In order to offer more teaching for this course, some of the review lectures are Mathematics 2 times (Mondays and Thursdays, both aud. 7, both 1215—14). These lectures are indicated under 'Place' (the title of that column cannot be changed by user (i.e. teachers)).
This version: September 7th (updated with more references). Updates (corrections and other) will be announced on the course webpage http://www.uio.no/studier/emner/sv/oekonomi/ECON4140/h12/ .| Date | Teacher | Place | Topic | Lecture notes / comments |
| 21.08.2012 | NCF? | ? | Review of some basics and terminology; Vectors; Convex sets? | The new material for this lecture, will be convex sets, which you probably know by intuition. However, the approach will be more rigorous. Part of the purpose is to offer an introduction to more formal proofs, done from axioms rather than from intuition. You might need it in applications to e.g. foundational microeconomics (say, preferences may or may not be convex). Fortunately, it is less exam relevant than scary. Read: FMEA 2.2 / MAII 4.2.? |
| 22.08.2012 | NCF? | ? | Concave and convex functions? | This lecture will re-establish convexity and concavity of functions in a more general set-up than in MM1/Maths 2 (for example, without assuming differentiability). FMEA 2.2—2.4 / MAII 2.2, 4.5–4.6.? |
| 28.08.2012 | NCF? | ? | Concave, convex, quasiconcave and quasiconvex functions.? | This lecture will introduce quasiconvexity and quasiconcavity, which you might need in relation to convex preferences in microeconomics. FMEA 2.4—2.5 / MAII 4.6–4.7.? |
| 29.08.2012 | NCF? | ? | Quadratic forms and definiteness of matrices? | This lecture will introduce quadratic forms and definiteness. Concepts like minors (?underdeterminanter?) will be established to this end. Later (probably the subsequent week), we will connect this to the 2nd order tests for concavity/convexity/max/min. FMEA 1.7—1.8 (1.8—1.9 in 1.ed) / MAII 4.3–4.4? |
| 30.08.2012 | NCF? | *Maths 2 for review*? | Maxima and minima. (Review.)? | Maths 2 lecture for review You will need the 2nd order conditions in two variables before going on to the generalizations to multiple variables. If you need any review of this, then visit this Mathematics 2 lecture, 1215—1400 in auditorium 7.? |
| 03.09.2012 | NCF? | *Maths 2 for review*? | Lagrange's method (review)? | Maths 2 lecture for review In case you need a review of Lagrange's method, it is this week's topic in Mathematics 2, both Monday and Thursday (auditorium 7, 1215–14 both days). FMEA 3.3—3.4 / MAII 8.4–8.6.? |
| 04.09.2012 | NCF? | ? | Quadratic forms cont'd; Maxima and minima: the extreme value theorem and the envelope theorem? | This week's lectures will in part elaborate more on quadratic forms and definiteness (with and without linear constraints), and in part cover unconstrained max/min. The new material is 2nd order tests in several variables. Before that, basic concepts like the extreme value theorem will be reviewed briefly, and also the envelope theorem. If you need more than a brief reminder of these topics, you should consider visiting the Maths 2 lecture on August 30th, as we will not spend much time on it in Maths 3.? |
| 05.09.2012 | NCF? | ? | As Tuesday? | ? |
| 06.09.2012 | NCF? | *Maths 2 for review*? | Lagrange's method (review)? | Maths 2 lecture for review As Monday. More examples.? |
| 10.09.2012 | NCF? | *Maths 2 for review*? | Why Lagrange's method works. Then: introduction to nonlinear programming (i.e., optimization under inequality constraints)? | Maths 2 lecture for review If you need to refresh your basic knowledge of Kuhn–Tucker's conditions for maximization under inequality constraints, you should visit this Mathematics 2 lecture. Lecture will be based on Maths 2 curriculum (the EMEA, not FMEA treatment of Kuhn–Tucker), but you might use FMEA 3.5–3.6 (MAII: 8.5–8.6) for review. Skip – for now – the discussion on constraint qualification.? |
| 11.09.2012 | NCF? | ? | Lagrange's method: sufficient conditions and the constraint qualification? | There is a set of sufficient conditions, not covered in Maths 2, based on definiteness for quadratic forms subject to linear constraints. Furthermore, Lagrange's method may indeed fail. This lecture will elaborate on why, and how to patch up. FMEA 3.3–3.4 (skip – for now – the rank condition in Thm 3.3.1). (MAII 8.3–8.4)? |
| 12.09.2012 | NCF? | ? | Nonlinear programming. Kuhn–Tucker? | A very brief theory review (if you need more, please visit Monday's Maths 2 lecture), and examples. ? |
| 13.09.2012 | ? | *Maths 2 for more examples*? | Nonlinear programming. Kuhn–Tucker. Sensitivity.? | Maths 2 lecture If you want to see more examples of the Kuhn–Tucker theory, you should visit this Maths 2 lecture. Also covered: the shadow price interpretation of the multipliers.? |
| 17.09.2012 | NCF? | *Maths 2 for review (if you really need it)*? | The intermediate value theorem. Introduction to integration? | Maths 2 lecture for review Most of you won't need this lecture, which introduces to Maths 2 the intermediate value theorem (?skj?ringssetningen?) and then the integral.? |
| 18.09.2012 | NCF? | ? | Nonlinear programming: the constraint qualification and mixed constraints? | This week will cover the part of the Kuhn–Tucker theory that is too sophisticated for Mathematics 2, including harder examples. We will see why the Kuhn--Tucker conditions (like Lagrange) sometimes fail. We will introduce the mixed (both equality and inequality) constraints case, and we will establish some properties of the value function. FMEA, rest of chapter 3. (MAII resten av kap 8)? |
| 19.09.2012 | NCF? | ? | Nonlinear programming: the constraint qualification and mixed constraints? | As Tuesday? |
| 20.09.2012 | NCF? | *Maths 2 for review*? | Methods of integration (review)? | Maths 2 lecture for review. If you need to review your skills in integration, visit this Mathematics 2 lecture.? |
| 24.09.2012 | NCF? | *Maths 2 for review*? | Methods of integration (review)? | Maths 2 lecture for review: As previous Thursday.? |
| 25.09.2012 | NCF? | ? | The Leibniz rule for differentiation of integrals; Multiple integration? | This lecture will elaborate on integrals. We will cover differentiation of integrals depending on a parameter, and introduce the double integral. FMEA 4.1, 4.2, 4.4 / MAII 6.1–6.2, 6.4? |
| 26.09.2012 | NCF? | ? | Multiple integration? | FMEA 4.5 / MAII 6.5? |
| 27.09.2012 | NCF? | *Maths 2 for review*? | 1st order differential equations (review)? | Maths 2 lecture for review This week's topic in Mathematics 2, is 1st order differential equations. You might want to join for review. This is the introductory part. Based on EMEA, not FMEA, but you might read: FMEA: 5.1, 5.3–5.4? |
| 01.10.2012 | NCF? | *Maths 2 for review*? | 1st order differential equations (review) ? | Maths 2 lecture for review This Mathematics 2 lecture elaborates further on 1st order differential equations.? |
| 02.10.2012 | NCF? | ? | 2nd order differential equations? | This lecture will introduce second-order differential equations and give the solution for some cases. FMEA 6.1—6.3; MAII 2.1–2.3? |
| 03.10.2012 | NCF? | ? | 2nd order differential equations? | More on second-order differential equations. Trigonometric functions. FMEA 6.1—6.4; MAII 2.1–2.3, 2.6? |
| 04.10.2012 | NCF? | *Maths 2 for review*? | 1st order diff.eq's: directional diagrams? | Maths 2 lecture for review Graphical representation of 1st order differential equations. May or may not be relevant to Maths 3's treatment on phase diagrams. FMEA 5.2? |
Week 41 is teaching-free. No lectures nor seminars this week.
| Date | Teacher | Place | Topic | Lecture notes / comments |
| 16.10.2012 | NCF? | ? | Systems of differential equations I? | This week's lecture will cover systems of linear differential equations. A subsequent lecture (the 30th) will give a linear algebra-based approach to the generic case. FMEA 6.5—6.7 / MAII 2.7–2.9? |
| 17.10.2012 | NCF? | ? | Systems of differential equations II? | As Tuesday? |
| 23.10.2012 | BD? | ? | Linear independence and rank; Linear equations systems? | This lecture will cover some results from linear algebra, with applications e.g. to superfluous equations in equation systems. FMEA 1.2—1.4 (1.3—1.5 in 1.ed) / LA 7.1, 7.4, 8.1, 10.1? |
| 24.10.2012 | BD? | ? | Eigenvectors and eigenvalues? | Given a square matrix A. Question: for what vectors x does there exist a number λ such that Ax = λx? These (eigen-)vectors and numbers (eigenvalues) have applications to be covered in the subsequent lecture. FMEA 1.5, 1.7 (1.6, 1.8 in 1.ed) / LA 10.3, 10.5 ? |
| 30.10.2012 | BD? | ? | Eigenvectors and eigenvalues: applications? | Eigenvectors and eigenvalues will be applied to two different problems known from earlier in the course:
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| 31.10.2012 | BD? | ? | Difference equations? | Discrete-time evolutionary equations: tomorrow's state = function of past (1st order: function merely of today's state). FMEA 11.1, 11.3, 11.4 / MAII 9.1–9.3, 9.4 ? |
| 06.11.2012 | BD? | ? | Difference equations. Dynamic programming.? | To be introduced: the problem of dynamic optimization where a difference equation depends on a parameter of our choice. Applications to consumption/saving trade-off. FMEA 11.4, 12.1 / MAII 9.4, 10.1? |
| 07.11.2012 | BD? | ? | Dynamic programming.? | This lecture will conclude the dynamic programming topics. Proof by induction may be covered if not done already, subject to time. FMEA 12.1—12.3; MAII 10.1, 10.3, 10.5? |
| 13.11.2012 | NCF? | ? | Calculus of variations? | The historical approach to continuous-time dynamic optimization. FMEA 8.1—8.4 / MAII 11.1–11.4? |
| 14.11.2012 | NCF? | ? | Optimal control theory I? | Continuous-time dynamic optimization. FMEA 9.1—9.4 / MAII 12.1–12.4? |
| 20.11.2012 | NCF? | ? | Optimal control theory II? | FMEA 9.5—9.7 / MAII 12.5–12.7? |
| 21.11.2012 | NCF? | ? | Optimal control theory III? | FMEA 9.8—9.9 / MAII 12.8–12.9 ? |
| 06.12.2012 | ? | ? | Extra lecture: Review?? | (This was at December 6th)? |