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The midterm exam will be on Wednesday 14 October from 15h00 to 17h00 in Room 117.
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 (the password for all recordings is Password0. )
Video Recordings (the password for all recordings is Password0. )
Lecture Notes
Lecture Notes
Past Exams
Past Exams
2023 intermediate test ..... Solutions
2023 midterm exam ...... Solutions
2024 intermediate test ..... Solutions
2024 midterm exam ..... 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
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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