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, and a more complete list will be available well before the exam (not all parts of all sections will be included in the curriculum).
| Date: | Topic: | [FMEA]: |
| Aug 26 0800-1045 : C1-060 |
Lecture 1: Eivind Eriksen Linear systems; Gaussian elimination; Rank of a matrix |
[LSGE] Ch. 1 - 3 |
| Sep 01 1700-1945 : C1-010 |
Lecture 2: Eivind Eriksen Matrices; Matrix algebra; Minors and rank |
Ch. 1.1, 1.3 - 1.4, 1.9 |
| Sep 02 0800-1045 : C1-060 |
Lecture 3: Eivind Eriksen Vectors; Linear independence; Linear independence and rank |
Ch. 1.1 - 1.3 |
| Sep 09 0800-1045 : C1-060 |
Lecture 4: Eivind Eriksen Eigenvalues and Eigenvectors; Diagonalization |
Ch. 1.5 - 1.6 |
| Sep 16 0800-1045 : C1-060 |
Lecture 5: Eivind Eriksen Quadratic Forms; Quadratic forms with linear constraints |
Ch. 1.7 - 1.8 |
| Sep 23 0800-1045 : C1-060 |
Lecture 6: Eivind Eriksen Convex and Concave functions; Hessians |
Ch. 2.2 - 2.3 |
| Sep
30 1400-1500 |
Midterm: Midterm 30/09/2011 - Solutions to Midterm 30/09/2011 Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures. Helpful notes on How to find out if a matrix is diagonalizable and How to sketch a subset of the plane Midterm Sep 2010: Midterm 24/09/2010 - Solutions to Midterm 24/09/2010 Mock Midterm Sep 2010: Mock Midterm 17/09/2010 - Solutions to Mock Midterm 17/09/2010 Re-take Midterm May 2011: Midterm 24/05/2011 - Solutions to Midterm 24/05/2011 |
|
| Oct 07 0800-1045 : C1-060 |
Lecture 7: Eivind Eriksen Extreme points; Lagrange Problems |
Ch. 3.1 - 3.3 |
| Oct 14 0800-1045 : C1-060 |
Lecture 8: Dag Einar Sommervoll Bordered Hessians; Envelope Theorems; Kuhn-Tucker problems |
Ch. 3.4 - 3.6 |
| Oct 21 0800-1045 : C1-060 |
Lecture 9: Dag Einar Sommervoll Kuhn-Tucker problems; Differential equations |
Ch. 5.1 - 5.3 |
| Oct 28 0800-1045 : C1-060 |
Lecture 10: Dag Einar Sommervoll First order differential equations |
Ch. 5.4 - 5.7 |
| Nov 04 0800-1045 : C1-060 |
Lecture 11: Dag Einar Sommervoll Second order linear differential equations |
Ch. 6.1 - 6.4 |
| Nov 11 0800-1045 : C1-060 |
Lecture 12: Eivind Eriksen Difference equations |
Ch. 11.1 - 11.4 |
| Nov 18 0800-1045 : C1-060 |
Lecture 13: Eivind Eriksen Difference equations, Revision (with emphasis on constrained optimization) |
Ch. 6.4, 11.4 |
| Dec
12 0900-1200 |
Final
exam: Final Exam 12/12/2011 - Solutions to Final Exam 12/12/2011 Relevant material for final exam: All lectures and all exercise problems. |
|
| Jan 25 0800-1045 : C2-060 | Extra Lecture 1: Eivind Eriksen Optimalization problems: Computing derivatives and Hessians, finding stationary point, classifying stationary points | |
| Jan 26 1700-1945 : C2-040 | Extra Lecture 2: Eivind Eriksen Optimalization problems: Determining if functions are convex/concave, finding points that satisfy first order conditions and constraints | |
| Jan 27 1400-1645 : C2-080 | Extra Lecture 3: Eivind Eriksen Matrices: Computing determinants and ranks, finding eigenvectors and eigenvalues, determine if a matrix is diagonalizable | |
| Feb 01 0800-1045 : C2-040 | Extra Lecture 4: Eivind Eriksen Matrices: Checking eigenvectors; Differential equations: Linear, separable, linear with non-constant coefficients, exact | |
| Feb 02 1700-1945 : C2-060 | Extra Lecture 5: Eivind Eriksen Difference equations: Linear. Lagrange problems. | |
| Feb 03 1400-1645 : C2-060 | Extra Lecture 6: Eivind Eriksen Optimalization problems: Constrained problems (Langrange, Kuhn-Tucker, bordered Hessian). Solutions to Problems. | |
| Feb 06 2012 1800-2100 | Extra Final
exam Re-take: Final Exam 06/02/2012 - Solutions to Final Exam 06/02/2012 Relevant material for final exam: All lectures and all exercise problems. | |
| Feb 07 2012 1500-1600 | Extra Midterm Re-take: Midterm 07/02/2012 - Solutions to Midterm 07/02/2012 Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures. | |
| Apr 19 2012 0900-1000 |
Midterm Re-take: Midterm 19/04/2012 - Solutions to Midterm 19/04/2012 Relevant material for Midterm: Lecture 1-6 and Exercise problems from these lectures. |
|
| June 06 2012 0900-1200 |
Final
exam Re-take: Final Exam 06/06/2012 - Solutions to Final Exam 06/06/2012 Relevant material for final exam: All lectures and all exercise problems. |
|
| Date: | Lecture: | Exercise Problems: |
| Lecture 1 | Problem Sheet 1: Problem 1 - 18 | |
| Lecture 2 | Problem Sheet 2: Problem 1 - 25 | |
| Lecture 3 | Problem Sheet 3: Problem 1 - 15 | |
| Lecture 4 | Problem Sheet 4: Problem 1 - 12 ; Optional Problems 13 - 15 | |
| Sep 15 1700-1945 : C1-060 | Problem Session 1: Eivind Eriksen Selected Problems from Problem Sheet 1-3 Handwritten notes from class | Problem Sheet 1: 8, 12c, 14, 16 Problem Sheet 2: 11, 16d, 18b, 19, 20b, 23 Problem Sheet 3: 5, 6, 7, 11, 12, 14 |
| Lecture 5 | Problem Sheet 5: Problem 1 - 10 | |
| Lecture 6 | Problem Sheet 6: Problem 1 - 12 (figures from the textbook for Problem 1 and 3) | |
| Sep 29 1700-1945 : C1-060 | Problem Session 2: Eivind Eriksen Selected Problems from Problem Sheet 4-6: Handwritten notes from class | Problem Sheet 4: 2a, 3b, 5, 9 Problem Sheet 5: 4, 5, 10 Problem Sheet 6: 2acf, 4 |
| Lecture 7 | Problem Sheet 7: Problem 1 - 14 | |
| Oct 13 1700-1945 : C1-010 | Problem Session 3: Dag Einar Sommervoll Selected Problems from Problem Sheet 7: Handwritten notes from class | Problem Sheet 5: 6, 7 Problem Sheet 6: 7, 8, 9 Problem Sheet 7: 1, 2, 3, 4, 9, 12, 13, 14 |
| Lecture 8 | Problem Sheet 8: Problem 1- 8 | |
| Oct 20 1700-1945 : C1-060 | Problem Session 4: Dag Einar Sommervoll Selected Problems from Problem Sheet 7-8: Handwritten notes from class | Problem Sheet 7: 10, 11 Problem Sheet 8: 1, 9 |
| Lecture 9 | Problem Sheet 9: Problem 1 - 5 (Problem 4-5 are repeated from Problem Sheet 8) | |
| Lecture 10 | Problem Sheet 10: Problem 1 - 10 | |
| Nov 03 1700-1945 : C1-060 | Problem Session 5: Dag Einar Sommervoll Selected Problems from Problem Sheet 9-10: Handwritten notes from class | Problem Sheet 9: 5 Problem Sheet 10: 2, 3cd, 5, 6, 7b, 8 |
| Lecture 11 | Problem Sheet 11: Problems 1 - 11 | |
| Lecture 12 | Problem Sheet 12: Problems 1 - 13 | |
| | Lecture 13 | Problem Sheet 13: Problem 1 - 3 For solutions, see lecture notes for Lecture 13: |
| Nov 21 - Note date! 1700-1945 : C1-060 | Problem Session 6: Eivind Eriksen Selected Problems from Problem Sheet 11-12: Handwritten notes from class | Problem Sheet 11: 3, 6a, 7, 8, 9 Problem Sheet 12: 6c, 8, 10ad, 11, 12 |