MAT 1120 — §101, Fall '12 (124)

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.'

Week 1

Tuesday, Aug 21 — First day of class
◊ Read the Summaries for Chapters 2 & 3; pages 149 and 196.
◊ Derivative Review problems; #1, 5, 9, ... (every other odd).
Wednesday, Aug 22
§5.1, pg 311. No 1 → 4, 5, 9, 13, 15, 19, 21, 23, 27, 29; 37, 45, 48, 57, 65, 71. LA 68. (LA = look at, think about)
Friday, Aug 24
§5.2, pg 320. No 3 → 8, 51.
§5.3, pg 330. No 1 → 8, 9, 13, 16, 27, 33.

Week 2

Monday, Aug 27
§5.4, pg. 340. No 1 → 14; 15, 17, 23, 27, 31, 37, 41, 47, 51, 59, 63, 67, 71.
◊ Introduction to Maple (see Opening the Portal and the Maple Portal).
1. Work through "Talking to Maple" in the Portal.
2. Work through "Putting Your Ideas Together" in the Portal.
3. Compute the exact value of \(\displaystyle S = \sum_{k=1}^{100} \frac1k\).
4. Find \(\displaystyle \frac{d^{\,3}}{dx^3}\,g(x)\) when \( g(x)=x^x \).
5. Plot the function \(\displaystyle F(x) = \int_{\,0}^{\,x} \frac{\sin(t)}{t}\,dt \).
Tuesday, Aug 28
◊ The Substitution Worksheet. No 22 → 33.
¤ 'How to' get hints for integration using Maple. Maple Worksheet or PDF.
Wednesday, Aug 29
◊ Use Maple to integrate:
1. \(\displaystyle \int \frac1{x^2-10x+24}\,dx\)
2. \(\displaystyle \int \frac1{x^2-10x+25}\,dx\)
3. \(\displaystyle \int \frac1{x^2-10x+26}\,dx\)
and compare the results. Explain what is happening.
◊ What does Maple give for
1. \(\displaystyle \int \frac{7x^4}{1+x^7}\,dx\)
2. \(\displaystyle \int_0^x \cos\left(\frac12 \pi\, t^2\right)\,dt\)
3. \(\displaystyle \int_0^x \sec\left(\frac12 \pi\, t^2\right)\,dt\)
and what does it mean?
Friday, Aug 31
¤ Quiz today! — A sample quiz from Calc 1.

◊ Using Pg 74 of Gradshteyn and Ryzhik's Table of Integrals, Series, and Products, determine \(\displaystyle \int \frac{1}{8+x^3}\,dx\).
§5.6, pg. 354. No 1 → 5, 15; 23, 33.

Week 3

Monday, Sep 3
☀ No classes — Labor Day
Tuesday, Sep 4
§6.1, pg. 381. No 1 → 3, 11, 15, 25; 53.
◊ The Approximating Integrals in Maple handout.
¤ What happens to "+C" when approximating integrals?
Wednesday, Sep 5
§6.2, pg. 391. No 1 → 4, 9ad, 11, 25, 27, 29, 33.
◊ Approximate integration Homework Sheet, due Friday, Sep 7.
Maple is available in the public computer labs at Appalachian; see the list and a map.
In Maple, typing e^x doesn't give the function \(e^x\) since e just represents a letter, not Euler's number. Choose one of:
- First enter e:=exp(1.0), then you can use e^x for \(e^x\).
- Or use the Expression palette (left side of the window) clicking on \(e^a\)
- Or type exp(u) for \(e^u\).
Friday, Sep 7
◊ The Homework Sheet is due today!
¤ Pg 405. Problem 5. Look at Pg 404. Problem 3.
¤ Read §7.1.

Week 4

Monday, Sep 10
§ 7.1, pg. 420. No 1, 2, 5; 15, 19.
Tuesday, Sep 11
§ 7.1, pg. 420. No 7, 9, 11, 12; 23, 39, 43, 44, 57.
Wednesday, Sep 12
§ 7.2, pg. 428. No 3, 6, 11, 13; 21, 27.
Friday, Sep 14
§ 7.2, pg. 428. No 7, 15, 17; 29, 43, 45.
❀ Extra Credit: Make a spreadsheet that calculates the arclength of the function \(y=e^x\) for \(x\in[0..3]\) using Simpson's rule with 14 panels. Include a graph of the function. Your spreadsheet should show the computation for each of the 14 panels.

Week 5

Monday, Sep 17
§7.4, pg. 446. No 1 → 10, 15, 21; 25, 27, 31.
Tuesday, Sep 18
◊ Old homework problems are a good way for your group to study.
¤ Bring lots of problems for the review.
Wednesday, Sept 19
◊ Review Day
Friday, Sep 21
◊ Test today!
¤ Test 1 Topics
— Remember to bring your calculator (Are the batteries good?) and your one-page 'formula sheet'.
¤ “Battery Check and Contrast Set Up: Press [2nd] and the up or down blue arrow keys to darken or lighten the screen contrast. While doing this a number appears in the upper right hand corner of the screen counting up or down depending on which arrow you press. These numbers also give an indication of your battery strength. Adjust the screen to the correct contrast and check the number in the upper right hand corner. If the number is 8 or above, change batteries. After the change, readjust the contrast.”

Week 6

Monday, Sep 24
§8.1, pg. 464. No 1, 3, 7, 9, 11, 21; 25.
Tuesday, Sep 25
§8.1, pg. 464. No 19; 29, 33, 35, 37 → 57 odd.
Wednesday, Sep 26
¤ In Class Homework sheet
§8.2, pg. 473. No 1, 5, 6, 7.
— Remember the Rational Root Theorem:
If \(p(x) = a_0+a_1 x+a_2 x^2 +\cdots+a_n x^n\) has a factor \((x-r)\) for some rational number \(r\), then \(r = \pm(\text{factor of }a_0) / (\text{factor of }a_n)\).
Friday, Feb 28
§8.2, pg. 473. No 19, 23; 25, 27, 37.
¤ Use the \(p(x)/q{\prime}(x)\) identity (see the "Partial Fraction Examples" handout) to find the partial fraction form of
1. \(f(x) = \dfrac{2x+3}{x^2+x-6}\).
2. \(g(x) = \dfrac{x^3}{x^2-1}\).
3. \(h(x) = \dfrac{1}{x^3-2x^2+x}\).
§8.3, pg. 481. No 1, 2, 4, 5.

Week 7

Monday, Oct 1
§8.3, pg. 481. No 1, 2, 4, 5, 11, 13; 39.
◊ Problem 4 from the Trigonometric Integrals handout.
❀ Extra Credit for Friday's quiz: Mathematician's Coincident Birthday
Tuesday, Oct 2
§8.3, pg. 481. No 27, 31, 35; 53.
Wednesday, Oct 3
§8.4, pg. 484. No 1, 3, 5, &c. (These are essentially the review problems for Chapter 8).
Friday, Oct 5
¤ Take-home Quiz today! — Due Monday, Oct 8, at 9:00 am.
◊ Carefully evaluate the integrals showing all the details of your computations:
1. \(F_1 = \displaystyle\int \frac{1}{\sqrt{x^2-1}}\,dx\)
  \(\qquad\) HINT: Show a substitution transforms the integral to \(\displaystyle\int\sec(\theta)\,d\theta\). De-substitutify to get \(F_1=\ln\!\left(x+\sqrt{x^2-1}\right)+C\).
2. \(F_2 = \displaystyle\int \frac{1}{\sqrt{x^2+1}}\,dx\)
  \(\qquad\) HINT: Show a substitution transforms the integral to \(\displaystyle\int\sec(\theta)\,d\theta\). De-substitutify to get \(F_2=\ln\!\left(x+\sqrt{x^2+1}\right)+C\).
◊ Trigonometric Substitution chart.

Week 8

Monday, Oct 8
§9.1, pg. 501. No 1, 3, 5, 9, 13, 17, 21.
¤ Taylor's theorem was Corollary II in Taylor's book Methodus incrementorum directa et inversa (1717)
Tuesday, Oct 9
§9.2, pg. 508. No 2, 3; 7, 9.
Wednesday, Oct 10
§9.2, pg. 508. No 10, 11, 13.
◊ Read §9.3.
¤ The Voting Systems project — Due Monday, Oct 15.
Friday, Oct 12
◊ Fall Break — no classes
¤ Last day to register to vote for the upcoming election.
◊ Let's be careful out there! — Sgt Esterhaus

Week 9

Monday, Oct 15
§10.1, pg. 529. No 1 → 6, 11, 17, 18.
Tuesday, Oct 16
§10.1, pg. 529. No 13, 19.
◊ Read §10.2.
Wednesday, Oct 17
◊ Review Day
¤ Test 2 Topics
— Prepare your two 'formula sheets'.
Friday, Oct 19
◊ Test today!
— Remember to bring your calculator (Are the batteries good?) and your two formula sheets.

Week 10

Monday, Oct 22
◊ Read §10.3.
¤ Calculus 1 Topics List with derivative formulas.
Tuesday, Oct 23
§10.3. pg. x. No 1, 3, 5, 19, 21.
Wednesday, Oct 24
§11.1, pg 553. No 1 → 17 odd, 18, 25; 27, 29, 33, 39, 46 → 49; Look at 50.
Thursday, Oct 25
¤ Last day to drop a class.
Friday, Oct 26
§11.2, pg 564. No 1, 3, 5, 7, 8, 9.

Week 11

Monday, Oct 29
§11.2, pg 564. No 13, 17; 27, 29, 31, 35, 39, 45, 53.
¤ Maple Code: Simple Series Plotter (Copy and paste into Maple.)

     	  a(n) := 1/n;
	  s(N) := sum(a(j),j=1..N);
	  M := 200:
	  plot([a(k), s(k)], k=1..M, style=point, numpoints=M, color=[red,blue], legend=[a[k], S[N]]);

Tuesday, Oct 30
❄ No class today due to adverse weather.
— [You can always check the "ASU Snow Line" 262-SNOW (7669) for current operating status.]
Wednesday, Oct 31
☝ The annual fire drill for Walker Hall will occur on Wednesday, Oct 31 at 8:50 a.m. — we will have class after the drill!
◊ §11.3, pg 573. No 1 → 23 odd.
¤ The Maple Series Test Calculator worksheet my be useful.
Friday, Nov 2
¤ No formal class today — watch for a link to the quiz below!
◊ Quiz 4: due Monday at 9:00 am.

Week 12

Monday, Nov 5
§11.3, pg 573. No 31 → 37 odd, 45 → 53 odd, Look at 43 & 44.
Tuesday, Nov 6 — Don't forget to vote!
◊ Do the problems on the Series Problems handout.
◊ The Convergence Comparison handout.
Wednesday, Nov 7
§11.4, pg 582. No 1, 3, 7, 9, 11; 15, 19 → 25, Look at 27..
Friday, Nov 9
§11.5, pg 589. No 1 → 10; 11, 15, 21.

Week 13

Monday, Nov 12 — Veteran's Day Be sure to thank them!
§11.5, pg 589. No 25, 27 → 32, 39, 43, 47.
Tuesday, Nov 13
§11.6, pg 595. No 1 → 11 odd; 17, 19, 22, 29, 31, 33, 35, 40ab.
Wednesday, Nov 14
§11.7, pg 602. No 1, 3, 5.
◊ Maple Taylor series worksheet.
Friday, Nov 16
¤ Next test: two weeks from today...
§11.7, pg 602. No 7, 9, 11, 12.

Week 14

Monday, Nov 19
◊ Using the technique we looked at in Fresnel Integrals, find a "short polynomial" approximating the Fresnel Cosine integral.
Tuesday, Nov 20
§11.6, pg 596. No 41, 53, 53.
Wednesday, Nov 21
◊ Thanksgiving Break — no classes
Friday, Nov 16
◊ Thanksgiving Break — no classes

Week 15 ♞ (This Week)

Monday, Nov 26
Tuesday, Nov 27
Wednesday, Nov 28
Friday, Nov 30
◊ Test today
¤ Test 3 Topics

Week 16

Monday, Dec 3
¤ Define \(N(x) = \displaystyle\int_0^x e^{-t^2}\,dt\).
1. Explain why \(N(x)\) is an antiderivative of \(e^{-x^2}\).
2. Explain why \(N(x)\) is not an elementary antiderivative of \(e^{-x^2}\).
◊ The proof.
Tuesday, Dec 4
¤ Review: Chap 6, 7
◊ Copies of Tests, Quizzes, and Topics sheets
Wednesday, Dec 5
¤ Review: Chap 8, 9
Friday, Dec 7
¤ Review: Chap 10, 11

Final Exam Week

Wednesday, Dec 12
◊ Final Exam on 12/12/12 at 12:00 pm to 2:30 pm
¤ Bring:
- Your calculator (with fresh batteries)
- Several pencils
- Any notes
¤ Do not bring: any books.
¤ Your cell phone must be silent. You may not use it during the test.

“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.”

— Charles Babbage in Passages from the Life of a Philosopher

Last modified: Wednesday, 01-Feb-2023 08:32:12 EST

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