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 |
---|---|---|---|---|
Welcome! | ||||
Points and Vectors in \(\Bbb R^n\) | I, F | 1 | [SB 204] 1, 3, 4; [W 302] 1, 6, 13; [W 306] 1-11 | |
The Dot Product | I, F | 1 | [SB 220] 10-13, 15, 20, 22; [W 312] 1-5, 6-10^{1}, 16-19, 23 | |
The Cross Product | I, F | 2 | [SB 221] 23(f); [W 316] 1-8 | |
Lines in \(\Bbb R^n\) | I, F | 2 | [SB 225] 29, 31; [W 321] 7, 10, 12-15, 17, 21, 22 | |
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 | |
Systems of Linear Equations | II, F | 3 | [SB 128] 2^{3}, 3, 7; [SB 133] 10, 12; [SB 140] 15-18; [SB 149] 20, 21, 23 | |
The Theory of Endogenous and Exogenous Variables | II, F | 4 | [S 151] 25, 30^{4}; [AP] | |
Matrix Algebra | II, F | 4 | [SB 159] 1-5; [SB 161] 6, 7; [AP] | |
The Algebra of Square Matrices | II, F | 5 | [SB 172] 15, 18, 19^{5}, 20, 22, 25(c, d), 27(c), 28; [SB 193] 6, 7^{6}, 9^{7}; [SB 196] 11-14; [AP] | |
Linear Independence | II, F | 5 | [SB 243] 2, 3, 6; [AP] | |
IS-LM Analysis | II, F | 5 | [SB 198] 15, 17 | |
Linear Subspaces of \(\Bbb R^n\) | II, F | 6 | [SB 246] 9, 10; [SB 755] 1-4 | |
Bases and Dimension of Linear Subspaces | II, F | 7 | [SB 249] 12, 14; [SB 771] 12; [SB 764] 10; [AP] | |
Functions Between Euclidean Spaces | II, F | 7 | [SB 286] 2^{8}, 9(a, b, c), 10 | |
Special Kinds of Functions | II, F | 7 | [SB 292] 11, 12, 15; [SB 299] 23, 24; [AP] | |
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 | |
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] | |
The Multivariable Chain Rule | III, F | 8 | [SB 318] 11, 13, 14; [SB 327] 21, 22; [W 366] 1-4; [AP] | |
Implicit Functions | III, F | 9 | [SB 342] 1, 3-9 | |
Systems of Implicit Functions | III, F | 9 | [SB 358] 16-24 | |
Definiteness of Quadratic Forms | III, F | 10 | [SB 386] 1, 2; [SB 392] 6 | |
Unconstrained Optimization | III, F | 10 | [SB 402] 1, 2 (check your answers!) | |
Constrained Optimization | F | 10 | [SB 423] 2, 3; [W 382] 5, 8, 10, 13, 14, 16; [AP] (check your answers!) | |
Double Integrals | F | 10 | [W 393] 1, 2, 5, 6; [AP] (check your answers!) | |
Examples of Double Integrals | F | [W 393] 3, 4, 9-13, 32(a, b, d, e) (check your answers!) | ||
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"