Discrete Calculus10m
Challenge Homework: Discrete Calculus4m
Week
2
1 hour to complete

## 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 <b>numerical analysis</b>, answering such questions as <i>"how do we approximate solutions to differential equations?"</i> and <i>"how do we approximate definite integals?"</i> Perhaps unsurprisingly, Taylor expansion plays a pivotal role in these approximations....
2 videos (Total 34 min), 1 quiz
2 videos
Numerical Integration16m
1 practice exercise
Core Homework: Numerical O.D.E.s4m
Week
3
2 hours to complete

## 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 <b>series</b>. The determination of convergence for such will occupy our attention for this module. I hope you haven't forgotten your big-O notation --- you are going to need it!...
4 videos (Total 65 min), 6 quizzes
4 videos
Convergence Tests I16m
Convergence Tests II16m
Absolute & Conditional14m
6 practice exercises
Core Homework: Infinite Series10m
Challenge Homework: Infinite Series4m
Core Homework: Convergence Tests I16m
Challenge Homework: Convergence Tests I4m
Core Homework: Convergence Tests II6m
Core Homework: Absolute & Conditional4m
Week
4
2 hours to complete

## 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. ...
4 videos (Total 59 min), 5 quizzes
4 videos
Taylor Series Redux15m
Approximation and Error17m
BONUS!9m
5 practice exercises
Core Homework: Power Series12m
Challenge Homework: Power Series8m
Core Homework: Taylor Series Redux8m
Challenge Homework: Taylor Series Redux4m
Core Homework: Approximation and Error10m
4.8
26 Reviews

### Top Reviews

By MMJan 11th 2016

This course is tricky and also excellent. I am a computer science student from germany, and it took me quite some time and effort to pass it. The course is well structured, and can be done in time.

By RBFeb 11th 2017

Feeling really great after finishing the course. Learnt a lot and gained deeper insights into the calculus.\n\nLooking forward to Multi Variable Calculus.

## Instructor

### Robert Ghrist

Professor
Mathematics and Electrical & Systems Engineering