Calculus 1C: Coordinate Systems & Infinite Series from edX

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.

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What you'll 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

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Enhances understanding and describes functions profoundly with the help of infinite exploration

Builds a strong foundation for learners in single variable calculus

Develops professional skills and deep expertise in single variable calculus

Introduces parameterized curves and polar coordinates, which are essential concepts in calculus

Emphasizes practical applications of calculus in scientific computing, making it highly relevant to learners pursuing careers in STEM fields

Reviews summary

Informative course in coordinate systems

This course offers a good introduction to coordinate systems and infinite series. Students find that the videos help to present the material clearly. The practice exercises and problem sets provide additional opportunities to apply knowledge.

Videos present material well.

"Another excellent MIT course. The videos, exercises and the problem sets are too good."

Discussion forum is excellent.

"Add to all this a lively discussion forum where the staff and TA's are always there to help you out."

Career center

Learners who complete Calculus 1C: Coordinate Systems & Infinite Series will develop knowledge and skills that may be useful to these careers:

Computer Scientist

Computer Scientists design and develop computer software and systems. They use their knowledge of calculus to analyze the performance of algorithms and to develop new and improved algorithms. This course may be useful for computer scientists who need to understand the mathematical principles behind computer science.

See salaries and explore the career path for Computer Scientist

Biostatistician

Biostatisticians use statistical methods to analyze and interpret data from biological and medical studies. They may work in academia, industry, or government, and they use their skills to help researchers understand the causes and treatments of diseases, and to develop new drugs and treatments. This course may be useful for biostatisticians who need to understand the mathematical principles behind statistical methods.

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Physicist

Physicists study the fundamental laws of nature. They use their knowledge of calculus to analyze physical phenomena and to develop new and improved theories of physics. This course may be useful for physicists who need to understand the mathematical principles behind physical models.

See salaries and explore the career path for Physicist

Data Scientist

Data Scientists use statistical and computational methods to analyze and interpret data. They may work in academia, industry, or government, and they use their skills to help businesses and organizations make better decisions. This course may be useful for data scientists who need to understand the mathematical principles behind statistical methods.

See salaries and explore the career path for Data Scientist

Economist

Economists study the production, distribution, and consumption of goods and services. They use their knowledge of calculus to analyze economic models and to develop new and improved policies. This course may be useful for economists who need to understand the mathematical principles behind economic models.

See salaries and explore the career path for Economist

Petroleum Engineer

Petroleum Engineers design and develop methods for extracting oil and gas from the Earth. They use their knowledge of calculus to analyze the flow of oil and gas through reservoirs and to develop new and improved methods for extracting oil and gas. This course may be useful for petroleum engineers who need to understand the mathematical principles behind petroleum engineering models.

See salaries and explore the career path for Petroleum Engineer

Civil Engineer

Civil Engineers design and build infrastructure, such as bridges, roads, and buildings. They use their knowledge of calculus to analyze the forces and stresses that act on these structures, and to develop new and improved designs. This course in particular may be useful in areas such as structural analysis and geotechnical engineering.

See salaries and explore the career path for Civil Engineer

Nuclear Engineer

Nuclear Engineers design and operate nuclear power plants. They use their knowledge of calculus to analyze the nuclear reactions that take place in nuclear reactors, and to develop new and improved designs for nuclear power plants. This course may be useful for nuclear engineers who need to understand the mathematical principles behind nuclear engineering models.

See salaries and explore the career path for Nuclear Engineer

Aerospace Engineer

Aerospace Engineers design and develop aircraft, missiles, spacecraft, and other related systems. They use their knowledge of calculus to analyze the forces and stresses that act on these vehicles, and to develop new and improved designs. This course in particular may be useful in areas such as computational fluid dynamics and trajectory optimization.

See salaries and explore the career path for Aerospace Engineer

Electrical Engineer

Electrical Engineers design and develop electrical systems, such as power plants, electrical grids, and electronic devices. They use their knowledge of calculus to analyze the flow of electricity and to develop new and improved designs. This course in particular may be useful in areas such as power systems analysis and control systems.

See salaries and explore the career path for Electrical Engineer

Industrial Engineer

Industrial Engineers design and improve industrial processes. They use their knowledge of calculus to analyze the efficiency of production lines and to develop new and improved methods for producing goods and services. This course may be useful for industrial engineers who need to understand the mathematical principles behind industrial engineering models.

See salaries and explore the career path for Industrial Engineer

Geologist

Geologists study the Earth's physical structure and history. They use their knowledge of calculus to analyze geological data and to develop new and improved models of the Earth's systems. This course may be useful for geologists who need to understand the mathematical principles behind geological models.

See salaries and explore the career path for Geologist

Financial Analyst

Financial Analysts use financial data to make investment recommendations. They use their knowledge of calculus to analyze financial models and to develop new and improved investment strategies. This course may be useful for financial analysts who need to understand the mathematical principles behind financial models.

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Mechanical Engineer

Mechanical Engineers design and build machines, such as engines, turbines, and robots. They use their knowledge of calculus to analyze the forces and stresses that act on these machines, and to develop new and improved designs. This course in particular may be useful in areas such as solid mechanics and fluid mechanics.

See salaries and explore the career path for Mechanical Engineer

Materials Scientist

Materials Scientists study the properties of materials and develop new and improved materials for use in a wide variety of applications. They use their knowledge of calculus to analyze the mechanical, electrical, and thermal properties of materials and to develop new and improved materials. This course may be useful for materials scientists who need to understand the mathematical principles behind materials science models.

See salaries and explore the career path for Materials Scientist

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Calculus 1C

Coordinate Systems & Infinite Series

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Informative course in coordinate systems

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