- Notice that some Maths 3 lectures are put up here, in order to offer you more teaching for the optimization part of the course. These Maths 3 lectures are indicated under the ?Place? heading (I do not have access to change headings). Maths 3 times are Tuesday 1015–1200, Wednesday 1215–1400, both in auditorium 2.
- In the references to Lecture notes / comments English: the ?EMEA? abbreviation is to the English ?Essential Mathematics for Economic Analysis?, 3rd or 4th edition. The references in slanted font is for those who choose to use the Norwegian books: MA1 (med ref. til 7. og 8. utgave), MA2, LA.
- This version October 28th, updated the October 29th lecture up past the November 1 message :-o
| Date | Teacher | Place | Topic | Lecture notes / comments |
| 20.08.2012 | BD? | ? | 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 ? |
| 23.08.2012 | BD? | ? | 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).? |
| 27.08.2012 | BD? | ? | 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.? |
| 30.08.2012 | NCF? | ? | 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.) ? |
| 03.09.2012 | NCF? | ? | Constrained maxima and minima: Lagrange I (review.)? | EMEA 14.1—14.4 / MA1 14.1–14.4 ? |
| 06.09.2012 | NCF? | ? | The extreme value theorem. Sufficiency with Lagrange's method? | EMEA 13.5, 14.5—14.7 / MA1 13.5, 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. ? |
| 10.09.2012 | NCF? | ? | Nonlinear programming: optimization under inequality constraints? | EMEA 14.8—14.9 (&14.10 in 4th ed.) / deler av MA2 8.7–8.8, 8.10–8.11 Kuhn--Tucker's necessary conditions give a bit more information than just solving for interior stationary points and then using Lagrange on the boundary.? |
| 12.09.2012 | NCF? | *Maths 3 lecture – recommended*? | Nonlinear programming? | This Maths 3 lecture will elaborate on Kuhn–Tucker's conditions. Recommended for Maths 2 students.? |
| 13.09.2012 | NCF? | ? | Nonlinear programming: sufficient conditions and sensitivity? | EMEA 14.8—14.9 (&14.10 in 4th ed.) / deler av MA2 8.7–8.8, 8.10–8.11 More Kuhn--Tucker. With sufficient conditions and sensitivity (the envelope theorem).? |
| 17.09.2012 | NCF? | ? | 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 week: EMEA 9.1—9.6 / MA1 10.1–10.4, 10.6–10.7.? |
| 18.09.2012 | NCF? | *Maths 3 lecture*? | Nonlinear programming. The envelope theorem.? | Maths 3 lecture. As previous Thursday, but more examples.? |
| 20.09.2012 | NCF? | ? | Integration and methods of integration. ? | EMEA 9.1—9.6 / MA1 10.1–10.4, 10.6–10.7? |
| 24.09.2012 | NCF? | ? | Integration and methods of integration. ? | EMEA 9.1—9.6 / MA1 10.1–10.4, 10.6–10.7? |
| 27.09.2012 | NCF? | ? | First-order differential equations (separable and linear)? | EMEA 9.8, FMEA 5.1—5.4 / MA1 10.10, MA2 1.1–1.4? |
| 01.10.2012 | NCF? | ? | Differential equations cont'd? | As Sep 27th? |
| 04.10.2012 | NCF? | ? | Differential equations cont'd.? | Reading list as Sep. 27th; this lecture will also cover graphical representation.? |
Week 41 is teaching-free. No lectures nor seminars this week.
The course will now switch to linear algebra topics.
| Date | Teacher | Place | Topic | Lecture notes / comments |
| 15.10.2012 | BD? | ? | 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)? |
| 18.10.2012 | BD? | ? | Matrices and matrix operations. Linear equation systems.? | EMEA 15.1—15.4 / LA 3.1–3.4 (st?ttelitt.: FAMLA 1.5–1.6)? |
| 22.10.2012 | BD? | ? | 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)? |
| 25.10.2012 | BD? | ? | 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) ? |
| 29.10.2012 | BD? | ? | Determinants. Inverse matrices. Possibly 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)? |
No lecture Nov. 1st.
| Date | Teacher | Place | Topic | Lecture notes / comments |
| 05.11.2012 | BD? | ? | Cramér's rule. Remaining topics – if any – 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 |
| 08.11.2012 | BD? | ? | 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) ? |
| 12.11.2012 | BD? | ? | 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) ? |
| 15.11.2012 | BD? | ? | Linear and quadratic approximation. Taylor’s formula.? | EMEA 7.4—7.6 / MA1 7.4–7.6 (gml.utg.: ogs? 7.3)? |
| 19.11.2012 | BD? | ? | Homogeneous and homothetic functions.? | EMEA 12.6—12.7 / MA1 12.6-12.7 (gml.utg.: 11.12–11.13) ? |
| 22.11.2012 | NCF? | ? | Leftovers from homogeneous and homothetic functions + extensions of the integral concept.? | The definite integral as we know it until now, is only well-defined 'inside a bounded box'. What happens if the function or the scope is unbounded? EMEA 9.7 / MA1 10.9? |
| 06.12.2012 | ? | ? | Extra lecture: Review? | I will put up some extra review lecture, but the time is up for discussion; the exam is 11th of December.? |