| • The homework will be posted around a week in advance.
It will not be graded, but similar exercises will appear on the quiz
during recitation. |
| • Problems marked with (M) require the use of the Maple
software and are optional. An introduction to using Maple, and where to find it
at UPenn, can be
found on the official MAT 240 page. The Maple
section on that page contains demonstrations
of the Maple functions that you will need for this course.
|
| • Occasionally the homework will contain extra-credit problems.
They will be more challenging, and they can be turned in for grading during the
recitation. The grade for the extra credit problems may decide borderline
letter grade decisions.
|
- Week 1 (Thu. Jan 17, Tue. Jan. 22): Matrix
operations, systems of linear equations, rank
- • Sec. 8.1: 3, 13, 18, 23, 27, 33, 36 (Hint: a matrix is symmetric if
it equals its own transpose)
- • Sec.8.2: 5, 7, 9(M), 21(M)
- • Sec.8.3: 1, 5, 9(M), 13, 18
- • For the exercises requiring Maple, check out demo #2 on the demonstrations
page. Open it in Maple, and then copy the commands you need in your
own Maple file.
- Week 2 (Thu. Jan 24, Tue. Jan. 29): Determinants, inverses, eigenvalues
- • Sec.8.4: 3, 5, 21, 28, 29
- • Sec.8.5: 4, 7, 8, 16, 24, 37, 39
- • Sec.8.6: 5, 21, 27, 32, 39, 49, 51
- • Sec.8.8: 1, 7, 15, 21
- • Extra credit problems: Due Thursday, Jan.
31 in class
- Week 3 (Thu. Jan 31, Tue. Feb 5): Eigenvalues, orthogonal matrices, diagonalization
- • To illustrate Thursday's lecture about eigenvalues/eigenvectors, here is an applet that plots the eigenvectors of a 2 x 2 matrix. Directions for using the applet: the blue vector can be dragged along the unit circle; the red vector is what happens to the blue one when multiplied by the matrix A. The eigenvectors, if they exist, can also be displayed on the graph by clicking in the box at the top. Play around with a few matrices to see what they do to vectors! Try the examples from class, and the ones from the homework.
- • Sec.8.8: 5, 17, 18
- • Sec.8.10: 1, 7, 19
- • Sec.8.12: 5, 15
- • Extra credit problems: Due Thursday, Feb.
7 in class
- • The MAPLE worksheet I used in class is here. To execute the commands, click on the exclamation point buttons on the menu on top.
- Week 4 (Thu. Feb. 7, Tue. Feb. 12): Orthogonal and symmetric matrices, review of multivariable calculus
- • Before Tuesday's lecture, review Sections 9.1 and 9.4-9.6. We will be covering this material in class, but rather fast before we move on.
- • Sec. 8.10: 16, 21
- • Sec. 8.12: 19(M), 25, 37, 38, 39
- • Sec. 9.1: 2, 11, 13, 17, 25, 35, 39
- • Sec. 9.4: 3, 11
- • Sec. 9.5: 9, 38, 39, 41
- • Sec. 9.6: 17, 15, 33, 38, 39
- Week 5 (Thu. Feb. 14, Tue. Feb. 19): Divergence and curl, line integrals, First Midterm
- • There will be no quiz the week of the midterm.
- • Sec. 9.7: 1(M), 9, 27, 33, 39
- • Sec. 9.8: 3, 5, 9, 19, 25, 33
- Week 6 (Thu. Feb. 21, Tue. Feb. 26): Path independence, Double integrals in cartesian and polar coordinates, Green's theorem
- • Sec. 9.9: 3, 13, 17, 23, 27
- • Sec. 9.10: 9, 11, 17, 23, 37, 39, 45
- • Sec. 9.11: 3, 5, 9, 13, 27, 31
- • Sec. 9.12: 1, 3, 9, 13, 15, 17, 23, 25, 29
- • Extra credit, due Tue Mar. 4 in class: 21, 22 (in 21 (a), there is a typo: there shouldn't be a circle over the integral, since the line segment C is not a closed loop) Hint: Take a point inside the polygon, and use Green's theorem for the n triangles formed by the point and consecutive vertices of the polygon.
- Week 7 (Thu. Feb. 28, Tue. Mar. 4, Thu. Mar. 6): Surface integrals, Stokes' Theorem, Triple integrals, Divergence theorem
- • If you are curious how the Stokes' and Green's theorems were
discovered, here is an interesting
article
on their history (you need to access it from the UPenn domain to be able
to download it).
- • Sec. 9.13: 1, 5, 11, 19, 27, 33, 37
- • Sec. 9.14: 1, 3, 5, 11, 15, 17
- • Sec. 9.15: 1, 5, 11, 17, 21, 53, 77
- • Sec. 9.16: 3, 7, 11, 15, 17
- • Chapter 9 review problems from past finals: Spring 2007 #10, #11, #12, #13; Fall 2006: #6, #7, #8
- Week 8 (Tue. Mar. 18, Thu. Mar. 20): Change of variables, Differential equations
- • Sec. 9.17: 27, 29
- • The Maple worksheet shown in class: you can use it as a template for studying other first order differential equations.
- • Sec. 2.2: 17, 25
- • Sec. 2.3: 23, 27
- • Sec. 2.4: 1, 13, 31
- • Sec. 2.5: 5, 13, 19, 25, 33
- • Extra credit problems: due Tue. Mar. 25 in class
- Week 9 (Tue. Mar. 25, Thu. Mar. 27): Linear equations, Homogeneous linear equations with constant coefficients
- • Sec. 3.1: 15, 18
- • Sec. 3.3: 9, 11, 15, 21, 23, 33, 43-48
- • Extra Credit: Sec. 2.5, ex. 35, 36 (due Thursday, April 3rd, in class)
- Week 10 (Tue. April 1, Thu. April 3): Spring/mass systems, Solving nonhomogenous equations by undetermined coefficients
- • Sec. 3.8: 3, 7, 17, 25, 31
- • Sec. 3.4: 8, 9, 11, 19, 33
- Week 11 (Tue. April 8, Thu. April 10): Midterm, Cauchy-Euler equations, Linear systems
- • Sec. 3.6: 1, 11, 15, 27, 31
- • Sec. 10.2: 3, 13, 21,33
- • A very readable discussion of linear systems with nice pictures can be found in these lecture notes (see Lectures 16 and 17, starting on p. 61). Check out also the applet pplane, which is helpful to visualize phase portraits of systems of first order equations.
- Week 12 (Tue. April 15, Thu. April 17): Linear systems (continued)
- • Sec. 10.2: 7, 19, 35
- • Sec. 10.1: 5, 11
- • Sec. 10.3: 1, 3, 7
- Week 12 (Tue. April 22, Thu. April 24): Series solutions
- • Sec. 5.1: 3, 9, 11, 15, 21, 31
- • Sec. 5.2: 5, 11, 15, 21, 27(optional), 33(optional)
- Week 13 (Tue. April 29): Bessel functions
- • Sec. 5.3: 1, 5, 9, 11, 15, 25, 33
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