Math 21b Homework Assignments

The homework assignments listed below are the assignments for MWF sections of Math 21b. The dates indicated are the dates the homework was assigned. The Tues-Thurs section has the same assigned problems, but grouped differently.

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HW #1 (Sept 25): Read section 1.1 of the text and do problems 1.1/11,16,17,20,29,36.

HW #2 (Sept 27): Read section 1.2 and do problems 1.2/6,9,20,33,37,42.

HW #3 (Sept 29): Read section 1.3 and do problems 1.3/1,14,25,34,48,50.

Solutions to HW #1 - HW #3

HW #4 (Oct 2): Read section 2.1 and do problems 2.1/5,8,24-30,38,42,43.

HW #5 (Oct 4): Read section 2.2 and do problems 2.2/1,6,7,10,14,20,41,47.

HW #6 (Oct 6): Read section 2.3 and do problems 2.3/10,20,26,30,40,41,42,49(optional, but interesting).

Solutions to HW #4 - HW #6

HW #7 (Oct 11): Read section 2.4 and do problems 2.4/14,17,19,22,29,35,43,44,74.

HW #8 (Oct 13): Read section 3.1 and do problems 3.1/11,22,24,31,36,39,45.

HW #9 (Oct 16): Read section 3.2 and do problems 3.2/6,18,23,24,38,40,48,50.

Solutions to HW #7 - HW #9
HW #8 corrections: In  problem 24, the solution should read: "a line in R³ passing through the origin, i.e. all vectors normal to the given plane."
The matrix given in the solution to Problem 31 is incorrect.
A correct answer would be any 3 x n matrix where the last n - 2 columns are linear combinations of the first two. Indeed, a 3 x 2 matrix is perfectly acceptable.
HW #9 corrections: In  problem 24, the equation is copied incorrectly.
The plane is x₁ + 2x₂ + 3x₃ = 0 and the second spanning vector should be (-3,0,1), not (-1,0,1).
In problem 50, the second part is missing. If V and W are two distinct lines in R³, then V+W is the plane containing both. [There should be an accompanying sketch of two lines and a plane.]

HW #10 (Oct 18): Read section 3.3 and do problems 3.3/8,20,22,24,30,31,32,44.

HW #11 (Oct 20): Read sections 4.1 and 4.2 and do problems 4.1/6,12,16,26 and 4.2/2,4,14.

HW #12 (Oct 23): Read sections 4.2 and 4.3 and do problems 4.2/18,28,34 and 4.3/8,9,11,18,20.

Solutions to HW #10 - HW #12

HW #13 (Oct 25): Read section 4.4 and the Supplement on Least Squares Approximation in Economics. Do problems 4.3/34 and 4.4/10,22,26,32,41.

HW #14 (Oct 27): Read sections 5.1 and 5.2 and do problems 5.1/16,21-25,28,46 and 5.2/6,20.

HW #15 (Oct 30): Read sections 5.2 and 5.3 and do problems 5.2/8,30 and 5.3/2,7,14,17,25.

Solutions to HW #13 - HW #15

HW #16 (Nov 1): Read sections 6.1 and 6.2 and do problems 6.1/10,23,34,37,39 and 6.2/10,24-27.

HW #17 (Nov 3): Read section 6.2 and 6.3. Do problems 6.2/22,23,28 and 6.3/11,14,20,32,43.

Note: The three sections of Math 21b may have different dates assigned to these problems.
The dates shown are for the MWF10 section.

HW #18 (Nov 6): Read section 6.3 and 6.4. Do problems 6.3/19,34,44 and 6.4/20,24,30,32.

Solutions to HW #16 - HW #18

HW #19 (Nov 8): Read section 6.4 and 6.5. Do problems 6.4/36 and 6.5/8,12,22,28,40afg,42.

Fri, Nov 10 - Veterans Day - No classes

HW #20 (Nov 13): Read section 7.1 and do problems 7.1/1,3,6,8,14,21,24,28. (due Fri. Nov 17).

HW #21 (Nov 15): Read section 7.2 and do problems 7.2/14,15,21,22,23,35,54,60.

Solutions to HW #19 - HW #21
Correction: Problem 7.1/#8 should have the matrix B as
[1  9]
[9  7]

HW #22 (Nov 17): Read sections 7.2 and 7.3 and do problems 7.3/2,6,10,12,16,26,36. (due Wed. after Thanksgiving Break)

HW #23 (Nov 20): Read section 7.4 on quadratic forms. Do problems 7.4/3,6,10,14,15,23,24. (due Wed. after Thanksgiving Break)

MIDTERM #2 (Tuesday, Nov 21 - 7pm in Sci Ctr C)

HW #24 (Nov 29) Read sections 8.1 on continuous dynamical systems, i.e. systems of ordinary differential equations. Do problems 8.1/2,14,26,32,46,54.

Solutions to HW #22 - HW #24

HW #25 (Dec 1): Read sections 8.2 on the complex eigenvalue case for a linear system of ODE's.
Do problems 8.2/6,8,22,30,31,40.
Fall 2000 Solutions         Spring 2000 solutions

HW #26 (Dec 4): Read Section 8-3 Handout (Nonlinear Dynamical Systems) and do the accompanying problems 8.3/1,2,3,4,5.

HW #27 (Dec 6): Read section 9.1 from the text (Linear Spaces) and the accompanying Handout on Ordinary Linear Differential Equation. Do the problems from Section 9-1 Homework supplement, namely 9.1/65,66,67,68,69,54.

For Dec 11 - Dec 19, there will be one last supplement ("Chapter 10") covering Fourier Series and Partial Differential Equations.

HW #28 (Dec 8): Read section 9.4 and do problems 9.4/16,18,30,38,40,46.

HW #29 (Dec 11): [Due Fri, Dec 15] Read section 9.3 (Inner Product Spaces) and the 1st section of the "Chapter 10" supplement on Fourier Series. Do problems 9.3/4,8,10,12,26,28 and 10.1/1,2.
Note: In the solution to problem 9.3/12, the answer given [ a(0) = pi/(2*(2^.5)) ] should just be pi/(2^.5).

HW #30 (Dec 13): [Due before Break] Read section 10.2 from the supplement (The Heat Equation). Do the accompanying problems 10.2/1,2,3,4,5,6.

HW #31 (Dec 15): [Due before Break] Read section 10.3 from the supplement (Laplace's Equation and the Wave Equation). Do accompanying problems 10.3/1,2,3,5.

HW #32 (Dec 18): Finish up any remaining details. No additional homework.

Question Center: In addition to class, problem sessions, and office hours, the Mathematics Department operates a Question Center in Loker on Sunday, Monday, Tuesday, Wednesday, and Thursday evenings from 8pm to 10pm. The Question Center will be staffed by Course Assistants from Math 1a, 1b, 21a, and 21b and by graduate students and others. You are encouraged to use this resource as you do your homework and when questions arise. It is intended to supplement the office hours held by your Section Leader.