18.02, Spring 1999 -- Brief Lecture notes,
Third part: Double integrals and line integrals

• Lecture 15: Mar 9. Review and start of double integrals: EP 14.1
  1. Review of Part II.
  2. Volume under a graph.
  3. Double integrals.
• Lecture 16: Mar 11. Double integrals: EP 14.2, 14.3, 10.2
  1. General regions.
  2. Change of order.
  3. Polar coordinates.
• Lecture 17: Mar 12 -- In-class test in Walker Covers all material in Lectures 9-14 inclusive.
• Lecture 18: Mar 16. Integrals in polar coordinates: EP 14.4 (concentrating on the Examples); SN~I.2; EP 14.5; centroid pp. 913--middle 915; moment of inertia pp.~918--9.
  1. Polar coordinates.
  2. Center of gravity.
  3. Change to polar coordinates.
• Lecture 19: Mar 18. Changing variables in double integrals: Sn Sect CV, EP sect 14.9.
  1. Moment of inertia.
  2. Changing variables.
  3. Jacobian determinant.
• Lecture 20: Mar 19. Vector fields. Line integrals in the plane. SN, Vector Calculus Sect 1, EP 15.1, 15.2.
  1. Vector fields.
  2. Line integral.
  3. Work.
• Lecture 21: Mar 30. Path independence, conservative fields. EP 15.3.
  1. Gradient fields.
  2. Fundamental theorem of calculus.
  3. Conservative fields.
• Lecture 22: April 1 Read: Notes pp. 2.1--2.5. EP pp. 980-982 covers about the same material; if you read the book, be sure to read the Notes p.~2.1.
  1. Criterion for conservative fields
  2. Differentials, exactness
  3. Finding potentials
• Lecture 23: April 2 Green's Theorem. Read EP, pp. 986-989
  1. Computing double integrals
  2. Computing line integrals
  3. Proof of Green's theorem.
• Lecture 24: April 6 Normal form of Green's theorem. Notes secs. 3 and 4; EP pp. 989--992 is similar.
  1. Flux and line integrals
  2. Flux form of Green's theorem
• Lecture 25: April 8 Extensions and applications of Green's Theorem. Read: Notes: Sections 5 and 6.
  1. Regions with holes
  2. Review
• Lecture 26: April 9 In-class test in Walker Covers all material in Lectures 15-24 inclusive, new materail in Lecture 25 not included.