Calculus is about the very large, the very small, and how things change. The surprise is that something seemingly so abstract ends up explaining the real world. Calculus plays a starring role in the biological, physical, and social sciences. By focusing outside of the classroom, we will see examples of calculus appearing in daily life.
This course is a first and friendly introduction to calculus, suitable for someone who has never seen the subject before, or for someone who has seen some calculus but wants to review the concepts and practice applying those concepts to solve problems.
Welcome to Calculus One Welcome to Calculus! Join me on this journey through one of the great triumphs of human thought.
Functions and Limits Functions are the main star of our journey. Calculus isn't numbers: it's relationships between things, and how one thing changing affects something else.
The End of Limits People have thought about infinity for thousands of years; limits provide one way to make such ponderings precise. Continuity makes precise the idea that small changes in the input don't affect the output much.
The Beginning of Derivatives It is time to change topics, or rather, to study change itself! When we wiggle the input, the output value changes, and that ratio of output change to input change is the derivative.
Techniques of Differentiation With the product rule and the quotient rule, we can differentiate products and quotients. And since the derivative is a function, we can differentiate the derivative to get the second derivative.
Chain Rule The chain rule lets us differentiate the composition of two functions. The chain rule can be used to compute the derivative of inverse functions, too.
Derivatives of Transcendental (Trigonometric) Functions So far, we can differentiate polynomials, exponential functions, and logarithms. Let's learn how to differentiate trigonometric functions.
Derivatives in the Real World Derivatives can be used to calculate limits via l'Hôpital's rule. Given a real-world equation involving two changing quantities, differentiating yields "related rates."
Optimization In the real world, we must makes choices, and wouldn't it be great if we could make the best choice? Such optimization is made possible with calculus.
Linear Approximation Replacing the curved graph by a straight line approximation helps us to estimate values and roots.
Antidifferentiation Antidifferentiation is the process of untaking derivatives, of finding a function whose derivatives is a given function. Since it involves working backwards, antidifferentiation feels like "unbreaking a vase" and can be just as challenging.
Integration By cutting up a curved region into thin rectangles and taking a limit of the sum of the areas of those rectangles, we compute (define!) the area of a curved region.
Fundamental Theorem of Calculus Armed with the Fundamental Theorem of Calculus, evaluating a definite integral amounts to finding an antiderivative.
Substitution Rule Substitution systematizes the process of using the chain rule in reverse. Considering how often we used the chain rule when differentiating, we will often want to use it in reverse to antidifferentiate.
Techniques of Integration Integration by parts is the product rule in reverse. Integrals of powers of trigonometric functions can be evaluated.
Applications of Integration We have already used integrals to compute area; integration can also be used to compute volumes.
MOOCs stand for Massive Open Online Courses. These arefree online courses from universities around the world (eg. StanfordHarvardMIT) 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.
This is indeed an awesome course. Unlike other online courses I have taken where the better students provide the lion's share of help on the forums, in Calculus One, the staff do an excellent job of monitoring the forums to help out. Just as often they comment on the less formal side discussions as well.
And Dr Fowler is indeed an awesome educator. His frenetic enthusiasm serves well to hold the students attention for what can sometimes be a very dry subject. My hat comes off to him.
The course provides an interactive problem solving site hosted by Ohio State U where one can practice solving problems. There is also a free .pdf textbook where one can do the same.
In sum, I recommend this course without reservation to anyone interested in a first yet in-depth exposure to calculus.
Great math teacher, wonderful course materials, very helpful course staff. Best example of how an online course should be. Course provided excellent tools to study - free textbook, platform for doing exercises, great quizzes and exams.
The lectures are very good and engaging. However, MOST of the quizzes I've taken so far, the material does not match what's taught in the lectures. For example, I finished a module ("Limits in Motion") teaching how to calculate speed of a moving objects accurately by using as small of time intervals as possible. I feel confident and interested to apply the strategies and techniques I've just learned to the quiz. However, the quiz has three questions, all giving me point coordinates, and asking me to determine the y-coordinate of the point B. I really pray my future professors don't teach this way. "POP QUIZ!!!" Wow.
Uno de los mejores cursos de matemática que he llevado. El profesor es muy motivante y entretenido. Enseña el porqué de cada tema y no simplemente deja ejercicios con reglas que sin sentido. Otro aspecto positivo es que los vídeos son cortos y eso hace que uno pueda relajarse y llevarlos cuando uno quiera. No sientes que le estás dedicando mucho tiempo.
One of the best MOOC couses I have taken. Jim is a wonderful teacher and is so enthusiatic gives us the desire to learn more. calculuts was one of my difficult subjects but I completed the course without any problems. I recommend it to anyone interested.
Just starting this. Very disappointing. The first video on functions freezes. The first quiz covers material not presented in the videos. Commenters said that there were assists that appeared when you got a quiz question wrong, but none appeared.
Of course, one could say, "Well, you should already know this stuff," but teaching one thing and quizzing on another is generally regarded as horrible teaching. And a MOOC with no explanation of how quiz answers are arrived at is just stupid.
Steven Blackcompleted this course, spending 3 hours a week on it and found the course difficulty to be medium.
Jim Fowler is an amazing professor, his enthusiasm is infectious. I took this class prior to taking calculus one in university and got an A easily while other students struggled to pass. I would recommend this for class for fun or function.
Tytus Metryckicompleted this course, spending 1 hours a week on it and found the course difficulty to be easy.
This is good intro calculus course. I used it while simultaneously going through MIT OCW calculus I, which is definitely more challenging. It really helps to have exposure to different stile of teaching and sometimes different perspective.