Calculus 1A: Differentiation from edX

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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 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.

What you'll learn

How to evaluate limits graphically and numerically
The physical meaning, and geometric interpretation of the derivative
To calculate the derivative of any function
To sketch many functions by hand
To make linear and quadratic approximations of functions
To apply derivatives to maximize and minimize functions and find related rates

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Suitable for students in high school or preparing for the AP* Exam

Emphasizes the physical meaning and geometric interpretation of the derivative

Provides a strong foundation for further studies in mathematics

Reviews summary

Excellent calculus course

Calculus 1A: Differentiation has received 5 reviews, all of which are 5-star reviews. Students are highly positive, reporting that the course materials are "excellent" and "very detailed and comprehensive". Overall, Calculus 1A: Differentiation appears to be a high-quality course that students find valuable.

Highly rated by students.

"An excellent course from MIT. Can't describe it but you have to take it to experience how good the course materials are."

Comprehensive course materials.

"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."

Career center

Learners who complete Calculus 1A: Differentiation will develop knowledge and skills that may be useful to these careers:

Aerospace Engineer

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Physicist

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Chemical Engineer

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Mechanical Engineer

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Geologist

Geologists study the Earth's physical structure and history. They work on a wide range of projects, from oil exploration to environmental remediation. Calculus 1A provides Geologists with a solid foundation in calculus, which is essential for understanding the mathematical models used to analyze geological data. The course also helps students develop problem-solving skills and critical thinking abilities, which are essential for success in this field. Taking this course is highly recommended for anyone interested in a career in geology.

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Civil Engineer

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Electrical Engineer

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Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. They must have a strong foundation in mathematics and economics, as well as the ability to communicate their findings clearly and concisely. Calculus 1A provides Financial Analysts with a solid foundation in calculus, which is essential for understanding the financial models used to analyze investments. The course also helps students develop problem-solving skills and critical thinking abilities, which are essential for success in this field. Taking this course is highly recommended for anyone interested in a career in financial analysis.

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Operations Research Analyst

Operations Research Analysts use mathematical and statistical techniques to solve problems in business and industry. They work on a wide range of projects, from improving supply chain efficiency to reducing manufacturing costs. Calculus 1A provides Operations Research Analysts with a solid foundation in calculus, which is essential for understanding the mathematical models used to solve business problems. The course also helps students develop problem-solving skills and critical thinking abilities, which are essential for success in this field. Taking this course is highly recommended for anyone interested in a career in operations research.

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Data Scientist

Data Scientists are responsible for collecting, analyzing, and interpreting data to help businesses make better decisions. They must have a strong foundation in mathematics and statistics, as well as the ability to program computers. Calculus 1A provides Data Scientists with a solid foundation in calculus, which is essential for understanding the statistical methods used to analyze data. The course also helps students develop problem-solving skills and critical thinking abilities, which are essential for success in this field. Taking this course is highly recommended for anyone interested in a career in data science.

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Software Engineer

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Statistician

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Teacher

Teachers lead classroom instruction of students at various grade levels, and work to help students reach their full potential. They create lesson plans, assess student performance, and provide students with feedback. Calculus 1A can be useful for Teachers of mathematics by strengthening your understanding of calculus and its applications, which can help you create engaging and effective lesson plans and provide your students with a deeper understanding of the subject.

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