Calculus IV: Vector Calculus (Line Integrals, Surface Integrals, Vector Fields, Greens' Thm, Divergence Thm, Stokes Thm, etc) **Full Course** Line Integrals in 3D // Formula & Three Applications
Line Integrals in 3D // Formula & Three Applications Transcript and Lesson Notes
In our previous two videos on line integrals (see vector calc playlist below) we focused on curves that lived in the xy-plane; that is, they were 2D curves and had a function "above" them. This gave a pleasing geometric
Quick Summary
In our previous two videos on line integrals (see vector calc playlist below) we focused on curves that lived in the xy-plane; that is, they were 2D curves and had a function "above" them. This gave a pleasing geometric
Key Takeaways
- Review the core idea: In our previous two videos on line integrals (see vector calc playlist below) we focused on curves that lived in the xy-plane; that is, they were 2D curves and had a function "above" them. This gave a pleasing geometric
- Understand how Math fits into Line Integrals in 3D // Formula & Three Applications.
- Understand how Solution fits into Line Integrals in 3D // Formula & Three Applications.
- Understand how Example fits into Line Integrals in 3D // Formula & Three Applications.
- Understand how vector calculus fits into Line Integrals in 3D // Formula & Three Applications.
Key Concepts
Full Transcript
In our previous two videos on line integrals (see vector calc playlist below) we focused on curves that lived in the xy-plane; that is, they were 2D curves and had a function "above" them. This gave a pleasing geometric interpretation. However, the curves can be 3D (or more) just as easily and in this video we will slightly adjust the formula to accommodate the extra dimension. While these are harder to graph, they have many nice applications such as the total mass of a variable density wire, the total volume of a variable diameter wire, and arclength of a curve. Plus, in future videos, we will see these are crucial for studying curves in a vector field. THE VECTOR CALCULUS PLAYLIST: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa OTHER COURSE PLAYLISTS: ►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 (Calc IV): https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1 ►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS ►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6 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 Line Integrals in 3D // Formula & Three Applications about?
In our previous two videos on line integrals (see vector calc playlist below) we focused on curves that lived in the xy-plane; that is, they were 2D curves and had a function "above" them. This gave a pleasing geometric
What key concepts are covered in this lesson?
The lesson covers Math, Solution, Example, vector calculus, multivariable calculus.
What should I learn before Line Integrals in 3D // Formula & Three Applications?
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: Math, Solution, Example, 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.
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