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| January 2009 |
| February 2009 |
| March 2009 |
| April 2009 |
| May 2009 |
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Homework will be posted on the class website on Mondays and due in section the following week. The homework will be based on the material covered in lectures that week. (For example, the first assignment will be assigned on Monday February 2 and due in section during the week of February 9. It will be based on material covered in lectures up to and including Monday February 2.)
You are allowed to work together in groups to solve the problems, and you are encouraged to do so. However, simply copying someone else's answers will not be tolerated. The homework is designed to prepare you for the exams, and so your eventual goal should be to learn how to solve problems by yourself under test conditions.
Below is an approximate outline for the course. The outline is "approximate" in the sense that it the course material will follow the topics listed below, however we may decide to cover some topics in more depth, or add some more advanced topics at the end of the course. There is some space in the last couple of weeks for this.
After class I'll update it with what we covered that day and any relevant homework assignments, so the "approximate outline" will become an "exact record" of the lectures.
| Date | Textbook Chapter | Recommended Reading for the next lecture | Homework Assignments |
| Monday January 26 |
Class Introduction 1.1: Vectors in 2 and 3 dimensions |
Read Theorem 1 on p27 and Examples 5 and 6 on pp29-30 | |
| Wednesday January 28 |
Both classes cancelled due to weather | Check out the Cross Product Applet For interest: Read the historical note on pp54-61 |
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| Friday January 30 |
1.2: The inner product, length and distance 1.3: Matrices, determinants and the cross product |
Read "Properties of Determinants" on pp40-41 Read "Properties of the cross product" on p46. |
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| Monday February 2 |
1.3: Matrices, determinants and the cross product (cont.) | Read Example 1 on p67 and Example 2 on p70 | Due in section the week of Feb 9 1.1: 6, 13, 16, 25 1.2: 2, 8, 14, 19, 20 1.3: 3, 4 Practice Problems (not to be turned in) 1.1: 7, 19, 20, 26 1.2: 13, 15, 18, 24, 27 |
| Wednesday February 4 |
1.4: Cylindrical and spherical co-ordinates 2.1: The Geometry of Real-Valued Functions |
Read Examples 4 and 5 on pp100-103 | Practice Problems 1.4: 1, 2, 3, 9, 12, 13 2.1: 1, 2 |
| Monday February 9 |
2.1: Geometry of real-valued functions 2.2: Limits |
Due in section the week of Feb 16 1.3 6, 7, 15(b)(c), 16(a) 1.4: 4, 5, 8, 14, 15 Practice Problems (not to be turned in) 2.1: 5, 7, 12, 17, 29, 32 |
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| Wednesday February 11 |
2.2: Limits (cont.) |
Read Theorem 6 on p121, and Examples 12, 14 and 15 on pp121-124 | Practice Problems 2.2: 8(a), 8(c), 9(c), 18 |
| Friday February 13 |
2.3: Differentiation |
Read Examples 3 and 4 on pp130-131, and Example 5 on pp133-134. Check out Joel Kramer's notes about epsilon-delta proofs. |
Practice Problems 2.3: 1(b), 2(b), 3(b), 3(e), 5 |
| Monday February 16 |
2.3: Differentiation (cont.) | Read Examples 7, 8 and 9 on pp136-137. Read Theorem 9 on p137 and Example 10 on p138, also look at Figure 2.3.4 and understand why the function is not differentiable. |
Due in section the week of February 23 2.1: 1, 3, 8, 12, 16, 28, 30 2.2: 2, 4, 7(a), 8(c), 10(c), 19 2.3: 1(a), 1(c), 2(a), 2(c) Practice Problems 2.3: 8(a), 8(c), 10, 12(a), 13(a), 15 |
| Wednesday February 18 |
2.5: Properties of the derivative | Read Examples 2 and 3 on pp156-157. | Practice Problems 2.5: 1, 3(b), 5(b), 8, 9 |
| Friday February 20 |
2.4: Introduction to Paths and Curves 2.6: Gradients and Directional Derivatives |
Read Theorem 13 and Example 4 on p166 Read Theorem 14 and Example 5 on pp167-168. |
Practice Problems 2.4: 1, 3, 7, 15 2.6: 1, 2(b), 3(b), 6(c) |
| Monday February 23 |
2.6: Gradients and Directional Derivatives (cont.) 3.1: Iterated Partial Derivatives |
Read Example 6 on pp169-170. Read Examples 4 and 5 on pp185-186. |
Due in section the week of March 2 2.2: 22(b), 25 2.3: 1(b), 2(b), 3(b), 8(c), 10, 15 2.4: 2, 13 2.5: 3(a), 3(b), 5(a), 13, 19 2.6: 1, 2(c) Practice Problems 2.6: 6(a), 11, 14(a), 16 3.1: 2, 7(a), 8(a), 11, 19 |
| Wednesday February 25 |
3.2: Taylor's Theorem | Read Examples 1, 2, 3 on pp199-201 Read the proof of Theorem 3 on pp197-198 |
Practice Problems 3.2: 1, 5, 6, 7(b) |
| Friday February 27 |
3.3: Extrema of Real-Valued Functions | Read Theorem 6 on p216 and read Examples 6 and 7 on pp216-217 | Practice Problems 3.3: 3, 5, 9, 14, 23 |
| Monday March 2 |
3.4: Constrained Extrema and Lagrange Multipliers | Read Theorem 8 on p226 and Examples 1 and 2 on pp228-230. | Practice Problems 3.4: 1, 3, 10, 13 |
| Wednesday March 4 |
3.4: Constrained Extrema and Lagrange Multipliers (cont.) | Read Example 7 on pp234-235 and Example 10 on pp237-238. Read Example 1 on pp247-248. |
Practice Problems 3.4: 11, 17, 20, 29, 31 |
| Friday March 6 |
3.5: The implicit function theorem 4.2: Arc Length |
Read Example 2 on pp249-250 and Example 4 on p253 Read Example 4 on p277 and Example 6 on p279. Read "Justification for the arc-length formula" on pp280-281 |
Practice Problems 3.5: 2, 3, 10 4.2: 1, 3, 6, 11 |
| Monday March 9 |
4.3: Vector Fields 4.4: Divergence and Curl |
Read Theorem 1 on p303 and Theorem 2 on p304 | Due in section the week of March 23 3.3: 3, 8, 18 3.4: 4, 5, 20 3.5: 2, 10 4.2: 2, 10, 12 Practice Problems 4.3: 2, 6, 10, 14, 18 4.4: 2, 14 |
| Wednesday March 11 |
4.4: Divergence and Curl 5.1: Introduction to Double Integrals |
Midterm: Evening of March 11 | |
| Friday March 13 |
5.1: Introduction to Double Integrals 5.2: The Double Integral over a rectangle |
Read "Reduction to iterated integrals" and work through Examples 3 and 4 on pp322-325. Read Theorem 3 on p334 (Fubini's Theorem) |
Practice Problems 4.4: 5, 11, 17, 31 5.1: 1(b), 1(c), 2(b), 2(c), 6, 8 5.2: 1(b), 4, 5, 11 |
| Week of March 16 |
Spring Break | No Class | |
| Monday March 23 |
5.3: The Double Integral over more general regions | Read Example 2 on pp345-346 Read Theorem 4 on p344 and Theorem 4' on p347. |
Due in section the week of March 30 5.1: 1(a), 1(b), 1(c), 1(d), 2(a), 2(b), 2(c), 2(d), 8 5.2: 1(a), 1(c), 2(c), 4, 6, 11 Practice Problems 5.3: 1(b), 1(d), 2(a), 2(e), 3, 12 |
| Wednesday March 25 |
5.3: The Double Integral over more general regions 5.4: Changing the order of integration |
Read Examples 1 and 2 on pp349-351. | Practice Problems 5.4: 1(b), 2(b), 2(c), 77 |
| Friday March 27 |
5.5: The Triple Integral | Read Examples 1 and 2 on pp356-357, and Examples 5 and 6 on pp361-363. | Practice Problems 5.5: 2, 5, 6, 9 |
| Monday March 30 |
5.5: Triple Integrals (cont.) 6.1: The Change of Variables Formula |
Read Examples 1 and 2 on pp369-371. Read the background to the change of variables formula on pp376-381 |
Due in section the week of April 6 5.3: 1(d), 2(e), 6, 12, 16 5.4: 1(b), 2(a), 2(b), 2(c), 8, 10 5.5: 2, 4, 7 Practice Problems 5.5: 13, 17, 19, 23, 25 |
| Wednesday April 1 |
6.2: The Change of Variables Formula (cont.) | Read Examples 4 and 5 on pp384-386. Read "Change of Variables for Spherical Co-ordinates" on pp388-389, and work through Example 6 onp389. |
Practice Problems 6.2: 1, 3, 11, 21, 23 |
| Friday April 3 |
6.2: The Change of Variables Formula (cont.) | Read ahead to "Applications of Integration": Example 3 on p396 and Example 6 on p400. | Practice Problems 6.2: 5, 9, 14, 17 |
| Monday April 6 |
6.3: Applications of Integration | Read Example 3 on p396 and Example 6 on p400. | Due in section the week of April 13 6.1: 2, 4, 7 6.2: 1, 4, 14, 21, 23 Practice Problems 6.3: 3, 5, 6 |
| Wednesday April 8 |
6.3: Applications of Integration (cont.) 7.1: The path integral |
Read Example 2 on pp424-425. Read Examples 1 and 2 on pp432-433. |
Practice Problems 6.3: 14 7.1: 1, 3, 6 |
| Friday April 10 |
7.2: Line integrals | Read Theorems 1 and 2 on p437 and p439, and work through Example 8 on p438. | Practice Problems 7.1: 7, 10, 13 7.2: 1, 4 (important!) |
| Monday April 13 |
7.2: Line integrals (cont.) | Read Theorem 3 and Example 9 on p440. Read Example 10 on p443. |
Due in section the week of April 20 6.3: 4, 5, 13, 14 7.1: 2, 3, 6 Practice Problems 7.2: 7, 11, 13 |
| Wednesday April 15 |
7.2: Line integrals (cont.) | Read Example 11 on pp445-446. Read Example 2 on p455. |
Practice Problems 7.2: 17, 19 |
| Friday April 17 |
7.3: Parametrised surfaces | Read Examples 3 and 4 on pp457-458. Read Example 1 on pp463-464. |
Practice Problems 7.3: 1, 3, 13 |
| Monday April 20 |
7.3: Parametrised surfaces (cont.) 7.4: Area of a surface |
Read the "Definition of Surface Area", and the "Justification of the Area Formula" on pp461-463. Read "Surfaces of Revolution" on pp466-467. |
Due in section the week of April 27 7.2: 2, 11, 16 7.3: 2, 6 Practice Problems 7.3: 17 7.4: 2, 5, 10 |
| Wednesday April 22 |
7.5: Integrals of scalar functions over surfaces 7.6: Surface integrals of vector fields |
Read "Surface integrals over graphs" on pp476-480, and work through Examples 2, 3, 4. Read Theorem 1 on p522, and verify Green's theorem on a rectangle. |
Practice Problems 7.4: 4, 17, 19, 20 7.5: 1, 3 |
| Friday April 24 |
7.6: Surface integrals of vector fields (cont.) 8.1: Green's Theorem |
Read "The physical interpretation of surface integrals" on pp490-494, and work through Examples 4 and 5. Read Theorem 6 on p538 and "The curl as circulation per unit area" on pp539-542. |
Practice Problems 7.6: 1, 3, 6, 9, 10 8.1: 1, 2, 3 More Challenging (if you have time) 7.6: 11, 12, 13, 18 |
| Monday April 27 |
8.1: Green's theorem (cont.) Intro to Stokes' Theorem, Gauss' Theorem |
Read Examples 1 and 2 on pp535-537. Read Examples 3, 4 and 5 on pp567-570. Read the proof of Gauss' Law on pp569-570, and the application of Gauss' Law to electromagnetism in Example 6 on p572. |
Practice Problems 8.1: 5, 7, 9, 12 |
| Wednesday April 29 |
8.2: Stokes' Theorem | Read Example 3 on p538 and Example 5 on pp543-544. | Practice Problems 8.2: 3, 5, 7, 14, 25 More challenging (if you have time) 8.2: 26, 27 |
| Friday May 1 |
8.4: Gauss' Theorem | Read Example 5 on pp569-570. | Practice Problems 8.4: 1, 3, 4, 5, 9, 10 More challenging (if you have time) 8.4: 14, 16, 19, 22 |