To compute arc length
Methods for parameterizing curves
To do calculus in polar coordinates
How to approximate functions with Taylor polynomials
To determine convergence properties of infinite series
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.
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.
18.01.2x Calculus 1B: Integration