Department of Economics / Nils Framstad, room 1133, ES

ECON3120/4120 Mathematics 2, fall term 2007 – rev. Feb 13
“Lecture-free week” split between March 14 (last Friday before Easter) and March 25 (first Tuesday after Easter) for lectures, and week 10 for seminars. Please keep an eye on the ECON4120 home page, http://www.uio.no/studier/emner/sv/oekonomi/ECON4120/v08/
Lectures, starting week 3 (Jan. 15):  
Tuesday	08.15—10.00, auditorium 2, ES, and
Friday		14.15—16.00, auditorium 2, ES
except: Friday Jan. 18 and Friday March 14 through Tuesday March 25.
Seminars, starting week 6 (Feb. 4):
Seminar 1:	Monday	10:15—12:00, Grupperom 4 Georg Sverdrups hus, or
Seminar 2:	Wednesday 	10:15—12:00, Seminarrom 150 Harriet Holters hus, or
Seminar 3:	Thursday 	16:15—18:00, Seminarrom 150 Harriet Holters hus
Seminar leader all seminars: Li Zhang. No seminars during week 10.
Exam
June 3, 09.00—12.00. Closing date May 20.
Note: In order to be allowed to sit for the exam, you must complete two compulsory term papers (problem sets) satisfactorily. See schedule below for deadlines.
Curriculum
The curriculum includes the curriculum of the mathematics part of the course ECON2200 Mathematics I/Micro I. You do not need both the English and Norwegian books! 
Reading list for English speaking students:
•	“EMEA”:  K. Sydsæter and P. Hammond: Essential Mathematics for Economic Analysis, 2nd ed., FT Prentice Hall (2006).  The entire book, except Sections 10.5—10.7 and 16.9 and Chapter 17.  (You can also use the first edition from 2002:  The entire book, except Sections 10.5—10.7 and 16.9.)
•	“FMEA”:  Knut Sydsæter, Peter Hammond, Atle Seierstad, and Arne Strøm:  Further Mathematics for Economic Analysis, FT Prentice Hall (2005).  Sections 5.1—5.4 and selected parts of Sections 3.5—3.8.
Reading list for Norwegian speaking students: 
•	”MA1”: Knut Sydsæter: Matematisk analyse, bind 1, 7. utg., Gyldendal Akademisk (2000). Pensum er kapitlene 1–14 og appendiks A, med unntak av avsnittene 6.7, 6.9, 8.5–8.7, 10.5, 12.8 og A.4. 
•	”MA2”: Knut Sydsæter, Atle Seierstad og Arne Strøm: Matematisk analyse, bind 2, 4. utg., Gyldendal Akademisk (2002). Pensum er avsnittene 1.1–1.4 og utvalgte deler av avsnittene 8.7–8.11.
•	”LA”: Knut Sydsæter og Bernt Øksendal: Lineær algebra 4. utg., Universitetsforlaget (1996). Pensum er avsnittene 2.1–2.4, 2.6, 3.1–3.5, 4.1, 5.1–5.5, 6.1–6.3.
Som støttelitteratur med litt annen fremstilling, kan man eventuelt laste ned heftet Flervariabel analyse med lineær algebra fra kurssiden i MAT1110 (”FAMLA”), se referanser i planen nedenfor.

Schedule (updated Feb 13, still with reservations for changes)

Tue 15. Jan	Exponential and logarithmic functions.  (Review.) 
EMEA 4.9—4.10, 6.10—6.11
MA1 3.9–3.10, 5.10–5.11	
Fri 18. Jan	No lecture	
Tue 22. Jan	Compound interest and present values. Indefinite expressions.
EMEA 7.12, 10.1—10.3
MA1 6.5, 8.1–8.3	
Fri 25. Jan	Implicit differentiation. Slopes of level curves. (Review.) 
EMEA 12.1—12.4, 
MA1 12.1–12.2; 	
Tue 29. Jan	Limits and continuous functions. The intermediate value theorem 
EMEA 7.8—7.11, 9.1—9.4
MA1 MA1 6.1–6.4, 6.6, 6.8, 10.1–10.4	
Fri 01. Feb	Integration and methods of integration. 
EMEA 9.1—9.6
MA1 10.1–10.4, 10.6–10.7	
Tue 04. Feb	Methods of integration.
EMEA 9.5—9.6
MA1 10.6–10.7	
Fri 08. Feb	Extensions of the integral concept.
EMEA 9.7
MA1 10.9	
Tue 11. Feb	First-order differential equations.  Separable differential equations.  
EMEA 9.8,  FMEA 5.1—5.3
MA1 10.10, MA2 1.1–1.3	
Fri 15. Feb	Separable and linear differential equations.
FMEA 5.3—5.4
MA2 1.3–1.4 

Term paper 1 announced	
Tue 19. Feb	Linear differential equations.
FMEA 5.4
MA2 1.4	
Fri 22. Feb	Vectors. Scalar products.  Straight lines and planes.
EMEA 15.7—15.9
LA  2.1–2.4, 2.6 (støttelitt.: FAMLA 1.1–1.2 og s. 30 i 1.4)	
Tue 25. Feb	Matrices.
EMEA 15.1—15.4
LA 3.1–3.4 (støttelitt.: FAMLA 1.5–1.6)	
Fri 29. Feb	Matrices.  Gaussian elimination.
EMEA 15.5—15.6
LA 3.5, 4.1 (støttelitteratur: FAMLA 1.5–1.6, 4.1–4.4)	
Week 10	Lectures as usual, but no seminars.	
Tue 04. Mar	Determinants.
EMEA  16.1—16.3 
LA 5.1–5.3 (støttelitt.: FAMLA 1.8 unntatt kryssprodukt/orientering) 	
Thu 06. Mar	Deadline, term paper 1, at 1400 hours	
Fri 07. Mar	Determinants. Inverse matrices.
EMEA 16.4—16.6
LA 5.4–5.5, 6.1 (støttelitt.: FAMLA 1.8 s. 68 unntatt orientering, 4.5; 1.7, 4.9)	
Tue 11. Mar	Inverse matrices. Cramer’s rule. 
EMEA 16.7—16.8
LA 6.2–6.3 (støttelitt.: FAMLA 1.7, 4.5, 4.9; Cramers regel i oppgave 4.9.11)	
Fri 14. Mar	No lecture	
Week 12	Easter (no lectures nor seminars)	
Tue 25. Mar	No lecture	
Fri 28. Mar	Chain rules and differentials revisited. Differentiation in equation systems. 
EMEA 7.1—7.3, 12.8—12.11
MA 1 11.9–11.10, 12.4–12.6	
Tue 01. Apr	Homogeneous and homothetic functions.
EMEA 12.6—12.7
MA1 11.12–11.13	
Fri 04. Apr	Maxima and minima. Review. 
EMEA 8.1—8.7, 13.1—13.2
MA1  9.1–9.7 (kort repetisjon), 13.1–13.4	
Tue 08. Apr	Maxima and minima.  Envelope theorem.
EMEA 13.3—13.7
MA 13.5–14.6	
Fri 11. Apr	Constrained maxima and minima.  Review. 
EMEA 14.1—14.4
MA1  14.1–14.4

Term paper 2 announced	
Tue 15. Apr	Constrained maxima and minima.  Envelope theorem.
EMEA 14.5—14.6
MA1  14.5–14.6	
Fri 19. Apr	Nonlinear programming.
EMEA 14.7
Deler av MA2  8.7–8.8, 8.10–8.11	
Tue 22. Apr	Nonlinear programming.
EMEA 14.8.
Deler av MA2  8.7–8.8, 8.10–8.11.	
Fri 25. Apr	Linear and quadratic approximation. Taylor’s formula.
EMEA 7.4—7.6.
MA1 7.3–7.6	
Mon 28. Apr	Deadline, term paper 2, at 1400 hours.	
Tue 29. Apr	Elasticities.  Elasticity of substitution. Finding elasticities of implicit functions.
EMEA 7.7, 11.8, 12.5
MA1 5.12–5.13, 11.11, 12.7	
Fri 02. May 	No lecture unless needed	
Tue 06. May	Final review and summing up, possibly with term paper 2 covered.