Class Diary

For the homework problems listed below, the ones marked with * should be turned in and graded. The others are non-graded problems.

• Monday, January 14 -
  • Class: Intro to class. Single-variable calculus vs. multi-variable calculus. Covered Section 1.1 (Vectors).
  • Read: Section 1.1 of the text. The first few pages will probably be review.
  • Do: 1.1.7, 1.1.9*, 1.1.10*, 1.1.11, 1.1.16*, 1.1.17.
• Tuesday, Jaunary 15 -
  • Class: Covered Section 1.2 (Applications in geometry and physics). Started Section 1.3 (The Dot Product), stated Theorem 1.3 and Theorem 1.4.
  • Read: Section 1.2, and Section 1.3 (up to page 23).
  • Do: 1.2.2*, 1.2.6*, 1.2.16.
• Wednesday, January 16 -
  • Class: Finished Section 1.3. Applications of projections to physics, and to finding the distance between a point and a line.
  • Read: The rest of Section 1.3.
  • Do: 1.3.3, 1.3.7, 1.3.10*, 1.3.16, Find the distance between the point (0,0,0) and the line through (1,1,1) and (2,3,4)*.
• Thursday, January 17 -
  • Class: Covered Section 1.4, focusing on multiplying matrices and computing determinants.
  • Read: Section 1.4.
  • Do: 1.4.9, 1.4.16*, 1.4.18, 1.4.22, 1.4.28*.
• Tuesday, January 22 -
  • Class: Covered Section 1.5, focusing on Theorem 1.10 and its various applications.
  • Read: Section 1.5.
  • Do: 1.5.3, 1.5.8*, 1.5.20*, 1.5.24.
• Wednesday, January 23-
  • Class: Covered Section 2.1.
  • Read: Section 2.1.
  • Do: 2.1.7, 2.1.11*, 2.1.13, 2.1.20*, 2.1.30*, 2.1.34*.
• Thursday, January 24-
  • Class: Covered Section 2.2, with a focus on finding and plotting level curves.
  • Read: Section 2.2.
  • Do: 2.2.11, 2.2.14*, 2.2.18, 2.2.34, 2.2.36*, 2.2.39, 2.2.42*.
• Monday, January 28-
  • Class: No lecture. Students worked in groups on problems from the handout.
  • Read: Skim Section 2.3 in preparation for Tuesday.
• Tuesday, January 29-
  • Class: Covered limits (most of Section 2.3).
  • Read: Section 2.3 (don't worry about the epsilon and delta stuff), through pg. 84.
  • Do: 2.3.6, 2.3.8*, 2.3.10, 2.3.12*, 2.3.21*.
• Wednesday, January 30-
  • Class: Covered continuity (the rest of Section 2.3), and defined partial derivatives, gradient, and derivative.
  • Read: Section 2.4 through pg. 100.
  • Do: 2.4.4, 2.4.7, 2.4.10, 2.4.14*, 2.4.22*, 2.4.23, 2.4.28*.
• Thursday, Janury 31-
  • Class: Covered the definition of differentiability and linear approximations (most of the rest of Section 2.4).
  • Read: The rest of Section 2.4.
  • Do: 2.4.36, 2.4.42*, 2.4.44* [to prove the function is differentiable, use Theorem 2.5], 2.4.45, 2.4.50*, 2.4.60, 2.4.64*, 2.4.66*.
• Monday, February 4-
  • Class: Covered theorems about differentiability and continuity (the rest of Section 2.4). Discussed function from R to R^m as curves. Started Section 2.6.
  • Read: Any parts of Section 2.4 that you weren't clear on the first time.
  • Do: 2.4.67* [use Theorem 2.5], and this problem*.
• Tuesday, February 5-
  • Class: Stated Theorems 2.6 and 2.7 from Section 2.6. Worked the examples 2.64 and 2.66.
  • Read: Section 2.6.
  • Do: 2.6.21*, 2.6.22*, and this problem*.
• Wednesday, February 6-
  • Class: Finished Section 2.6 and started Section 2.7.
  • Read: Any parts of Section 2.6 that you aren't clear on.
  • Do: 2.6.4, 2.6.6*, 2.6.12, 2.6.16*, 2.6.27*, 2.6.28*.
• Thursday, February 7-
  • Class: Covered almost all of Section 2.7.
  • Read: Section 2.7.
  • Do: 2.7.6, 2.7.10*, 2.7.16, 2.7.20*, 2.7.29*, 2.7.37, 2.7.40*.
• Monday, February 11-
  • Class: Review for exam.
  • Read: Any material you need to review.
  • Do: Study!
• Tuesday, February 12-
  • Class: Exam 1.
  • Read: Something relaxing.
  • Do: Relax.
• Wednesday, February 13-
  • Class: Talked about force fields and potentials from Section 2.7 (examples 2.89 and 2.91). Covered Section 2.8. Discussed the equation for a torus in cylindrical coordinates.
  • Read: Section 2.8. For Thursday, read Section 4.1.
  • Do: 2.7.62*, 2.8.1, 2.8.2*, 2.8.5*, 2.8.6*.
• Thursday, February 14-
  • Class: Intro to Chapter 4, statement and proof of Theorem 4.1.
  • Read: Section 4.2 for Monday.
  • Do: 4.1.2*, 4.1.5, 4.1.12, 4.1.13*, 4.1.16*.
• Monday, February 18-
  • Class: Returned exams, finished covering section 4.1. Started talking about Taylor's theorem.
  • Read: Skim section 4.3. I may start this section on Tuesday.
  • Do: 4.1.17, 4.1.18*, 4.2.12*.
• Tuesday, February 19-
  • Class: Covered section 4.2, started section 4.3.
  • Read: Section 4.3.
  • Do: 4.2.21*, 4.2.22*, 4.2.23, 4.2.30*.
• Wednesday, February 20-
  • Class: Covered most of Section 4.3 (up through the end of pg. 250).
  • Read: Any parts of Section 4.3 you aren't clear on.
  • Do: 4.3.1, 4.3.4*, 4.3.8, 4.3.10*, 4.3.16*, 4.3.18*.
• Thursday, February 21-
  • Class: Finished Section 4.3 and started Section 4.4.
  • Read: Section 4.4, Section 4.6 for Monday, and this handout on (unusual) examples of max/min.
  • Do: 4.3.21, 4.3.22*, 4.3.25*, 4.3.27, 4.3.30*.
• Monday, February 25-
  • Class: Finished Section 4.4 (material after Example 4.44 will not be covered on homework or exams). Started Section 4.6 and talked about the physical interpretation of divergence.
  • Read: Section 4.6, Section 5.1 (for Tuesday).
  • Do: 4.4.4, 4.4.10*, 4.4.14*, 4.4.21, 4.4.24*, this problem*, 4.6.7, 4.6.8*, 4.6.9, 4.6.10, 4.6.13*, 4.6.17.
• Tuesday, February 26-
  • Class: Discussed the physical interpretation of curl and Theorem 4.13. Briefly discussed properties of paths (Section 5.1) and defined path integrals (Definition 5.8 in Section 5.2).
  • Read: Section 5.2 and Section 5.3 (for Wednesday).
  • Do: 4.6.21, 4.6.22*, 4.6.29, 4.6.30*, 4.6.32, 5.2.4*, 5.2.15*, this problem*.
• Wednesday, February 27-
  • Class: Finished Section 5.2, began Section 5.3 including Definition 5.9, Example 5.17, Definition 5.10 and the discussion following Example 5.21.
  • Read: Section 5.4 (for Thursday).
  • Do: 5.3.6*, 5.3.9, 5.3.13*, 5.3.18*, this problem*.
• Thursday, February 28-
  • Class: Discussed two examples from Section 5.3, began Section 5.4.
  • Read: This website has a java applet that helps visualizing the behavior of velocity and force fields.
  • Do: Find questions about exam material to ask in class on Monday.
• Monday, March 3-
  • Class: Review.
  • Read: Review material.
  • Do: Study!
• Tuesday, March 4-
  • Class: Exam II.
  • Do: Relax.
• Wednesday, March 5-
  • Class: Discussed Section 5.4, including Theorems 5.4 and 5.5.
  • Read: Any parts of Section 5.4 you didn't understand the first time.
  • Do: 5.4.2*, 5.4.3*, 5.4.11*, Solve 5.4.15 and find the typo*, 5.4.16.
• Thursday, March 6-
  • Class: Concluded the discussion of Section 5.4.
  • Read: Section 6.1 for next Monday.
  • Do: 5.4.18*, 5.4.21, 5.4.28, 5.4.30*, this problem*, and this problem*.
• Monday, March 10-
  • Class: Covered Section 6.1.
  • Read: Section 6.2 for Tuesday.
  • Do: 6.1.2*, 6.1.5, 6.1.9*, 6.1.11, 6.1.21*, and this problem*.
• Tuesday, March 11-
  • Class: Covered Section 6.2.
  • Read: Section 6.3 for Wednesday.
  • Do: 6.2.4, 6.2.7, 6.2.10*, 6.2.12, 6.2.16*, 6.2.20, 6.2.22*, 6.2.28*, 6.2.30*, 6.2.33.
• Wednesday, March 12-
  • Class: Covered Section 6.3.
  • Read: Section 6.4 for Thursday.
  • Do: 6.3.5, 6.3.8*, 6.3.12, 6.3.20*, 6.3.22*.
• Thursday, March 13-
  • Class: Computing a one-variable integral by writing it as a double integral.
  • Read: Class notes.
  • Do: this problem*.
• Monday, March 24-
  • Class: Covered Section 6.4, change of variables in double integrals.
  • Read: Section 6.5 for tomorrow.
  • Do: 6.4.3, 6.4.4*, 6.4.6, 6.4.8*, 6.4.15*, 6.4.16, 6.4.22*, 6.4.25, 6.4.30*, 6.4.33.
• Tuesday, March 25-
  • Class: Interpretation of the Jacobian, examples of change of variables. Started Section 6.5.
  • Read: Any parts of Section 6.5 you aren't clear on.
  • Do: No new homework questions.
• Wednesday, March 26-
  • Class: Examples of triple integrals.
  • Read: Section 7.1 for the future.
  • Do: 6.5.3*, 6.5.8*, 6.5.12, 6.5.20*, 6.5.25*, 6.5.28, and this problem*.
• Thursday, March 27-
  • Class: Computed the error integral and used this to derive a formula for the volume of an n-dimensional sphere.
  • Read: Something to recover from class.
  • Do: this problem*.
• Monday, March 31-
  • Class: No lecture. Students worked in groups on problems from the handout.
  • Read: Other applications of integration handout.
  • Do: No new homework questions.
• Tuesday, April 1-
  • Class: Covered Section 7.1.
  • Read: Section 7.2 for tomorrow.
  • Do: 7.1.1*, 7.1.7, 7.1.8*, 7.1.12, 7.1.14*, 7.1.17, 7.1.25*, 7.1.27*, and this problem*.
• Wednesday, April 2-
  • Class: Covered Section 7.2.
  • Read: Section 7.3 for tomorrow.
  • Do: 7.2.12*, 7.2.13*, 7.2.15, 7.2.23, 7.2.24*. (For 7.2.24, it is not necessary to know what the normal and binormal vectors to a curve are. These are a pair of orthogonal vectors that span the plane whose normal vector is the tangent vector to the curve).
• Thursday, April 3-
  • Class: Covered Section 7.3 and computed an electric field using a surface integral.
  • Read: Section 7.4 for tomorrow.
  • Do: 7.3.2, 7.3.8*, 7.3.15*, 7.3.18(parts a and d only)*, and this problem*.
• Monday, April 7-
  • Class: Answered questions about parametrizations and homework. Started Section 7.4.
  • Read: Any material involving surfaces or parametrizations that you aren't clear on.
  • Do: 7.4.6*, 7.4.12*, 7.4.17*.
• Tuesday, April 8-
  • Class: Covered Example 7.40, talked about Gauss' law and how to use it to compute the electric field generated by a symmterical charge distribution.
  • Read: Section 7.5 for tomorrow.
  • Do: 7.3.17* (the idea is to use geometric and symmetry arguments alone), and this problem*.
• Wednesday, April 9-
  • Class: Covered Section 7.5. Talked about property (f) of integrals, computing total mass, center of mass, and moments of inertia.
  • Read: Section 8.1 for tomorrow.
  • Do: 7.5.12*, 7.5.13*.
• Thursday, April 10-
  • Class: Overview of Chapter 8. Statement, motivation and interpretation of Green's theorem.
  • Read: Review material.
  • Do: No new homework.
• Monday, April 14-
  • Class: Review
  • Read: Nothing new.
  • Do: Study!
• Tuesday, April 15-
  • Class: Exam.
  • Read: Something relaxing.
  • Do: Relax!
• Wednesday, April 16-
  • Class: Applications of Green's theorem.
  • Read: Section 8.2 for tomorrow.
  • Do: 8.1.8, 8.1.9*, 8.1.10*, 8.1.14, 8.1.17*, and this problem*.
• Thursday, April 17-
  • Class: Returned exams, corrected error from previous day, and started talking about the Divergence theorem.
  • Read: Nothing new.
  • Do: Nothing new.
• Monday, April 21-
  • Class: Proved the Divergence theorem in the plane (using Green's theorem). Stated the Divergence theorem and worked an example.
  • Read: Section 8.3 for tomorrow.
  • Do: Decide when you want me to make up office hours I am cancelling (we'll discuss this in class tomorrow), 8.2.2*, 8.2.6*, 8.2.22*, 8.2.29*, and this problem*.
• Tuesday, April 22-
  • Class: Example 8.12 from Section 8.2. Stated Stokes' theorem, talked about the boundary of surfaces, and orienting the boundary.
  • Read: Nothing new.
  • Do: 8.3.2*, 8.3.6*, 8.3.11, 8.3.16*, 8.3.18*, and this problem*.
• Wednesday, April 23-
  • Class: Proved a special case of Stokes' theorem using Green's theorem and the Divergence theorem. Explained how one can use Stokes' theorem (Example 8.17).
  • Read: Section 8.4 for tomorrow.
  • Do: 8.3.24*, this problem*.
• Thursday, April 24-
  • Class: Explained the physical interpretation of Stokes' theorem and curl of a three-dimensional vector field. Discussed the problem of uncurling a vector field, and its application to reducing a given surface integral to a line integral.
  • Read: Nothing new.
  • Do: this problem*, and this problem*.
• Monday, April 28-
  • Class: Talked about manifolds and differential forms.
  • Read: Nothing new.
  • Do: Study!

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