• Announcements: The last homework of the semester, HW11, is now available online and due next Monday. The Final Exam 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.

• Fundamental Theorem of Calculus for Line integrals (theory and proof): Download file or watch below

• Example of computing line integral of a conservative vector field using the Fundamental Theorem of Calculus: Download file or watch below

• Computing above line integral using an explicit parametrization as an illustration: Download file or watch below

• Theorem about equivalent characterizations of conservative vector fields (very important): Download file or watch below

• Revisiting an important example from the previous lecture, in light of the above characterizations of conservative vector fields: 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 Fundamental Theorem of Calculus for Line Integrals of Vector Fields

• External link 2: Fundamental Theorem of Calculus for Line Integrals by PatrickJMT (video): Watch on YouTube

• External link 3: Another example of applying Fundamental Theorem of Calculus for Line Integrals (video): Watch on YouTube

• External link 4: Yet another example of applying Fundamental Theorem of Calculus for Line Integrals, on 3D (video): Watch on YouTube