Multivariable Calculus

Announcements

1. The classes and TDs on Monday 9 October and Wednesday 11 October are cancelled.

2. They will be replaced by three supplementary classes:

   • Tuesday 26 September, 10h30 - 13h00

   • Tuesday 3 October, 11h00 -13h00

   • Tuesday 17 October, 10h30-13h00

3. ​The final exam (for DU MMEF)  and midterm exam (for QEM) has been rescheduled from 18 October to Monday 23 October 12h30-14h30.  (Instead, there will be an ordinary CM/TD lecture on Wednesday, 18 October from 15h00-18h30.)

Lecture schedule for twelve classes (provisional)

1. (§1.1-1.3,§1.7) Review of linear algebra and quadratic forms.

2. (§2.1-§2.2) Gradients & directional derivatives; convex sets

3. (§2.3) Concave and convex functions 

4. (§2.4-2.5) (Quasi)concave and (quasi)convex functions

5. (§2.5-2.6) Quasiconcave and quasiconvex functions, Taylor’s theorem

6. (§2.7), The Implicit  and Inverse Function Theorems

7. (§2.9) Differentiability, the chain rule.

8. (§4.1-4.2) One-dimensional integration; Leibniz formula

9. (§4.3-4.4) The Gamma function; multiple integrals on product domains

10. (§4.5-4.6) Double integrals on general domains; multiple integrals;

11. (§4.7) Change of variables

12. (§4.8) Generalized integrals

Advice: I will follow the textbook closely. Thus, it is strongly recommended that you obtain a copy of the textbook, and read the recommended sections of the book before each lecture. Come to class prepared to ask questions. Be an active learner. After each class, review the exercises solved in class, and solve the other assigned problems.

Recommended problems

 (This list is updated regularly, so please check frequently.  All recommended problems are from the textbook  by Sydsaeter et al.) 

• ​Section 1.2: #2, #3, #4, #6.

• Section 1.3:  #1.

• Section 1.7: #1, #3, #5, #7.

• Section 2.1: #1, #2, #3, #4, #7, #8.  (We already did #2(a) and #4 in class last week.)

• Section 2.2: #2, #3, #4, #5, #6.  (We already did #5 in class.)

• Section 2.3: #4, #5, #6, #7, #8, #9.   Also: prove Theorem 2.3.4(b) and prove parts (b), (c) and (d) of Theorem 2.3.5.

• Section 2.4: #1, #2, #3, #4, #5.  Also: prove parts (b), (c), (d) and (f) of Theorem 2.4.2.

• Section 2.5: #1, #2, #6 ,#10 and #11.  Also: prove part (b) of Theorem 2.5.2.

• Section 2.6: #1 and #2.

• Section 2.7: #1, #2 and #4.

• Section 2.9: #1.

• Section 4.1:  #1, #2, #3, #4, and #5.

• Section 4.2: #1, #3, and #5.

• Section 4.3: #1 and #2.

• Section 4.4: #1.

• Section 4.5: #1, #4, and #6.

• Section 4.7: #1, #2, #3, and #5.