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Instructor: Marcus Pivato (Centre d'Économie de la Sorbonne)
Summary: This is the first half of the QEM course Optimization. We will cover the differentiation and integration of functions of several variables, along with qualitative properties (concavity, etc.) of such functions.
Textbook: Further Mathematics for Economic Analysis (2nd edition), by Knut Sydsaeter, Peter Hammond, Atle Seierstad, and Arne Strøm.
Click here for the course outline
Classes: Monday 11h00-12h30, Wednesday 15h00-16h30, MSE Room 117.
TD: Monday 12h30-14h30, Wednesday 16h30-18h30, MSE Room 117.
Marking scheme:
20% Attendance (participation in TDs)
80% Midterm Exam (Wednesday 15 October, 12h30-14h30)
The exam will be based on the lists of recommended problems which I will give you each week. It is strongly recommended that you try to solve all of these problems during the semester, as a way of studying for the exam.
Video Recordings
Video Recordings
Video recording of Monday 6 October
Video recording of Wednesday 8 October
Video recording of Friday 10 October
Video recording of Monday 13 October
Video recording of Tuesday 14 October
Video recording of Wednesday 15 October
Lecture Notes
Lecture Notes
Past Exams
Past Exams
2023 intermediate test (with solutions)
2023 midterm exam (with solutions)
2024 intermediate test (with solutions)
2024 midterm exam (with solutions)
Other books
Other books
Aside from the text by Sydsaeter et al, here are some other textbooks that you might find useful:
Mathematics for Economists, by Carl P. Simon, Lawrence Blume (Norton, 1994)
Mathematics for Economists: An introductory textbook (5th Edition), by Malcolm Pemberton, Nicholas Rau (Manchester University Press, 2023)
Mathematics for Economics (3rd edition) by Michael Hoy, John Livernois, Chris Mckenna, Ray Rees,and Thanasis Stengos (MIT Press, 2011)
Announcements
Announcements
The class and TD on Monday 29 September and Wednesday 1 October are cancelled.
They will be replaced by supplementary classes on the following dates:
Friday, 10 October 13h00-16h30 in room TBA
Tuesday, 14 October 16h00-19h30 in room S17
3. The midterm exam will be on Wednesday 15 October from 17h00 to 18h30 in Room 117.
Lecture schedule for twelve classes (provisional)
Lecture schedule for twelve classes (provisional)
(§1.1-1.3,§1.7) Review of linear algebra and quadratic forms.
(§2.1-§2.2) Gradients & directional derivatives; convex sets
(§2.3) Concave and convex functions
(§2.4-2.5) (Quasi)concave and (quasi)convex functions
(§2.5-2.6) Quasiconcave and quasiconvex functions, Taylor’s theorem
(§2.7), The Implicit and Inverse Function Theorems
(§2.9) Differentiability, the chain rule.
(§4.1-4.2) One-dimensional integration; Leibniz formula
(§4.3-4.4) The Gamma function; multiple integrals on product domains
(§4.5-4.6) Double integrals on general domains; multiple integrals;
(§4.7) Change of variables
(§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
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.
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