# Calculus 1C: Coordinate Systems & Infinite Series

## David Jerison, Gigliola Staffilani, Jennifer French, Karene Chu, MITx

Master the calculus of curves and coordinate systems; approximate functions with polynomials and infinite series. Part 3 of 3.

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

This course, in combination with Parts 1 and 2, covers the AP* Calculus BC curriculum.

Calculus 1A: Differentiation

Calculus 1B: Integration

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.

### What will you learn

• 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

Dates:
• 26 February 2020
Course properties:
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• Language: English

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