| Date | Teacher | Place | Topic | Lecture notes / comments |
| 22.08.2011 | ?
| ?
| Introduction to the course; Exponential and logarithmic functions (review); Interest and present values ?
| exp and ln: Basic properties will be reviewed. Read:
EMEA 4.9—4.10, 6.10—6.11 / MA1 3.9–3.10, 5.10–5.11.Interest rates ('annual' vs 'monthly' rate, 'annual' vs 'monthly' accumulation):
EMEA 10.1—10.3 / MA1 8.1–8.3 ?
|
| 24.08.2011 | ?
| ?
| Limits and continuity; Indefinite expressions.?
| Limits and continuity: EMEA 7.8—7.9 / MA1 6.1–6.3 .Indefinite expressions (limits that tend to '0/0' etc.):
EMEA 7.12 / MA1 6.4 (som var 6.5 i 7. utg).?
|
| 29.08.2011 | ?
| ?
| Elasticities. Elasticity of substitution. Finding elasticities of implicit functions.?
| EMEA 7.7, 11.8, 12.5 / MA1 5.12, 11.8, 12.5
(gml. utg.: 5.12–5.13, 11.11, 12.7) Note: This topic used to be at the very end of the course, but is now moved due to needs of other courses. The precise content might have to be adjusted.?
|
| 31.08.2011 | ?
| ?
| Maxima and minima. (Review.)?
| EMEA 8.1—8.7, 13.1—13.2 /
MA1 9.1–9.7 (kort repetisjon), 13.1–13.5 (ikke 13.5 i gml. utg.) ?
|
| 31.08.2011 | ?
| 1 hour of the Maths 3 lecture.?
| Maxima and minima: the extreme value theorem and the envelope theorem.?
| EMEA 13.3—13.7 / MA1 resten av kap. 13. ?
|
| 05.09.2011 | ?
| ?
| Constrained maxima and minima: Lagrange I (review.)?
| EMEA 14.1—14.4 /
MA1 14.1–14.4 ?
|
| 07.09.2011 | ?
| ?
| Lagrange's method: existence, sufficiency and sensitivity.?
| EMEA 14.5—14.7 / MA1 14.5–14.6, deler av MA2 8.7–8.8, 8.10–8.11 The ECON2200 conditions are of the 'necessary' type. There are some (not too strong!) sufficient conditions. Otherwise, we might try to apply the extreme value theorem to ensure existence. Sensitivity: another application of the envelope theorem.?
|
| 07.09.2011 | ?
| Maths 3 lecture: totally voluntary!?
| More on Lagrange's method?
| If you are interested -- but this is not exam relevant -- you might get an explanation on why Lagrange's method might break down, plus a more powerful set of sufficent conditions.?
|
| 12.09.2011 | ?
| ?
| Nonlinear programming: optimization under inequality constraints?
| EMEA 14.8—14.9 / deler av MA2 8.7–8.8, 8.10–8.11 Kuhn--Tucker's necessary conditions gives a bit more information than just solving for interior stationary points and then using Lagrange on the boundary.?
|
| 14.09.2011 | ?
| ?
| Nonlinear programming: optimization under inequality constraints?
| EMEA 14.8—14.9 / deler av MA2 8.7–8.8, 8.10–8.11 More Kuhn--Tucker. With sufficient conditions.?
|
| 14.09.2011 | ?
| 1 hour of the Maths 3 lecture?
| Nonlinear programming. The envelope theorem.?
| EMEA 14.8—14.9 / deler av MA2 8.7–8.8, 8.10–8.11 If the value function is differentiable, then the envelope theorem holds like in the Lagrange case, but differentiability much more often breaks down.?
|
| 19.09.2011 | ?
| ?
| The intermediate value theorem; Introduction to integration.?
| If f(a)<0<f(b) and f is continuous on [a,b], then it has a zero somewhere between a and b -- without the need to find it. Read: EMEA 7.10 (not Newton's method) / MA1 6.5 (ikke Newtons metode)Integration: If you know the function F', what is then F? References for this Monday and Wednesday: EMEA 9.1—9.6 / MA1 10.1–10.4, 10.6–10.7.?
|
| 21.09.2011 | ?
| ?
| Integration and methods of integration. ?
| EMEA 9.1—9.6 / MA1 10.1–10.4, 10.6–10.7?
|
| 26.09.2011 | ?
| ?
| First-order differential equations (separable and linear)?
| EMEA 9.8, FMEA 5.1—5.4 / MA1 10.10, MA2 1.1–1.4?
|
| 28.09.2011 | ?
| ?
| Differential equations cont'd?
| As Sep 23rd?
|
| 03.10.2011 | ?
| ?
| Differential equations cont'd.?
| As Sep. 23rd.?
|
| 05.10.2011 | ?
| *AUD 3 Helga Eng (next to the physics building)*?
| Extensions of the integral concept.?
| EMEA 9.7 / MA1 10.9?
|
Week 41 is teaching-free. No lectures nor seminars this week.
Week 42 will start off with linear algebra, which is something totally new and -- at least the first few weeks -- fairly easy.
| Date | Teacher | Place | Topic | Lecture notes / comments |
| 17.10.2011 | ?
| ?
| Vectors. Scalar products. Straight lines and planes w. applications to budget constraints. Possibly: introduction to matrices.?
| Vectors are introduced, first as 'lists of numbers' for book-keeping, then tools for manipulating. The scalar product as a total cost, and the hyperplane as a budget constraint.EMEA 15.7—15.9 / LA 2.1–2.4, 2.6 (st?ttelitt.: FAMLA 1.1–1.2)?
|
| 19.10.2011 | ?
| ?
| Matrices and matrix operations. Linear equation systems.?
| EMEA 15.1—15.4 / LA 3.1–3.4 (st?ttelitt.: FAMLA 1.5–1.6)?
|
| 24.10.2011 | ?
| ?
| Linear equations: Gaussian elimination. A bit about the inverse.?
| EMEA 15.5—15.6 / LA 3.5, 4.1 (st?ttelitteratur: FAMLA 1.5–1.6, 4.1, 4.5)?
|
| 26.10.2011 | ?
| ?
| Gaussian elimination. Introduction to determinants?
| EMEA 15.5—15.6, 16.1—16.3 / LA 3.5, 4.1 , 5.1–5.3 (st?ttelitt.: FAMLA 4.1--4.4, 1.8 unntatt kryssprodukt/orientering) ?
|
| 31.10.2011 | ?
| ?
| Determinants. Inverse matrices. Cramér's rule?
| EMEA 16.1—16.8 _ /
LA 5.1–5.5, 6.1–6.3 (st?ttelitt.: FAMLA 1.7, 1.8 unntatt orientering,, 4.5, 4.9; Cramers regel i oppgave 4.9.11)?
|
| 02.11.2011 | ?
| ?
| Remaining bits on equation systems and inverse matrices?
| ?
|
The course will now return to analysis topics, but some linear algebra will be utilized.
| Date | Teacher | Place | Topic | Lecture notes / comments |
| 07.11.2011 | ?
| ?
| Implicit differentiation. Slopes of level curves. (Review.) Chain rules and differentials.?
| EMEA 12.1—12.4 /
MA1 12.3-4
(gml utg: 12.1–12.2) ?
|
| 09.11.2011 | ?
| ?
| Chain rules and differentials. Differentiation in equation systems. ?
| The objective of this lecture is to enable you to find derivatives of functions given implicitly by systems of equations. This is one core topic of the course, despite being only one double lecture.EMEA 7.1—7.3, 12.8—12.11 /
MA1 kap 12 (gml utg: 11.9–11.10, 12.4–12.6) ?
|
| 14.11.2011 | ?
| ?
| Linear and quadratic approximation. Taylor’s formula.?
| EMEA 7.4—7.6 / MA1 7.4–7.6 (gml.utg.: ogs? 7.3)?
|
| 16.11.2011 | ?
| ?
| Homogeneous and homothetic functions.?
| EMEA 12.6—12.7 / MA1 12.6-12.7 (gml.utg.: 11.12–11.13) ?
|
| 21.11.2011 | ?
| ?
| Extra lecture: Review?
| I will put up some extra review lecture, but the time is up for discussion; the exam is as late as 15th of December.?
|