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102Syll0809Spring
Course: MATH 102, Fall 2008School: Duke
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for Syllabus Math 102, Spring '08-'09, Clark Bray Mathematics for Economists, Simon and Blume; Notes on Integrals for Math 102, Bray (Note: New homework problems will be added throughout semester; be sure you are looking at a current version!) Linear Algebra (S&B) 7.1 - Gaussian and Gauss-Jordan Elimination 7.2 - Elementary Row Operations 7.3 - Systems With Many or No Solutions 7.4 - Rank - The...
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for Syllabus Math 102, Spring '08-'09, Clark Bray
Mathematics for Economists, Simon and Blume; Notes on Integrals for Math 102, Bray (Note: New homework problems will be added throughout semester; be sure you are looking at a current version!)
Linear Algebra (S&B)
7.1 - Gaussian and Gauss-Jordan Elimination 7.2 - Elementary Row Operations 7.3 - Systems With Many or No Solutions 7.4 - Rank - The Fundamental Criterion 7.5 - Linear Implicit Function Theorem 8.1 - Matrix Algebra 8.2 - Special Kinds of Matrices 8.3 - Elementary Matrices 8.4 - Algebra of Square Matrices 9.1 - Determinant of a Matrix 9.2 - Uses of the Determinant 9.3 - IS-LM Analysis via Cramer's Rule 10.1 - Points and Vectors in Euclidean Space 10.2 - Vectors 10.3 - Algebra of Vectors 10.4 - Length and Inner Product in R^n 10.5 - Lines 10.6 - Planes 10.7 - Economic Applications 11.1 - Linear Independence 11.2 - Spanning Sets 11.3 - Basis and Dimension in R^n Exercises: 3, 7, 8 Exercises: 9, 10, 11, 12 Exercises: 15, 16, 17, 18, 19 Exercises: 21, 23, 24 Exercises: 25, 29, 30 Exercises: 1, 3, 4(once), 5b Exercises: 7, 9, 10 Exercises: 12, 14 Exercises: 18, 19ad, 20c, 21, 23, 28 Exercises: 5, 6, 9 Exercises: 11, 13b, 14b Exercises: 17 Exercises: Exercises: 3, 4 Exercises: 8, 9 Exercises: 10a, 11b, 13, 19, 20, 24, 25, 26 Exercises: 27, 29, 31 Exercises: 32, 34, 37, 39, 40, 41 Exercises: Exercises: 1, 3, 4, 5b, 6, 7, 8 Exercises: 9, 10 Exercises: 14 Exercises: Exercises: 1, 2, 3, 6, 9, 10, AHP(1,2) Exercises: 11, 12, 14, 15, AHP(3) Exercises: Exercises: 22, 23(largest possible domain; let range = R^1), 24 Exercises: 1, 2 Exercises: Exercises: 3, 4, 5a Exercises: 7, 8, 9, 10 Exercises: 11, 12, 13, 14, 15, 16, 17 Exercises: 18, 19, 20 Exercises: 21(error in solutions), 22 Exercises: 1, 2, 5, 6, 7, 9 Exercises: 11, 10, 12, 13 Exercises: 15, 16, 17, 18, 19, 20, 21, 24 Exercises: 31 Exercises: 35, 36, 37, 38, 39 Exercises: Exercises: 1, 2, 3, 4 Exercises: 6c Exercises: Exercises: Exercises: Exercises: 4, 6, 7, 8, 11 Exercises: Exercises: 2, 4, 5, 6, 7, 8 Exercises: 10, 11, 14 Exercises: 15 (`<=37' not `>=37') Exercises: BEW(1,2) Exercises: ALJ(1, 2, 10, 11, 15, 23, 24), BEW(1, 3) Exercises: ALJ(1, 2, 3, 6, 10, 19, 20, 23, 24), BEW(1, 3) Exercises: ALJ(2, 3, 4, 6, 7, 10, 11, 15, 16, 17) Exercises: BEW(2, 3, 5, 6, 7, 9, 10, 11, 13, 14) Exercises: BEW(1, 2, 5, 7, 8, 11, 12, 13, 15, 16, 17)
Calculus of Several Variables (S&B)
13.1 - Functions Between Euclidean Spaces 13.2 - Geometric Representations of Functions 13.3 - Special Kinds of Functions 13.4 - Continuous Functions 13.5 - Vocabulary of Functions 14.1 - Definitions and Examples 14.2 - Economic Interpretation 14.3 - Geometric Interpretation 14.4 - Total Derivative 14.5 - Chain Rule 14.6 - Directional Derivatives and Gradients 14.7 - Explicit Functions From R^n To R^m 15.1 - Implicit Functions a...
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Duke - MATH - 290
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Duke - MATH - 290
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Duke - MATH - 290
< minimal [ 2, 0, -1, -1 ; 0, 4, 2, 0 ; -1, 2, 10, 7 ; -1, 0, 7, 28 ] < 0 ; [ 64 , 56181887 ] ; [ ] ; [ ] > [ [ [ 4, 4, 0 ; 4, 38, 26 ; 0, 26, 110 ] ] , [ [ 2, -2, -1 ; -2, 36, 14 ; -1, 14, 28 ] ] ] [ [ < 0 ; [ 128
Duke - MATH - 290
< minimal [ 2, 0, -1, 0 ; 0, 4, 2, -2 ; -1, 2, 10, 4 ; 0, -2, 4, 28 ] < 0 ; [ 32 , 68417929 ] ; [ 2 ] ; [ ] > [ [ [ 4, 4, -2 ; 4, 38, 8 ; -2, 8, 28 ] ] , [ [ 2, -2, 0 ; -2, 36, 20 ; 0, 20, 108 ] ] ] [ [ < 0 ; [ 64 ,
Duke - MATH - 290
< minimal [ 2, 0, -1, -1 ; 0, 4, 2, 0 ; -1, 2, 10, 8 ; -1, 0, 8, 28 ] < 0 ; [ 64 , 125 , 357911 ] ; [ ] ; [ ] > [ [ [ 4, 4, 0 ; 4, 38, 30 ; 0, 30, 110 ] ] , [ [ 2, -2, -1 ; -2, 36, 16 ; -1, 16, 28 ] ] ] [ [ < 0 ; [
Duke - MATH - 290
< minimal [ 2, 0, -1, -2 ; 0, 4, 2, -4 ; -1, 2, 10, 0 ; -2, -4, 0, 28 ] < 0 ; [ 128 , 27 , 29791 ] ; [ ] ; [ ] > [ [ [ 4, 4, -4 ; 4, 38, -2 ; -4, -2, 26 ] ] , [ [ 2, -2, -2 ; -2, 36, 4 ; -2, 4, 24 ] ] ] [ [ < 0 ; [
Duke - MATH - 290
< minimal [ 2, 0, -1, -1 ; 0, 4, 2, -1 ; -1, 2, 10, 0 ; -1, -1, 0, 28 ] < 0 ; [ 32 , 4913 , 1295029 ] ; [ ] ; [ ] > [ [ [ 4, 4, -2 ; 4, 38, -2 ; -2, -2, 110 ] ] , [ [ 2, -2, -4 ; -2, 36, 4 ; -4, 4, 444 ] ] , [ [ 12, 0,
Duke - MATH - 290
< minimal [ 2, 0, -1, -2 ; 0, 4, 2, -2 ; -1, 2, 10, 0 ; -2, -2, 0, 28 ] < 0 ; [ 32 , 625 , 4913 ] ; [ 2 ] ; [ ] > [ [ [ 4, 4, -2 ; 4, 38, -2 ; -2, -2, 26 ] ] , [ [ 2, -2, -4 ; -2, 36, 4 ; -4, 4, 108 ] ] , [ [ 12, 0, -6 ;
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10120103581298014061148631579216222171381793718441185781981720035206692249524485250752548927598295103153832636331143331134455356183807338307399594015041630425944351644775448154803048172501235018950212502165082
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1. d2. a3. d4. c5. c d6. LRUFIFO0xFFFFEE44mm0xA10C0450mm0xFFFFEE88mm0xC4444464mm0xA10C0440hh0x77777770mm0xFFFFEE7Chh0xBA000440mm0xFFFFEE68hm0xA10C046ChmMiss ratio60%80%
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