• Announcements: This is the last lecture of the semester in which we discuss new material; the next lecture will be a revision for the Final Exam, which will be conducted remotely just like the Midterm Exam. It will be made available to you on Sunday 5/17 at 12.00pm (noon) EDT and will be due the next day, Monday 5/18 at 11.59pm (midnight) EDT. More details will come by email.

• Green's Theorem with holes (introduction and discussion): Download file or watch below

• Verifying Green's Theorem in an example with holes: Download file or watch below

• A quick tour of more advanced Vector Calculus (Part I: Flux integrals and the Gauss/Divergence Theorem): Download file or watch below

• A quick tour of more advanced Vector Calculus (Part II: An example of flux integrals via the Gauss/Divergence Theorem): Download file or watch below

• A quick tour of more advanced Vector Calculus (Part III: Stokes' Theorem): Download file or watch below

• Lecture Notes (static file from above videos): PDF file

• Alternative Lecture Notes (from last year): PDF file

• External link 1 (highly recommended, has many further examples!): Paul's Online Notes about Green's Theorem (regions with holes discussed towards the end), Paul's Online Notes about Surface integrals, Fluxes, Divergence Theorem, and Stokes Theorem (bonus topics).

• External link 2: A panoramic discussion of divergence and curl of vector fields, with beautiful graphics (video): Watch on YouTube

• External link 3: Example of using Stokes's Theorem (video): Watch on YouTube