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Intro

Coursera: Calculus: Single Variable

 with  Robert Ghrist
Class Central Course Rank
#2 in Subjects > Mathematics > Calculus

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:

  • the introduction and use of Taylor series and approximations from the beginning;
  • a novel synthesis of discrete and continuous forms of Calculus;
  • an emphasis on the conceptual over the computational; and
  • a clear, dynamic, unified approach.

THE COURSE CERTIFICATE OPTION

By signing up and paying a nominal fee (financial aid can be provided), you'll be eligible to earn a Course Certificate in this course, including a higher level of identity verification to your Coursera coursework. For each assignment, your identity is confirmed through your photo and unique typing pattern. If you earn a Course Certificate, you will also be given a personal URL through which your course records can be shared with employers and educational institutions.


THE COLLEGE CREDIT RECOMMENDATION OPTION

Note: The following only applies to sessions starting on September 8th, 2014, and prior. This Calculus course has been evaluated and recommended by the American Council on Education’s College Credit Recommendation Service (ACE CREDIT) for college credit so you can get a head start on your college education. More than 2,000 higher education institutions consider ACE credit recommendations for transfer to degree programs. If you add this option to sessions starting on or prior to September 8th, 2014, towards the end of the course, you will take an online proctored exam which will be combined with your coursework to determine your eligibility for college credit recommendation.

Syllabus

The course is divided into five "chapters":

CHAPTER 1: Functions
After a brief review of the basics, we will dive into Taylor series as a way of working with and approximating complicated functions. The chapter will use a series-based approach to understanding limits and asymptotics.

CHAPTER 2: Differentiation
Though you already know how to differentiate some functions, you may not know what differentiation means. This chapter will emphasize conceptual understanding and applications of derivatives.

CHAPTER 3: Integration
We will use the indefinite integral (an anti-derivative) as a motivation to look at differential equations in applications ranging from population models to linguistics to coupled oscillators. Techniques of integration up to and including computer-assisted methods will lead to Riemann sums and the definite integral.

CHAPTER 4: Applications
We will get busy in this chapter with applications of the definite integral to problems in geometry, physics, economics, biology, probability, and more. You will learn how to solve a wide array of problems using a consistent conceptual approach.

CHAPTER 5: Discretization
Having covered Calculus for functions with a single real input and a single real output, we turn to functions with a discrete input and a real output: sequences. We will re-develop all of Calculus (limits, derivatives, integrals, differential equations) in this new context, and return to the beginning of the course with a deeper consideration of Taylor series.
18 Student
reviews
Cost Free Online Course (Audit)
Pace Finished
Subject Calculus
Provider Coursera
Language English
Certificates Certificate Available
Hours 10-12 hours a week
Calendar
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FAQ View All
What are MOOCs?
MOOCs stand for Massive Open Online Courses. These are free online courses from universities around the world (eg. Stanford Harvard MIT) offered to anyone with an internet connection.
How do I register?
To register for a course, click on "Go to Class" button on the course page. This will take you to the providers website where you can register for the course.
How do these MOOCs or free online courses work?
MOOCs are designed for an online audience, teaching primarily through short (5-20 min.) pre recorded video lectures, that you watch on weekly schedule when convenient for you.  They also have student discussion forums, homework/assignments, and online quizzes or exams.

18 reviews for Coursera's Calculus: Single Variable

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12 out of 12 people found the following review useful
3 years ago
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Anonymous completed this course.
I've completed several MOOC's and this was definitely the best. Another reviewer has already commented on the fact that Professor Ghrist designed this course specifically for the MOOC platform, with lots of great animations that help illustrate the concepts. I will also add that Professor Ghrist actively monitors the f Read More
I've completed several MOOC's and this was definitely the best. Another reviewer has already commented on the fact that Professor Ghrist designed this course specifically for the MOOC platform, with lots of great animations that help illustrate the concepts. I will also add that Professor Ghrist actively monitors the forums (more than any other online professor I've seen) and very frequently takes the time to respond to his students. Even if it's only to offer encouragement for students expressing frustration. This class really demonstrates the beauty of a MOOC done right.
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5 out of 5 people found the following review useful
3 years ago
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Matt completed this course.
Robert Ghrist produced the most beautiful course I've seen on Coursera. It is a single variable calculus course designed for those who have already seen calculus at some level. The production quality of the video lectures is second to none. They were designed specifically for the Coursera course and they display how e Read More
Robert Ghrist produced the most beautiful course I've seen on Coursera. It is a single variable calculus course designed for those who have already seen calculus at some level.

The production quality of the video lectures is second to none. They were designed specifically for the Coursera course and they display how effective a mooc can be in the hands of a great teacher like Professor Ghrist. The course is split into five separate chapters: function, differentiation, integrations, applications, and discretization with a grand total of 53 lectures (54 if you count the introduction). The videos average about 15 minutes of length and EVERY video is followed by a problem set of roughly 10 problems. In other words, by the time you complete this course you will have done over 500 problems, not including the chapter tests and final exam.
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2 out of 3 people found the following review useful
4 years ago
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Anonymous completed this course.
This is a long course of currently 14 weeks, covering functions, Taylor series, differentiation, integration, limits, convergence, sums and more. By the excellent presentation of the course (course-wiki, videos and fora) I improved in all of it's topics. Because of the professor's clear articulation, the videos were a Read More
This is a long course of currently 14 weeks, covering functions, Taylor series, differentiation, integration, limits, convergence, sums and more. By the excellent presentation of the course (course-wiki, videos and fora) I improved in all of it's topics.

Because of the professor's clear articulation, the videos were acoustical very good understandable.

The nice animations made them also substantial clear.

Reading the course-wiki is enjoyable, too. Additional to the theory, the chapters contain examples with solutions to test your knowledge.

The homeworks were designated to help each other to understand the topics. As they were not graded, we discussed them in the fora, using LaTeX, which was fun.

To get a certificate, it was necessary to achieve sufficient points in quizzes and a final exam. It was a tough course, but really worth while.
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3 out of 3 people found the following review useful
3 years ago
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Bart completed this course.
I am in awe. Robert Ghrist mentioned in the forum he put in 18 months of solid work into this course and it shows. There are many ways to present calculus and his way is not the easiest route, but I believe it has many advantages over the other methods I've seen. Ghrist has a consistent way of explaining the material. Read More
I am in awe. Robert Ghrist mentioned in the forum he put in 18 months of solid work into this course and it shows. There are many ways to present calculus and his way is not the easiest route, but I believe it has many advantages over the other methods I've seen. Ghrist has a consistent way of explaining the material. And the lectures are a real joy. Colourful formula's dance across the screen with helpful animations. There are enough good examples. The fora are active and helpful. In most topics there are a few interesting bonus material video's which make the course less dry.

It does take some self discipline to actually learn all the material by heart and to do enough homework to prepare for the next quiz.
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1 out of 1 people found the following review useful
10 months ago
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Anonymous completed this course.
I've taken many MOOCs and this is by far the most well presented. Prof Ghrist clearly invested a huge amount of time and effort to put this together. It's also a somewhat different teaching approach so it's interesting even if you've already taken calculus before.

Note that this course has now been split into 5 smaller courses but the content is the same.
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1 out of 1 people found the following review useful
3 years ago
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Anonymous completed this course.
it is great.... the best thing is that it takes effort to explain the basic concept from depth. It is very important for people who need to learn the basic calculus in the short time. Professor G. also is really very good.. his way of teaching is very attractive and interesting. I want to thank him specially and also to University of Pennsylvania.
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1 out of 1 people found the following review useful
2 years ago
Amedeo Nannini completed this course, spending 6 hours a week on it and found the course difficulty to be medium.
The best course on Calculus Single Variable I have ever followed. Robert Ghrist is so nice and clever while explaining difficult concept. Better you have some prior knowledge of the stuff to deeply learn from this course. Not to be miss if you wish a beautiful learning experience on calculus.
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10 months ago
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Anonymous partially completed this course.
I am nearly finished with the fifth month. Prof G covers material very quickly. The quizzes near the end of the course include quiz questions that require getting 10 - 16 answers correct within a question in order to score that question correctly. To get a passing grade on one of these quizzes you may have to answer Read More
I am nearly finished with the fifth month. Prof G covers material very quickly. The quizzes near the end of the course include quiz questions that require getting 10 - 16 answers correct within a question in order to score that question correctly. To get a passing grade on one of these quizzes you may have to answer 20 questions correctly - miss one or two and you fail the quiz. I find this to be a diabolical and distinctly unhelpful way to learn the material. Still, very good course. Very challenging.
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3 years ago
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Anonymous completed this course.
This is definitely one of the most exciting courses around. Though accessible for beginners (like myself), it presents the material in a way that makes you curious and eager to dig deeper. And this is indeed the primary goal.
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2 years ago
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Anonymous completed this course.
I agree with everything that has been said above. Professor Ghrist is a great teacher. I enjoyed the course very much
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0 out of 2 people found the following review useful
2 years ago
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Anonymous partially completed this course.
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0 out of 1 people found the following review useful
10 months ago
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Amar Doshi audited this course.
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7 months ago
Mark Thompson partially completed this course.
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11 months ago
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Francisco Javier Jiménez completed this course.
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a year ago
Colin Khein completed this course.
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2 years ago
Nitin is taking this course right now.
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