MAT 2240 — §102, 103. Fall '16 (164).

Let us reflect that, having banished from our land that religious intolerance under which mankind so long bled and suffered, we have yet gained little if we countenance a political intolerance as despotic, as wicked, and capable of as bitter and bloody persecutions.

— Thomas Jefferson (1743-1826) in his First Inaugural Address.

Homework List

✈ Jump down to '♞ This Week.'

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Week 1

• Monday, Aug 15
  ◊ Convocation
  
  
• Wednesday, Aug 17
  ◊ Read §1.1, 1.2.
  §1.1. Pg 10; #1, 2, 6, 11, 15, 17, 29, 31, 33, 34.
  ¤ Check out Prof Bogacki's online “Linear Algebra Toolkit”
  
  
• Friday, Fri 19
  §1.2. Pg 21; #1, 3, 9, 13, 19, 21, 29, 33.
  
  

Week 2

• Monday, Aug 22
  §1.2. Pg 21; #22, 23, 24, (for CS or Computational Math majors:) 32.
  ◊ Read §1.3.
  
  
• Wednesday, Aug 24
  §1.3. Pg 32; #5, 9, 11, 13, 15, 19, 21, 26, 27, LA 28 ("LA" is "Look at"), (for Physics or Applied Math majors:) 29.
  
  
• Friday, Aug 26
  ¡Quiz today!
  §1.4. Pg 40; #1, 2, 4, 5, 7, 11, 13, 15, 17, 21.
  
  

Week 3

• Monday, Aug 29
  §1.5. Pg 47; #1, 3, 5, 7, 11, 13, 14, 15, 17, 19, 21, 23, 28 → 31.
  ◊ Parametric Vector Eg ← The example that fell apart in the 1:00 pm class, but with numbers that work.
  
  
• Wednesday, Aug 31
  §1.6. Pg 54; #1, 7, 12.
  ¤ Hints for #12:
  1. One equation for each node: A, B, and C.
  2. Flow into a node must equal flow out.
  3. All flows must be \(\ge 0\) gives a restriction on \(x_4\).
  
  
• Friday, Sept 2
  §1.7. Pg 60; #1, 3, 5, 9, 11, 15, 17, 21, 27, 42.
  
  

Week 4

• Monday, Sept 5
  ¤ No class — Labor Day
  
  
• Wednesday, Sept 7
  §1.7. Pg 60; #33 → 41.
  
  
• Friday, Sept 9
  ¡It's time to think about our first midterm exam next Friday!
  §1.8. Pg 68; #1, 2, 3, 5, 7, 8, 9, 11, 15, 16, 20, 21, 39.
  
  

Week 5

• Monday, Sept 12
  §1.9. Pg 78; #1, 3, 5, 11, 13, 15, 16, 17, 21, 25, 27, 40.
  
  
• Wednesday, Sept 14
  ◊ Supplementary Exercises. Pg 88; These are good test questions.
  ¤ For Monday, Sept 19
  • §1.10. Pg 87; #5, 13,
  • Read §2.1.
  
  
• Friday, Sept 16
  ◊ Test I is today — A chance to demonstrate your excellence!
  • You can bring one 8½"×11" sheet of notes.
  • You can bring a calculator; check the batteries!
  ¤ Test I Topics List
  
  

Week 6

• Monday, Sept 19 — «Avast ye, mateys! Talk like a pirate for a free Krispy Kreme!»
  §2.1. Pg 100; #1, 3, 7, 8, 9, 11, 17, 21, 40.
  ◊ Extend #40. Use the Maple statements (copy below, then paste into Maple )
  • gen := (i,j) -> piecewise(i+1=j, 1, 0):
    T := n -> Matrix(n,n, gen):
    S := T(5);
     to make a function \(T\) that produces square matrices with the given pattern of 1's.
     #40e. Replace the 5 with several larger values to discover a pattern in the powers \(S^k\) for \(k=1, 2, \dots\).
  
  
• Wednesday, Sept 21
  §2.2. Pg 109; #1, 3, 5, 8, 9, 13, 21, 31, 33.
  
  
• Friday, Sept 23
  §2.2. Pg 109; #7, 11, 15, 19, 41.
  §2.3. Pg 115; #1 → 9 odd. Look at: #13, 14.
  ◊ ¡Quiz next Friday!
  
  

Week 7

• Monday, Sept 26
  §2.3. Pg 115; #10, 11, 13, 14, 18, 19, 33, 36.
  
  
• Wednesday, Sept 28
  §2.5. Pg 129; $1, 3, 5, 7, 13, 17.
  ¤ Maple has a command LUDecomposition
      Enter: ? command to get help with any command.
  
  
• Friday, Sept 30
  ◊ ¡Quiz today!
  §2.8. Pg 151; #1 → 4, 5, 7, 9.
  ¤ Read either §2.6 (economics) or §2.7 (computer graphics) as your interest dictates.
  
  

Week 8

• Monday, Oct 3
  §2.8. Pg 151; #11, 13, 17, 19, 21, 25, 27, 29, 37.
  
  
• Wednesday, Oct 5
  §2.9. Pg 157; #1, 3, 5, 7, 11, 13, 15.
  
  
• Friday, Oct 7
  ¤ Group Project: Voting Methods — Due: Wed, Oct 19.
  §2.9. Pg 157; #17, 18, 19, 21, 25, 27, 29.
  
  

Week 9

• Monday, Oct 10
  § Chapter 2 Supplementary Exercises. Pg 160; the odd problems.
  
  
• Wednesday, Oct 12
  §3.1. Pg 167; #1, 3, 5, 13, 19, 21, 23, 24, 25, 27, 29, 33, 39, 43, 45, 46.
  ◊ For #45 & 46. Maple: A:=RandomMatrix(4,4, generator=-9..9). Two useful functions are Determinant and Transpose
  ¤ No 2:00 pm office hours today.
  ¡It's time to think about our second midterm exam next Friday!
  
  
• Friday, Oct 14
  ☝ No classes — ¡Fall Break!
       Let's be careful out there!
  
  

Week 10

• Monday, Oct 17
  §3.2. Pg 175; #1, 3, 7, 10, 15, 17, 19, 23, 25, 46 (cf. §2.3, Ex 9, pg. 115).
  ◊ For #45. In Maple, define a function for the condition number of a matrix with: CN := LinearAlgebra[ConditionNumber]:
     Then CN(A) will give the condition number of the matrix \(A\).
  
  
• Wednesday, Oct 19
  ◊ Review:
  § Chapter 2 Supplementary Exercises.
  § Chapter 3 Supplementary Exercises.
  
  
• Friday, Oct 21
  ◊ Test II is today — A chance to demonstrate your excellence!
  • You can bring two 8½"×11" sheet of notes.
  • You can bring a calculator; check the batteries!
  ¤ Test II Topics List
  
  

Week 11

• Monday, Oct 24
  §4.1. Pg 195; #1, 5→8, 9, 13, 19, 21, 24, 27. Look at: 32, 33.
  
  
• Wednesday, Oct 26
  §4.2. Pg 205; #1, 5, 7, 13, 25, 26.
  
  
• Friday, Oct 28
  §4.9. Pg 260; #1, 4, 5, 7.
  ◊ ¡Quiz next Friday!
  ¤ Analyze the state diagram for ASU using an initial class of \(2,\!500\) freshman.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  
  1. When have all the freshman either graduated or dropped out?
  2. What is the `four-year graduation rate'? `Five-year graduation rate'? `Six-year graduation rate'?
  3. What are the steady state class sizes if \(2,\!500\) freshman are admitted each year?
  4. How could transfer students be added to the model?
  Due: Wednesday 11/2/16.
  
  

Week 12

• Monday, Oct 31 — Allhallond-Eue!
  §5.1. Pg 271; #1, 3, 5, 9, 15, 19, 21, 29.
  
  
• Wednesday, Nov 2
  §5.2. Pg 279; #1→9 odd, 17, 18, 28.
  
  
• Friday, Nov 4
  ◊ ¡Quiz today! covering §4.9 & §5.1
  §5.5. Pg 300; #1, 3, 5, 9.
  
  

Week 13

• Monday, Nov 7
  ¤ Maple-based project: Matrix Algebra And Modular Arithmetic: Hill Codes (LIN06) — Due: 11/21/16.
  §5.6. Pg 309; #1, 3, 7, 15, LA 17.
  ◊ Leslie population models
  
  
• Tuesday, Nov 8 — Election Day!
  ➠     Vote!   Tagh do Cheann-suidhe!   Επιλέξτε Πρόεδρος σας!   Выберите ваш президент!
  
  
• Wednesday, Nov 9
  ◊ Eigenspaces Slides
  ¤ Problems:
  1. Determine the algebraic and geometric dimensions of each eigenvalue in the matrices: \[ \begin{bmatrix} 0 & -12 & -3 & 3 \\ -6 & 6 & 1 & -5 \\ 0 & 0 & -2 & 4 \\ 0 & 12 & 8 & -4 \end{bmatrix}, \quad \begin{bmatrix} 2 & -6 & 1 & 1 \\ 0 & 3 & -1 & 0 \\ -1 & -1 & 0 & 0 \\ -2 & 10 & -1 & -1 \end{bmatrix}, \quad \begin{bmatrix} 0 & -2 & 1 & -2\\ 2 & 2 & 0 & 3 \\ 2 & 4 & -1 & 5 \\ 0 & 3 & -2 & 2 \end{bmatrix} \]
  
  
• Friday, Nov 11 — Veteran's Day
  ¤ Problems:
  1. Plot the Gershgorin circles for the matrices: \[ \begin{bmatrix} 0 & -12 & -3 & 3 \\ -6 & 6 & 1 & -5 \\ 0 & 0 & -2 & 4 \\ 0 & 12 & 8 & -4 \end{bmatrix}, \quad \begin{bmatrix} 2 & -6 & 1 & 1 \\ 0 & 3 & -1 & 0 \\ -1 & -1 & 0 & 0 \\ -2 & 10 & -1 & -1 \end{bmatrix}, \quad \begin{bmatrix} 0 & -2 & 1 & -2\\ 2 & 2 & 0 & 3 \\ 2 & 4 & -1 & 5 \\ 0 & 3 & -2 & 2 \end{bmatrix} \]
  2. Use the Müntz power method to determine the dominant eigenvalue and its associated eigenvector for the above matrices.
  
  

Week 14

• Monday, Nov 14
  §6.1. Pg 336; #1, 3, 5, 9, 17, 18, 19.
  
  
• Wednesday, Nov 16
  §6.3. Pg 353; #18.
  
  1. Calculate the angle between the vectors \(\begin{bmatrix} 3 \\ 4 \end{bmatrix}\) and \(\begin{bmatrix} -8 \\ 6 \end{bmatrix}\).
  2. Find a unit vector that is \(60^o\) from the vector \(\begin{bmatrix} 1 \\ 2 \\ 3\end{bmatrix}\).
  3. Find the distance between the vectors \(\vec{v}_1(x) = x^2+1 \) and \(\vec{v}_2(x) = x^3-x \) w.r.t. the inner product \(\displaystyle \vec{v}\cdot\vec{u} = \int_{-1}^1 v(x)\,u(x)\,dx\).
  
  
• Friday, Nov 18
  §6.4. Pg 358; #1, 5, 9, 24.
  
  

Week 15    ♞  (This Week)

• Monday, Nov 21
  ¤ Topics List I
  → Chapter 1 Supplemental Problems: pg 88.
  → Chapter 2 Supplemental Problems: pg 160.
  
  
• Wednesday, Nov 23 — Thanksgiving Holidays
  
  
• Friday, Nov 25 — Thanksgiving Holidays
  
  

Week 16

• Monday, Nov 28
  ¤ Topics List II
  → Chapter 3 Supplemental Problems: pg 185.
  → Chapter 4 Supplemental Problems: pg 262.
  
  
• Wednesday, Nov 30 — Last day of classes.
  ¤ Topics List III
  → Chapter 5 Supplemental Problems: pg 326.
  → Chapter 6 Supplemental Problems: pg 390.
  
  ¤ Review sheets and practice exams from the authors.
  
  

¤ Exam Week

¤ The final is the last opportunity to demonstrate your excellence!
• You can bring any notes — but no books!
• You can use a calculator — check the batteries!
• Bring a spare pencil/pen/eraser.


• Tuesday, Dec 6
  §102 Final Exam — 9:00 - 11:30 am.
  
  
• Thursday, Dec 8
  §103 Final Exam — 9:00 - 11:30 am.
  
  

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“On two occasions I have been asked, ‘Pray, Mr. Babbage, if you put into the machine wrong figures, will the right answers come out?’ I am not able rightly to apprehend the kind of confusion of ideas that could provoke such a question.”

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