Optimization A: Multivariable Calculus

Announcements

1. The class and TD on Monday 29 September and Wednesday 1 October are cancelled.

2. They will be replaced by  supplementary classes (date to be announced)

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.  

• Section 2.2: #2, #3, #4, #5, #6.  

• 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.