GRA6035 Mathematics - 2012/13

Reading

Sydsæter, Hammond, Seierstad, Strøm: Further Mathematics for Economic Analysis, 2nd Edition, Prentice Hall 2008 [FMEA] - Compulsory reading
Eriksen: Linear Systems and Gaussian Elimination, Handout, 2011 [LSGE] - Compulsory reading

Simon, Blume: Mathematics for Economists, International Student Edition, Norton 1994 [ME] - Covers prerequisites (Ch. 1-5, A4) and parts of the material for the course
Strøm, Sydsæter, Seierstad, Hammond: Student's Manual for [FMEA] - Solutions to selected problems (marked SM = Student Manual)
Eriksen, Gustavsen: GRA6035 Mathematics, Manuscript, 2009-2010 - Lecture Notes for GRA6035 Mathematics used in 2009-2010 (including Problems and Exam Problems with Solutions)

All material covered by the lectures and problems is part of the curriculum for GRA 6035 Mathematics, and is relevant for the final exam. All material covered by Lecture 1-6 and all problems corresponding to these lectures is relevant for the midterm exam. The list of sections in [FMEA] in the Lecture Plan below is indicative of the curriculum of the course.

Lecture Plan

The lecture plan is tentative, and may be changed/updates during the semester. In some cases, only parts of the sections indicated in the Reading column is required for this course. Lecture notes and Problem Sheets will be uploaded as they become available (typically soon after the corresponding lecture). I have office hours Monday 12.00 - 14.00 in my office B4-032.

Date:	Topic:	Reading:	Problems:
Aug 23 0800-1045 : C1-060	Lecture 1 Linear systems; Gaussian elimination; Rank of a matrix	[LSGE] 1 - 3 [ME] 6.1, 7.1 - 7.4	Problem Sheet 1
Aug 30 0800-1045 : C1-060	Lecture 2 Matrices; Matrix algebra; Minors and rank	[FMEA] 1.1, 1.3 - 1.4 (1.9) [ME] 8.1 - 8.2, 8.4, 9.1 - 9.2	Problem Sheet 2
Sep 06 0800-1045 : C1-060	Lecture 3 Vectors; Linear independence; Linear independence and rank	[FMEA] 1.1 - 1.3 [ME] 10.1 - 10.3, 11.1 - 11.2	Problem Sheet 3
Sep 18 1700-1945 : C1-060	Lecture 4 Eigenvalues and Eigenvectors; Diagonalization	[FMEA] 1.5 - 1.6 [ME] 23.1 - 23.4, 23.7, 23.9	Problem Sheet 4 Solution Ex. 13-15
Sep 20 0800-1045 : C1-010	Lecture 5 Quadratic Forms; definiteness	[FMEA] 1.7 (1.8) [ME] 13.3, 16.1 - 16.2, 23.8	Problem Sheet 5
Oct 04 0800-1045 : C1-060	Lecture 6 - Note on Sets and Topoogy Convex sets; Convex and Concave functions; Hessians	[FMEA] 2.2 - 2.3 [ME] 12.3 - 12.5, 14.8, 21.1	Problem Sheet 6 Figures for Problem 1,3
Oct 11 0800-1045 : C1-060	Lecture 7 Extreme points; Lagrange Problems	[FMEA] 3.1 - 3.3 [ME] 17, 18.1 - 18.2, 21.2	Problem Sheet 7
Oct 12 1400-1500	Midterm Exam: Midterm 12/10/2012 - Solutions Midterm 12/10/2012 (Corrected) Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures.	Midterm Exam 09/2011 - Solutions More midterm exams are available from last year's course page
Oct 18 0800-1045 : C1-060	Lecture 8 Lagrange Problems; Envelope Theorems	[FMEA] 3.1, 3.3 - 3.4 [ME] 19.1 - 19.4	Problem Sheet 8
Oct 25 0800-1045 : B1-030	Lecture 9 Bordered Hessians, Kuhn-Tucker problems	[FMEA] 3.5 - 3.6 [ME] 18.3, 18.6	Problem Sheet 9
Nov 01 0800-1045 : C1-060	Lecture 10 - Review of integration - Integration problems Kuhn-Tucker example. First order differential equations. Separable.	[FMEA] 5.1 - 5.3 [ME] 24.1 - 24.2	Problem Sheet 10
Nov 08 0800-1045 : C1-060	Lecture 11 Linear and Exact differential equations. Second order linear differential equations	[FMEA] 5.4 - 5.7, 6.1 - 6.4 [ME] 24.3 - 24.4	Problem Sheet 11
Nov 15 0800-1045 : C1-060	Lecture 12 Second order linear differential equations. Difference equations	[FMEA] 6.1 - 6.4, 11.1 - 11.4 [ME] 23.2	Problem Sheet 12
Nov 22 0800-1045 : C1-060	Lecture 13 Difference equations. Stability. Revision of the course.	[FMEA] 11.3 - 11.4, 6.4 [ME] 23.2	Revision Problems Solutions Problem 3-4
Dec 10 1400-1645 : C1-000	Extra Problem Session Mock Exam - Solutions
Dec 13 0900-1200	Final exam: Final 13/12/2012 - Solutions Final 13/12/2012 Relevant material for final exam: All lectures and all exercise problems.

	Exam Problems A collection of earlier exam problems and mock exams in GRA6035
Apr 19 2013	Re-sit Midterm Exam: Midterm 19/04/2013 - Solutions Midterm 19/04/2013 Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures.
Jun 11 2013	Re-sit Final Exam: Final 11/06/2013 - Solutions Final 11/06/2013 Relevant material for final exam: All lectures and all exercise problems.

Problem Sessions

Date:	Lecture:	Problems:
Oct 02 1700-1945 : C2-060	Problem Session I Group 1	Problems - Solutions
Oct 09 1700-1945 : C2-060	Problem Session I Group 2	Problems - Solutions
Oct 16 1700-1945 : C2-060, C2-055	Problem Session II Group 1	Problems - Solutions (only part of Extra Lecture 2 and the exam problem is relevant in Solutions)
Oct 23 1700-1945 : C2-060, C2-055	Problem Session II Group 2
Nov 13 1700-1945 : C2-060, C2-055	Problem Session III Group 1	Problems - Solutions - More detailed solutions for Kuhn-Tucker problems
Nov 20 1700-1945 : C2-060, C2-065	Problem Session III Group 2