Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Finding the scalar potential function for a conservative vector field // Vector Calculus
Finding the scalar potential function for a conservative vector field // Vector Calculus Transcript and Lesson Notes
The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost tr
Quick Summary
The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost tr
Key Takeaways
- Review the core idea: The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost tr
- Understand how Solution fits into Finding the scalar potential function for a conservative vector field // Vector Calculus.
- Understand how Example fits into Finding the scalar potential function for a conservative vector field // Vector Calculus.
- Understand how math fits into Finding the scalar potential function for a conservative vector field // Vector Calculus.
- Understand how vector calculus fits into Finding the scalar potential function for a conservative vector field // Vector Calculus.
Key Concepts
Full Transcript
The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost trivially by just evaluating that potential function at the endpoints. But how do we FIND the scalar potential function? This video introduces that method. First we test that our vector field really is conservative using the test we saw previously. But after we know the method applies, we apply a trick involving alternating integration and differentiation to get a handle on the constants that come up, and ultimately get the scalar potential function. Finally we see an example were we use the potential function for a specific line integral. 0:00 Goals 1:00 Test for Conservative 2:50 Find Potential Function 9:43 Compute Line Integral MY VECTOR CALCULUS PLAYLIST: ►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 ►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m ► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n ►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd ►DIFFERENTIAL EQUATIONS: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 OTHER PLAYLISTS: ► Learning Math Series https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw ►Cool Math Series: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho BECOME A MEMBER: ►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join MATH BOOKS & MERCH I LOVE: ► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett SOCIALS: ►Twitter (math based): http://twitter.com/treforbazett ►Instagram (photography based): http://instagram.com/treforphotography
Lesson FAQs
What is Finding the scalar potential function for a conservative vector field // Vector Calculus about?
The fundamental theorem of line integrals told us that if we knew a vector field was conservative, and thus able to be written as the gradient of a scalar potential function, we could evaluate any line integral almost tr
What key concepts are covered in this lesson?
The lesson covers Solution, Example, math, vector calculus, calc 4.
What should I learn before Finding the scalar potential function for a conservative vector field // Vector Calculus?
Review the previous lessons in Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course**, then use the transcript and key concepts on this page to fill any gaps.
How can I practice after this lesson?
Practice by applying the main concepts: Solution, Example, math, vector calculus.
Does this lesson include a transcript?
Yes. The full transcript is visible on this page in indexable HTML sections.
Is this lesson free?
Yes. CourseHive lessons and courses are available to learn online for free.
Continue Learning
Continue this lesson in the app
Install CourseHive on Android or iOS to keep learning while you move.
