18.01x Single Variable Calculus

Overview

Courses

• Calculus 1A: Differentiation

  5.0 (7)

  6-10 hours a week, 41 weeks long

  View details

  How 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 modulesin this seriesare being offered as an XSeries on edX. Please visit Single Variable Calculus XSeries Program Pageto 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.

• Calculus 1B: Integration

  5.0 (1)

  6-10 hours a week, 41 weeks long

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  How 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.

• Calculus 1C: Coordinate Systems & Infinite Series

  5.0 (3)

  6-10 hours a week, 41 weeks long

  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.

  1. Changing Perspectives
     1. Parametric Equations
     2. Polar Coordinates
  2. Series and Polynomial Approximations
     1. Series and Convergence
     2. 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.