Lecture 19: Vector fields and line integrals in the plane
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Lesson Description:
Learn about vector fields and line integrals, what they mean, what they look like, and how to find them.
Denis Auroux. 18.02 Multivariable Calculus, Fall 2007. (Massachusetts Institute of Technology: MIT OpenCourseWare). http://ocw.mit.edu (Accessed March 21, 2009). License: Creative Commons Attribution-Noncommercial-Share Alike.
Additional Resources:
- Curves and Vector Fields Applet - A Java applet for curves and vector fields
- Lecture Notes - Lecture Notes from this lesson.
- Transcript of Lesson - Written transcript from this lesson.
- Problem Set - A problem set with some problems from this lecture.
Questions answered by this video:
- What are vector fields and how do you find one?
- What is a line integral and how do you find them?
- What does a vector field look like and what are some examples of vector fields?
- What does a velocity field for uniform rotation look like?
- How do you find the work done by a vector field?
- How do you find the work done by a force F = -yi + xj if the particle is moving along x = t, y = t^2 from t = 0 to 1?
- Why does the value of a line integral depend on the path taken?
- How do you simplify a line integral in 2 variables down to one variable?
- What is a geometric approach to line integrals?
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Staff Review
Vector fields and line integrals, two very important concepts in this course, are discussed in this lecture. They are explained theoretically, and examples are also shown. This is a great lecture on some difficult conceptual topics. This is a very complete and descriptive lesson.
