18.01x Single Variable Calculus
Massachusetts Institute of Technology via edX XSeries
Overview
Master the calculus of derivatives, integrals, coordinate systems, and infinite series.
In this series, you will learn the mathematical notation, physical meaning, and geometric interpretation of a variety of calculus concepts. Along with the fundamental computational skills required to solve these problems, you will also gain insight into real-world applications of these mathematical ideas.
Learner Testimonials
18.01.1x
"Very detailed and comprehensive to the point where it's not possible not to understand concepts or not to be able to solve challenging problems. We are all very fortunate that Professor Jerison and his team spent the time to put together this experience for us. I suspect that it's on an ongoing effort where changes are being made to facilitate learning. It is very rewarding. It can be time-consuming, but I finally realized that to really get math, it takes this much time and effort. Third course in the sequence in at this point, the only thing I am missing is more MIT math MOOCs." - Ivan (completed this course)
18.01.2x
"Part 2 of single variable calculus course is another great MIT course. The videos, exercises and problem sets are excellent. The pace of the course accommodates everyone from students, busy working professionals, etc., Add to this generous extensions of the due date by the course staff so that maximum students can learn and complete the course. A great way to learn single variable calculus." - Dna47a (completed this course, spending 10 hours a week on it and found the course difficulty to be medium)
18.01.3x
"Another excellent MIT course. The videos, exercises and the problem sets are too good. Add to all this a lively discussion forum where the staff and TA's are always there to help you out." - Dna47a (completed this course)
Syllabus
Course 1: Calculus 1A: Differentiation
Discover the derivative—what it is, how to compute it, and when to apply it in solving real world problems. Part 1 of 3.
Course 2: Calculus 1B: Integration
Discover the integral—what it is and how to compute it. See how to use calculus to model real world phenomena. Part 2 of 3.
Course 3: Calculus 1C: Coordinate Systems & Infinite Series
Master the calculus of curves and coordinate systems—approximate functions with polynomials and infinite series. Part 3 of 3.
Courses
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7 Reviews
13 weeks long, 6-10 hours a week
View detailsHow does the final velocity on a zip line change when the starting point is raised or lowered by a matter of centimeters? What is the accuracy of a GPS position measurement? How fast should an airplane travel to minimize fuel consumption? The answers to all of these questions involve the derivative.
But what is the derivative? You will learn its mathematical notation, physical meaning, geometric interpretation, and be able to move fluently between these representations of the derivative. You will discover how to differentiate any function you can think up, and develop a powerful intuition to be able to sketch the graph of many functions. You will make linear and quadratic approximations of functions to simplify computations and gain intuition for system behavior. You will learn to maximize and minimize functions to optimize properties like cost, efficiency, energy, and power.
The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.
Learn more about our High School and AP* Exam Preparation Courses
This course was funded in part by the Wertheimer Fund.
*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
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1 Reviews
15 weeks long, 6-10 hours a week
View detailsHow long should the handle of your spoon be so that your fingers do not burn while mixing chocolate fondue? Can you find a shape that has finite volume, but infinite surface area? How does the weight of the rider change the trajectory of a zip line ride? These and many other questions can be answered by harnessing the power of the integral.
But what is an integral? You will learn to interpret it geometrically as an area under a graph, and discover its connection to the derivative. You will encounter functions that you cannot integrate without a computer and develop a big bag of tricks to attack the functions that you can integrate by hand. The integral is vital in engineering design, scientific analysis, probability and statistics. You will use integrals to find centers of mass, the stress on a beam during construction, the power exerted by a motor, and the distance traveled by a rocket.
The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.
This course, in combination with Part 1, covers the AP* Calculus AB curriculum.
This course, in combination with Parts 1 and 3, covers the AP* Calculus BC curriculum.
[Learn more about our High School and AP* Exam Preparation Courses
](http://www.edx.org/high-school-initiative)This course was funded in part by the Wertheimer Fund.
*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
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3 Reviews
13 weeks long, 6-10 hours a week
View details
How did Newton describe the orbits of the planets? To do this, he created calculus. But he used a different coordinate system more appropriate for planetary motion. We will learn to shift our perspective to do calculus with parameterized curves and polar coordinates. And then we will dive deep into exploring the infinite to gain a deeper understanding and powerful descriptions of functions.How does a computer make accurate computations? Absolute precision does not exist in the real world, and computers cannot handle infinitesimals or infinity. Fortunately, just as we approximate numbers using the decimal system, we can approximate functions using series of much simpler functions. These approximations provide a powerful framework for scientific computing and still give highly accurate results. They allow us to solve all sorts of engineering problems based on models of our world represented in the language of calculus.
- Changing Perspectives
- Parametric Equations
- Polar Coordinates
- Series and Polynomial Approximations
- Series and Convergence
- Taylor Series and Power Series
The three modules in this series are being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Page to learn more and to enroll in the modules.
This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.
Learn more about our High School and AP* Exam Preparation Courses
This course was funded in part by the Wertheimer Fund.
*Advanced Placement and AP are registered trademarks of the College Board, which was not involved in the production of, and does not endorse, these offerings.
- Changing Perspectives
Taught by
Gigliola Staffilani, Karene Chu, Jennifer French, Stephen Wang and David Jerison
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