Math 202: Multivariable Calculus for Economists

This is the webpage for the Fall 2018 manifestation of Dr. Fitzpatrick's section of Math 202 at Duke University.

Exercises marked [SB k] refer to the kth page of Simon and Blume.

Exercises marked [W k] refer to the kth page of Whitman Calculus.

Exercises marked [AP] are additional problems written by me. Solutions to these problems will not be posted.

Date Started Topic Exam Quiz Exercises
Tue 28-Aug 2018 Welcome!      
Tue 28-Aug 2018 Points and Vectors in \(\Bbb R^n\) I, F 1 [SB 204] 1, 3, 4; [W 302] 1, 6, 13; [W 306] 1-11
Thu 30-Aug 2018 The Dot Product I, F 1 [SB 220] 10-13, 15, 20, 22; [W 312] 1-5, 6-101, 16-19, 23
Tue 04-Sep 2018 The Cross Product I, F 2 [SB 221] 23(f); [W 316] 1-8
Thu 06-Sep 2018 Lines in \(\Bbb R^n\) I, F 2 [SB 225] 29, 31; [W 321] 7, 10, 12-15, 17, 21, 22
Thu 06-Sep 2018 Planes in \(\Bbb R^n\) I, F 3 [SB 230]2 32, 34 (c, d), 35 (c, d), 36, 38-40; [W 321] 1-6, 8-9, 16
Tue 11-Sep 2018 Systems of Linear Equations II, F 3 [SB 128] 23, 3, 7; [SB 133] 10, 12; [SB 140] 15-18; [SB 149] 20, 21, 23
Tue 18-Sep 2018 The Theory of Endogenous and Exogenous Variables II, F 4 [S 151] 25, 304; [AP]
Tue 25-Sep 2018 Matrix Algebra II, F 4 [SB 159] 1-5; [SB 161] 6, 7; [AP]
Tue 25-Sep 2018 The Algebra of Square Matrices II, F 5 [SB 172] 15, 18, 195, 20, 22, 25(c, d), 27(c), 28; [SB 193] 6, 76, 97; [SB 196] 11-14; [AP]
Tue 02-Oct 2018 Linear Independence II, F 5 [SB 243] 2, 3, 6; [AP]
Thu 04-Oct 2018 IS-LM Analysis II, F 5 [SB 198] 15, 17
Thu 04-Oct 2018 Linear Subspaces of \(\Bbb R^n\) II, F 6 [SB 246] 9, 10; [SB 755] 1-4
Thu 11-Oct 2018 Bases and Dimension of Linear Subspaces II, F 7 [SB 249] 12, 14; [SB 771] 12; [SB 764] 10; [AP]
Tue 16-Oct 2018 Functions Between Euclidean Spaces II, F 7 [SB 286] 28, 9(a, b, c), 10
Tue 16-Oct 2018 Special Kinds of Functions II, F 7 [SB 292] 11, 12, 15; [SB 299] 23, 24; [AP]
Tue 23-Oct 2018 Partial Derivatives III, F 7 [SB 302] 1, 2; [SB 322] 18-20; [W 363] 1-7, 16, 17; [W 370] 1-6, 9, 10, 21(a, b); [W 372] 1-7, 10-12
Tue 30-Oct 2018 Linear Approximations III, F 8 [SB 307] 4(a, b)9; [SB 312] 6(a, b, c), 7-10; [SB 319] 15, 16; [W 338] 4, 5, 10-13; [AP]
Tue 30-Oct 2018 The Multivariable Chain Rule III, F 8 [SB 318] 11, 13, 14; [SB 327] 21, 22; [W 366] 1-4; [AP]
Tue 06-Nov 2018 Implicit Functions III, F 9 [SB 342] 1, 3-9
Thu 08-Nov 2018 Systems of Implicit Functions III, F 9 [SB 358] 16-24
Tue 13-Nov 2018 Definiteness of Quadratic Forms III, F 10 [SB 386] 1, 2; [SB 392] 6
Thu 15-Nov 2018 Unconstrained Optimization III, F 10 [SB 402] 1, 2 (check your answers!)
Tue 20-Nov 2018 Constrained Optimization F 10 [SB 423] 2, 3; [W 382] 5, 8, 10, 13, 14, 16; [AP] (check your answers!)
Tue 27-Nov 2018 Double Integrals F 10 [W 393] 1, 2, 5, 6; [AP] (check your answers!)
Tue 04-Dec 2018 Examples of Double Integrals F   [W 393] 3, 4, 9-13, 32(a, b, d, e) (check your answers!)
Tue 04-Dec 2018 Practice Problems F    

Footnotes:

1 Don't use a calculator, just give a symbolic answer.
2 Simon and Blume call a "point-normal equation" for a plane a "nonparametric equation."
3 Just use elimination.
4 Answer in the back is wrong!
5 If \(A^{-1}\) exists, then write \(A^{-1}\) as a product of elementary matrices.
6 Ignore Theorem 9.2. Compute each determinant using elementary row operations as we did in class.
7 Again, ignore Theorem 9.2. Compute each determinant using elementary row operations as we did in class
8 Draw the level sets only, not the graphs.
9 "marginal analysis" means "linear approximation"